Mathlib instance hierarchy

Instance graph.md

A tool to estimate "meaningful" edges betweeen typeclass instances in mathlib. Click the raw button on the SVG to zoom in on the graph.

You can regenerate the separate graphs with

lean --run instance_graph.lean > gviz/out.gviz
ccomps gviz/out.gviz "-zX#0" | dot | gvpack -g -m48 -Glabel=\"\" | neato -n2 -Tsvg > gviz/out-large.svg
ccomps gviz/out.gviz "-zX#1-" | dot | gvpack -g -m48 -Glabel=\"\" | neato -n2 -Tsvg > gviz/out-small.svg

(you might need to sudo apt install graphviz)

instance_graph.lean

import tactic.binder_matching
import system.io
import tactic.core
import all
.

open tactic

meta def process_decl (d : declaration) : tactic (name × list name) :=
do
  let ty := d.type,
  (binders, e) ← get_pi_binders_nondep ty,
  let binders := binders.filter (λ b, b.2.info = binder_info.inst_implicit),
  let binders := binders.map (λ b, b.2.type.get_app_fn.const_name),
  let binders := binders.filter (≠ name.anonymous),
  (clsname, args) ← pure e.get_app_fn_args,
  matching_args ← args.mfilter (λ a, do {
    t ← infer_type a,
    (a_binders, a_base) ← mk_local_pis t,
    expr.sort u ← pure a_base | pure ff,
    pure tt
  }),
  -- check this is an application with variables
  matching_args.mmap (λ a, guard a.is_local_constant <|> fail!"{a} is not a constant"),
  pure (clsname.const_name, binders)

meta def find_url (n : name) : format :=
format!"https://leanprover-community.github.io/mathlib_docs/find/{n}"

meta def write (f : format) : io unit :=
io.put_str_ln (f.to_string)

/-- A version of `list.map` for `io` that does not consume the whole stack -/
def list.mmap_io {α β : Type*} (f : α → io β) (l : list α) : io (list β) :=
do
  (_, bs) ← io.iterate (l, ([] : list β)) (λ state, do {
    (a :: as, bs) ← pure state | return none,
    b ← f a,
    return (some (as, b :: bs))
  }),
  pure bs

meta def main : io unit:=
do
  infos ← io.run_tactic $ environment.get_decls <$> get_env,
  write "digraph \"\" {",
  write "  ranksep=1;",
  write "  node[shape=\"box\",margin=\"0.1,0.1\",width=0,height=0,fontname=\"courier\"];",
  infos.mmap_io $ λ d, do {
    some _ ←  io.run_tactic $ try_core (has_attribute `instance d.to_name) | pure (),
    some (cls, edges) ←  io.run_tactic $ try_core (process_decl d) | pure (),
    write "",
    write format!"  \"{cls}\" [URL=\"{find_url(cls)}\"];",
    edges.mmap' (λ src, write format!"  \"{src}\" [URL=\"{find_url(src)}\"];"),
    match edges with
    | [] := pure ()
    | [src] := write format!"  \"{src}\" -> \"{cls}\"  [tooltip=\"{d.to_name}\",URL=\"{find_url(d.to_name)}\"];"
    | edges := do
      write format!"  \"{d.to_name}\" [shape=point,label=\"\",URL=\"{find_url(d.to_name)}\"];",
      write format!"  \"{d.to_name}\" -> \"{cls}\" [tooltip=\"{d.to_name}\",URL=\"{find_url(d.to_name)}\"];",
      edges.mmap' (λ src,
        write format!"  \"{src}\" -> \"{d.to_name}\" [tooltip=\"{d.to_name}\",URL=\"{find_url(d.to_name)}\"];")
    end
  },
  io.put_str_ln "}"

out-large.svg

<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
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<!-- Title: root Pages: 1 -->
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<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 3489)">
<title>root</title>
<polygon fill="white" stroke="transparent" points="-4,4 -4,-3489 18677.01,-3489 18677.01,4 -4,4"/>
<text text-anchor="middle" x="9336.51" y="-3.8" font-family="Times,serif" font-size="14.00">&quot;&quot;</text>
<!-- mul_action_with_zero -->
<g id="node1" class="node">
<title>mul_action_with_zero</title>
<g id="a_node1"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/mul_action_with_zero" xlink:title="mul_action_with_zero">
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<text text-anchor="middle" x="91" y="-1141.8" font-family="Courier,monospace" font-size="14.00">mul_action_with_zero</text>
</a>
</g>
</g>
<!-- mul_action -->
<g id="node2" class="node">
<title>mul_action</title>
<g id="a_node2"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/mul_action" xlink:title="mul_action">
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</a>
</g>
</g>
<!-- mul_action_with_zero&#45;&gt;mul_action -->
<g id="edge1" class="edge">
<title>mul_action_with_zero&#45;&gt;mul_action</title>
<g id="a_edge1"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/mul_action_with_zero.to_mul_action" xlink:title="mul_action_with_zero.to_mul_action">
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</a>
</g>
</g>
<!-- smul_with_zero -->
<g id="node3" class="node">
<title>smul_with_zero</title>
<g id="a_node3"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/smul_with_zero" xlink:title="smul_with_zero">
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</a>
</g>
</g>
<!-- mul_action_with_zero&#45;&gt;smul_with_zero -->
<g id="edge2" class="edge">
<title>mul_action_with_zero&#45;&gt;smul_with_zero</title>
<g id="a_edge2"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/mul_action_with_zero.to_smul_with_zero" xlink:title="mul_action_with_zero.to_smul_with_zero">
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</a>
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</g>
<!-- has_smul -->
<g id="node4" class="node">
<title>has_smul</title>
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</a>
</g>
</g>
<!-- mul_action&#45;&gt;has_smul -->
<g id="edge3" class="edge">
<title>mul_action&#45;&gt;has_smul</title>
<g id="a_edge3"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/mul_action.to_has_smul" xlink:title="mul_action.to_has_smul">
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<!-- smul_with_zero&#45;&gt;has_smul -->
<g id="edge4" class="edge">
<title>smul_with_zero&#45;&gt;has_smul</title>
<g id="a_edge4"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/smul_with_zero.to_has_smul" xlink:title="smul_with_zero.to_has_smul">
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</g>
<!-- module -->
<g id="node5" class="node">
<title>module</title>
<g id="a_node5"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/module" xlink:title="module">
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</a>
</g>
</g>
<!-- module&#45;&gt;mul_action_with_zero -->
<g id="edge5" class="edge">
<title>module&#45;&gt;mul_action_with_zero</title>
<g id="a_edge5"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/module.to_mul_action_with_zero" xlink:title="module.to_mul_action_with_zero">
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</a>
</g>
</g>
<!-- distrib_mul_action -->
<g id="node6" class="node">
<title>distrib_mul_action</title>
<g id="a_node6"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/distrib_mul_action" xlink:title="distrib_mul_action">
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<text text-anchor="middle" x="281" y="-1141.8" font-family="Courier,monospace" font-size="14.00">distrib_mul_action</text>
</a>
</g>
</g>
<!-- module&#45;&gt;distrib_mul_action -->
<g id="edge6" class="edge">
<title>module&#45;&gt;distrib_mul_action</title>
<g id="a_edge6"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/module.to_distrib_mul_action" xlink:title="module.to_distrib_mul_action">
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</g>
<!-- distrib_mul_action&#45;&gt;mul_action -->
<g id="edge7" class="edge">
<title>distrib_mul_action&#45;&gt;mul_action</title>
<g id="a_edge7"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/distrib_mul_action.to_mul_action" xlink:title="distrib_mul_action.to_mul_action">
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<!-- category_theory.limits.reflects_limits_of_size -->
<g id="node7" class="node">
<title>category_theory.limits.reflects_limits_of_size</title>
<g id="a_node7"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/category_theory.limits.reflects_limits_of_size" xlink:title="category_theory.limits.reflects_limits_of_size">
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</a>
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</g>
<!-- category_theory.limits.comp_reflects_limits -->
<g id="node8" class="node">
<title>category_theory.limits.comp_reflects_limits</title>
<g id="a_node8"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/category_theory.limits.comp_reflects_limits" xlink:title="category_theory.limits.comp_reflects_limits">
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<!-- category_theory.limits.reflects_limits_of_size&#45;&gt;category_theory.limits.comp_reflects_limits -->
<g id="edge8" class="edge">
<title>category_theory.limits.reflects_limits_of_size&#45;&gt;category_theory.limits.comp_reflects_limits</title>
<g id="a_edge8"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/category_theory.limits.comp_reflects_limits" xlink:title="category_theory.limits.comp_reflects_limits">
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<title>category_theory.limits.reflects_limits_of_size&#45;&gt;category_theory.limits.comp_reflects_limits</title>
<g id="a_edge9"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/category_theory.limits.comp_reflects_limits" xlink:title="category_theory.limits.comp_reflects_limits">
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<g id="node9" class="node">
<title>category_theory.limits.reflects_limits_of_shape</title>
<g id="a_node9"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/category_theory.limits.reflects_limits_of_shape" xlink:title="category_theory.limits.reflects_limits_of_shape">
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<g id="node12" class="node">
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<g id="edge15" class="edge">
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<g id="a_edge15"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/category_theory.limits.comp_reflects_limits_of_shape" xlink:title="category_theory.limits.comp_reflects_limits_of_shape">
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<!-- category_theory.functor.reflects_monomorphisms_comp -->
<g id="node13" class="node">
<title>category_theory.functor.reflects_monomorphisms_comp</title>
<g id="a_node13"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/category_theory.functor.reflects_monomorphisms_comp" xlink:title="category_theory.functor.reflects_monomorphisms_comp">
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<g id="a_edge76"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/category_theory.limits.has_image_comp_iso" xlink:title="category_theory.limits.has_image_comp_iso">
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<!-- category_theory.is_iso&#45;&gt;category_theory.limits.is_iso_coprod -->
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<title>category_theory.is_iso&#45;&gt;category_theory.limits.is_iso_coprod</title>
<g id="a_edge77"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/category_theory.limits.is_iso_coprod" xlink:title="category_theory.limits.is_iso_coprod">
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<title>category_theory.is_iso&#45;&gt;category_theory.limits.is_iso_coprod</title>
<g id="a_edge78"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/category_theory.limits.is_iso_coprod" xlink:title="category_theory.limits.is_iso_coprod">
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<!-- category_theory.is_iso&#45;&gt;category_theory.limits.pushout.map_is_iso -->
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<g id="edge81" class="edge">
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<g id="edge82" class="edge">
<title>category_theory.is_iso&#45;&gt;category_theory.limits.category_theory.category_struct.comp.has_image</title>
<g id="a_edge82"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/category_theory.limits.category_theory.category_struct.comp.has_image" xlink:title="category_theory.limits.category_theory.category_struct.comp.has_image">
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<title>category_theory.is_iso&#45;&gt;category_theory.limits.has_kernel_iso_comp</title>
<g id="a_edge83"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/category_theory.limits.has_kernel_iso_comp" xlink:title="category_theory.limits.has_kernel_iso_comp">
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<!-- category_theory.is_iso&#45;&gt;category_theory.limits.pullback.map_is_iso -->
<g id="edge84" class="edge">
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<g id="edge85" class="edge">
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<g id="edge86" class="edge">
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<!-- category_theory.epi&#45;&gt;category_theory.epi -->
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<!-- category_theory.epi&#45;&gt;category_theory.epi -->
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<!-- category_theory.epi&#45;&gt;category_theory.epi -->
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<!-- category_theory.epi&#45;&gt;category_theory.epi -->
<g id="edge100" class="edge">
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<!-- t2_space&#45;&gt;measure_theory.measure.regular.inv -->
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<!-- tendsto_Ixx_nhds_within&#45;&gt;filter.tendsto_Ixx_class -->
<g id="edge240" class="edge">
<title>tendsto_Ixx_nhds_within&#45;&gt;filter.tendsto_Ixx_class</title>
<g id="a_edge240"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/tendsto_Ixx_nhds_within" xlink:title="tendsto_Ixx_nhds_within">
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<!-- comm_monoid_with_zero -->
<g id="node114" class="node">
<title>comm_monoid_with_zero</title>
<g id="a_node114"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/comm_monoid_with_zero" xlink:title="comm_monoid_with_zero">
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<text text-anchor="middle" x="8847.01" y="-2758.8" font-family="Courier,monospace" font-size="14.00">comm_monoid_with_zero</text>
</a>
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</g>
<!-- monoid_with_zero -->
<g id="node115" class="node">
<title>monoid_with_zero</title>
<g id="a_node115"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/monoid_with_zero" xlink:title="monoid_with_zero">
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<text text-anchor="middle" x="9196.01" y="-2657.8" font-family="Courier,monospace" font-size="14.00">monoid_with_zero</text>
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</g>
<!-- comm_monoid_with_zero&#45;&gt;monoid_with_zero -->
<g id="edge241" class="edge">
<title>comm_monoid_with_zero&#45;&gt;monoid_with_zero</title>
<g id="a_edge241"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/comm_monoid_with_zero.to_monoid_with_zero" xlink:title="comm_monoid_with_zero.to_monoid_with_zero">
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<!-- comm_monoid -->
<g id="node116" class="node">
<title>comm_monoid</title>
<g id="a_node116"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/comm_monoid" xlink:title="comm_monoid">
<polygon fill="none" stroke="black" points="8584.01,-2677 8478.01,-2677 8478.01,-2646 8584.01,-2646 8584.01,-2677"/>
<text text-anchor="middle" x="8531.01" y="-2657.8" font-family="Courier,monospace" font-size="14.00">comm_monoid</text>
</a>
</g>
</g>
<!-- comm_monoid_with_zero&#45;&gt;comm_monoid -->
<g id="edge242" class="edge">
<title>comm_monoid_with_zero&#45;&gt;comm_monoid</title>
<g id="a_edge242"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/comm_monoid_with_zero.to_comm_monoid" xlink:title="comm_monoid_with_zero.to_comm_monoid">
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</g>
<!-- monoid -->
<g id="node117" class="node">
<title>monoid</title>
<g id="a_node117"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/monoid" xlink:title="monoid">
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<text text-anchor="middle" x="9021.01" y="-2455.8" font-family="Courier,monospace" font-size="14.00">monoid</text>
</a>
</g>
</g>
<!-- monoid_with_zero&#45;&gt;monoid -->
<g id="edge243" class="edge">
<title>monoid_with_zero&#45;&gt;monoid</title>
<g id="a_edge243"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/monoid_with_zero.to_monoid" xlink:title="monoid_with_zero.to_monoid">
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</g>
<!-- semigroup_with_zero -->
<g id="node118" class="node">
<title>semigroup_with_zero</title>
<g id="a_node118"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/semigroup_with_zero" xlink:title="semigroup_with_zero">
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<text text-anchor="middle" x="8573.01" y="-2556.8" font-family="Courier,monospace" font-size="14.00">semigroup_with_zero</text>
</a>
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</g>
<!-- monoid_with_zero&#45;&gt;semigroup_with_zero -->
<g id="edge244" class="edge">
<title>monoid_with_zero&#45;&gt;semigroup_with_zero</title>
<g id="a_edge244"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/monoid_with_zero.to_semigroup_with_zero" xlink:title="monoid_with_zero.to_semigroup_with_zero">
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</g>
<!-- mul_zero_one_class -->
<g id="node119" class="node">
<title>mul_zero_one_class</title>
<g id="a_node119"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/mul_zero_one_class" xlink:title="mul_zero_one_class">
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<text text-anchor="middle" x="9130.01" y="-2556.8" font-family="Courier,monospace" font-size="14.00">mul_zero_one_class</text>
</a>
</g>
</g>
<!-- monoid_with_zero&#45;&gt;mul_zero_one_class -->
<g id="edge245" class="edge">
<title>monoid_with_zero&#45;&gt;mul_zero_one_class</title>
<g id="a_edge245"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/monoid_with_zero.to_mul_zero_one_class" xlink:title="monoid_with_zero.to_mul_zero_one_class">
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</g>
<!-- comm_monoid&#45;&gt;monoid -->
<g id="edge246" class="edge">
<title>comm_monoid&#45;&gt;monoid</title>
<g id="a_edge246"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/comm_monoid.to_monoid" xlink:title="comm_monoid.to_monoid">
<path fill="none" stroke="black" d="M8583.71,-2647.9C8641.81,-2633.6 8737.51,-2607.7 8816.01,-2574.5 8881.31,-2546.8 8952.61,-2503.9 8991.51,-2479.2"/>
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</g>
<!-- comm_semigroup -->
<g id="node120" class="node">
<title>comm_semigroup</title>
<g id="a_node120"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/comm_semigroup" xlink:title="comm_semigroup">
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<text text-anchor="middle" x="7402.01" y="-2556.8" font-family="Courier,monospace" font-size="14.00">comm_semigroup</text>
</a>
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</g>
<!-- comm_monoid&#45;&gt;comm_semigroup -->
<g id="edge247" class="edge">
<title>comm_monoid&#45;&gt;comm_semigroup</title>
<g id="a_edge247"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/comm_monoid.to_comm_semigroup" xlink:title="comm_monoid.to_comm_semigroup">
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</g>
<!-- mul_one_class -->
<g id="node121" class="node">
<title>mul_one_class</title>
<g id="a_node121"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/mul_one_class" xlink:title="mul_one_class">
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<text text-anchor="middle" x="9197.01" y="-2354.8" font-family="Courier,monospace" font-size="14.00">mul_one_class</text>
</a>
</g>
</g>
<!-- monoid&#45;&gt;mul_one_class -->
<g id="edge248" class="edge">
<title>monoid&#45;&gt;mul_one_class</title>
<g id="a_edge248"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/monoid.to_mul_one_class" xlink:title="monoid.to_mul_one_class">
<path fill="none" stroke="black" d="M9045.11,-2444.4C9076.01,-2427.1 9129.51,-2396.9 9164.11,-2377.5"/>
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</g>
<!-- semigroup -->
<g id="node122" class="node">
<title>semigroup</title>
<g id="a_node122"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/semigroup" xlink:title="semigroup">
<polygon fill="none" stroke="black" points="8084.01,-2374 7994.01,-2374 7994.01,-2343 8084.01,-2343 8084.01,-2374"/>
<text text-anchor="middle" x="8039.01" y="-2354.8" font-family="Courier,monospace" font-size="14.00">semigroup</text>
</a>
</g>
</g>
<!-- monoid&#45;&gt;semigroup -->
<g id="edge249" class="edge">
<title>monoid&#45;&gt;semigroup</title>
<g id="a_edge249"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/monoid.to_semigroup" xlink:title="monoid.to_semigroup">
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<!-- semigroup_with_zero&#45;&gt;semigroup -->
<g id="edge250" class="edge">
<title>semigroup_with_zero&#45;&gt;semigroup</title>
<g id="a_edge250"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/semigroup_with_zero.to_semigroup" xlink:title="semigroup_with_zero.to_semigroup">
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<!-- mul_zero_class -->
<g id="node123" class="node">
<title>mul_zero_class</title>
<g id="a_node123"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/mul_zero_class" xlink:title="mul_zero_class">
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<text text-anchor="middle" x="9136.01" y="-2455.8" font-family="Courier,monospace" font-size="14.00">mul_zero_class</text>
</a>
</g>
</g>
<!-- semigroup_with_zero&#45;&gt;mul_zero_class -->
<g id="edge251" class="edge">
<title>semigroup_with_zero&#45;&gt;mul_zero_class</title>
<g id="a_edge251"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/semigroup_with_zero.to_mul_zero_class" xlink:title="semigroup_with_zero.to_mul_zero_class">
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<!-- mul_zero_one_class&#45;&gt;mul_one_class -->
<g id="edge252" class="edge">
<title>mul_zero_one_class&#45;&gt;mul_one_class</title>
<g id="a_edge252"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/mul_zero_one_class.to_mul_one_class" xlink:title="mul_zero_one_class.to_mul_one_class">
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<!-- mul_zero_one_class&#45;&gt;mul_zero_class -->
<g id="edge253" class="edge">
<title>mul_zero_one_class&#45;&gt;mul_zero_class</title>
<g id="a_edge253"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/mul_zero_one_class.to_mul_zero_class" xlink:title="mul_zero_one_class.to_mul_zero_class">
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<!-- comm_semigroup&#45;&gt;semigroup -->
<g id="edge254" class="edge">
<title>comm_semigroup&#45;&gt;semigroup</title>
<g id="a_edge254"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/comm_semigroup.to_semigroup" xlink:title="comm_semigroup.to_semigroup">
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<g id="node350" class="node">
<title>has_mul</title>
<g id="a_node350"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/has_mul" xlink:title="has_mul">
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</a>
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</g>
<!-- mul_one_class&#45;&gt;has_mul -->
<g id="edge895" class="edge">
<title>mul_one_class&#45;&gt;has_mul</title>
<g id="a_edge895"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/mul_one_class.to_has_mul" xlink:title="mul_one_class.to_has_mul">
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<g id="node468" class="node">
<title>has_one</title>
<g id="a_node468"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/has_one" xlink:title="has_one">
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</a>
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<!-- mul_one_class&#45;&gt;has_one -->
<g id="edge896" class="edge">
<title>mul_one_class&#45;&gt;has_one</title>
<g id="a_edge896"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/mul_one_class.to_has_one" xlink:title="mul_one_class.to_has_one">
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<!-- semigroup&#45;&gt;has_mul -->
<g id="edge897" class="edge">
<title>semigroup&#45;&gt;has_mul</title>
<g id="a_edge897"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/semigroup.to_has_mul" xlink:title="semigroup.to_has_mul">
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<!-- has_dvd -->
<g id="node469" class="node">
<title>has_dvd</title>
<g id="a_node469"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/has_dvd" xlink:title="has_dvd">
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</a>
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</g>
<!-- semigroup&#45;&gt;has_dvd -->
<g id="edge898" class="edge">
<title>semigroup&#45;&gt;has_dvd</title>
<g id="a_edge898"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/semigroup_has_dvd" xlink:title="semigroup_has_dvd">
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<!-- mul_zero_class&#45;&gt;has_mul -->
<g id="edge939" class="edge">
<title>mul_zero_class&#45;&gt;has_mul</title>
<g id="a_edge939"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/mul_zero_class.to_has_mul" xlink:title="mul_zero_class.to_has_mul">
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<g id="node445" class="node">
<title>has_zero</title>
<g id="a_node445"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/has_zero" xlink:title="has_zero">
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<!-- mul_zero_class&#45;&gt;has_zero -->
<g id="edge938" class="edge">
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<g id="a_edge283"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/normed_division_ring.to_has_norm" xlink:title="normed_division_ring.to_has_norm">
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<!-- normed_division_ring&#45;&gt;metric_space -->
<g id="edge284" class="edge">
<title>normed_division_ring&#45;&gt;metric_space</title>
<g id="a_edge284"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/normed_division_ring.to_metric_space" xlink:title="normed_division_ring.to_metric_space">
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<!-- division_ring -->
<g id="node146" class="node">
<title>division_ring</title>
<g id="a_node146"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/division_ring" xlink:title="division_ring">
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<!-- normed_division_ring&#45;&gt;division_ring -->
<g id="edge285" class="edge">
<title>normed_division_ring&#45;&gt;division_ring</title>
<g id="a_edge285"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/normed_division_ring.to_division_ring" xlink:title="normed_division_ring.to_division_ring">
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</g>
<!-- normed_ring -->
<g id="node147" class="node">
<title>normed_ring</title>
<g id="a_node147"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/normed_ring" xlink:title="normed_ring">
<polygon fill="none" stroke="black" points="6920.01,-3081 6814.01,-3081 6814.01,-3050 6920.01,-3050 6920.01,-3081"/>
<text text-anchor="middle" x="6867.01" y="-3061.8" font-family="Courier,monospace" font-size="14.00">normed_ring</text>
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</g>
<!-- normed_division_ring&#45;&gt;normed_ring -->
<g id="edge286" class="edge">
<title>normed_division_ring&#45;&gt;normed_ring</title>
<g id="a_edge286"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/normed_division_ring.to_normed_ring" xlink:title="normed_division_ring.to_normed_ring">
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<polygon fill="black" stroke="black" points="6859.4,-3090.14 6860.51,-3079.6 6853.07,-3087.14 6859.4,-3090.14"/>
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</g>
<!-- field&#45;&gt;division_ring -->
<g id="edge288" class="edge">
<title>field&#45;&gt;division_ring</title>
<g id="a_edge288"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/field.to_division_ring" xlink:title="field.to_division_ring">
<path fill="none" stroke="black" d="M8270.21,-3156.7C8325.91,-3140.4 8450.81,-3103.8 8523.91,-3082.4"/>
<polygon fill="black" stroke="black" points="8525.2,-3085.67 8533.81,-3079.5 8523.23,-3078.95 8525.2,-3085.67"/>
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</g>
<!-- semifield -->
<g id="node148" class="node">
<title>semifield</title>
<g id="a_node148"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/semifield" xlink:title="semifield">
<polygon fill="none" stroke="black" points="8749.01,-3081 8659.01,-3081 8659.01,-3050 8749.01,-3050 8749.01,-3081"/>
<text text-anchor="middle" x="8704.01" y="-3061.8" font-family="Courier,monospace" font-size="14.00">semifield</text>
</a>
</g>
</g>
<!-- field&#45;&gt;semifield -->
<g id="edge287" class="edge">
<title>field&#45;&gt;semifield</title>
<g id="a_edge287"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/field.to_semifield" xlink:title="field.to_semifield">
<path fill="none" stroke="black" d="M8270.11,-3159.1C8352.71,-3141.9 8591.81,-3092 8649.11,-3079.6"/>
<polygon fill="black" stroke="black" points="8650.24,-3082.93 8659.21,-3077.3 8648.69,-3076.11 8650.24,-3082.93"/>
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</g>
<!-- comm_ring -->
<g id="node149" class="node">
<title>comm_ring</title>
<g id="a_node149"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/comm_ring" xlink:title="comm_ring">
<polygon fill="none" stroke="black" points="8122.01,-2979 8032.01,-2979 8032.01,-2948 8122.01,-2948 8122.01,-2979"/>
<text text-anchor="middle" x="8077.01" y="-2959.8" font-family="Courier,monospace" font-size="14.00">comm_ring</text>
</a>
</g>
</g>
<!-- field&#45;&gt;comm_ring -->
<g id="edge289" class="edge">
<title>field&#45;&gt;comm_ring</title>
<g id="a_edge289"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/field.to_comm_ring" xlink:title="field.to_comm_ring">
<path fill="none" stroke="black" d="M8218.11,-3151.3C8193.61,-3136.3 8155.71,-3110.2 8131.01,-3079.5 8108.61,-3051.6 8092.81,-3012.9 8084.31,-2988.4"/>
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</g>
<!-- euclidean_domain -->
<g id="node150" class="node">
<title>euclidean_domain</title>
<g id="a_node150"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/euclidean_domain" xlink:title="euclidean_domain">
<polygon fill="none" stroke="black" points="8288.01,-3081 8140.01,-3081 8140.01,-3050 8288.01,-3050 8288.01,-3081"/>
<text text-anchor="middle" x="8214.01" y="-3061.8" font-family="Courier,monospace" font-size="14.00">euclidean_domain</text>
</a>
</g>
</g>
<!-- field&#45;&gt;euclidean_domain -->
<g id="edge290" class="edge">
<title>field&#45;&gt;euclidean_domain</title>
<g id="a_edge290"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/field.to_euclidean_domain" xlink:title="field.to_euclidean_domain">
<path fill="none" stroke="black" d="M8238.11,-3151.2C8233.61,-3135.3 8226.11,-3108.7 8220.61,-3089.5"/>
<polygon fill="black" stroke="black" points="8223.92,-3088.33 8217.91,-3079.6 8217.17,-3090.17 8223.92,-3088.33"/>
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</g>
<!-- normed_comm_ring&#45;&gt;normed_ring -->
<g id="edge291" class="edge">
<title>normed_comm_ring&#45;&gt;normed_ring</title>
<g id="a_edge291"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/normed_comm_ring.to_normed_ring" xlink:title="normed_comm_ring.to_normed_ring">
<path fill="none" stroke="black" d="M6983.51,-3151.4C6960.31,-3134.4 6920.41,-3105.1 6893.81,-3085.7"/>
<polygon fill="black" stroke="black" points="6895.83,-3082.84 6885.71,-3079.7 6891.67,-3088.46 6895.83,-3082.84"/>
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</g>
<!-- semi_normed_comm_ring -->
<g id="node151" class="node">
<title>semi_normed_comm_ring</title>
<g id="a_node151"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/semi_normed_comm_ring" xlink:title="semi_normed_comm_ring">
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<text text-anchor="middle" x="7287.01" y="-3061.8" font-family="Courier,monospace" font-size="14.00">semi_normed_comm_ring</text>
</a>
</g>
</g>
<!-- normed_comm_ring&#45;&gt;semi_normed_comm_ring -->
<g id="edge292" class="edge">
<title>normed_comm_ring&#45;&gt;semi_normed_comm_ring</title>
<g id="a_edge292"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/normed_comm_ring.to_semi_normed_comm_ring" xlink:title="normed_comm_ring.to_semi_normed_comm_ring">
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</g>
<!-- has_nndist -->
<g id="node152" class="node">
<title>has_nndist</title>
<g id="a_node152"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/has_nndist" xlink:title="has_nndist">
<polygon fill="none" stroke="black" points="6655.01,-2576 6557.01,-2576 6557.01,-2545 6655.01,-2545 6655.01,-2576"/>
<text text-anchor="middle" x="6606.01" y="-2556.8" font-family="Courier,monospace" font-size="14.00">has_nndist</text>
</a>
</g>
</g>
<!-- pseudo_metric_space&#45;&gt;has_nndist -->
<g id="edge293" class="edge">
<title>pseudo_metric_space&#45;&gt;has_nndist</title>
<g id="a_edge293"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/pseudo_metric_space.to_has_nndist" xlink:title="pseudo_metric_space.to_has_nndist">
<path fill="none" stroke="black" d="M6671.41,-2646.2C6658.81,-2629.8 6637.51,-2602 6622.61,-2582.6"/>
<polygon fill="black" stroke="black" points="6625.36,-2580.43 6616.51,-2574.6 6619.79,-2584.67 6625.36,-2580.43"/>
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</g>
<!-- uniform_space -->
<g id="node153" class="node">
<title>uniform_space</title>
<g id="a_node153"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/uniform_space" xlink:title="uniform_space">
<polygon fill="none" stroke="black" points="7077.51,-2475 6954.51,-2475 6954.51,-2444 7077.51,-2444 7077.51,-2475"/>
<text text-anchor="middle" x="7016.01" y="-2455.8" font-family="Courier,monospace" font-size="14.00">uniform_space</text>
</a>
</g>
</g>
<!-- pseudo_metric_space&#45;&gt;uniform_space -->
<g id="edge294" class="edge">
<title>pseudo_metric_space&#45;&gt;uniform_space</title>
<g id="a_edge294"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/pseudo_metric_space.to_uniform_space" xlink:title="pseudo_metric_space.to_uniform_space">
<path fill="none" stroke="black" d="M6767.71,-2653.2C6869.51,-2643.2 7030.21,-2620.4 7067.01,-2574.5 7090.01,-2545.9 7060.51,-2505.2 7037.71,-2480.9"/>
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</g>
<!-- has_edist -->
<g id="node154" class="node">
<title>has_edist</title>
<g id="a_node154"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/has_edist" xlink:title="has_edist">
<polygon fill="none" stroke="black" points="6435.01,-2475 6345.01,-2475 6345.01,-2444 6435.01,-2444 6435.01,-2475"/>
<text text-anchor="middle" x="6390.01" y="-2455.8" font-family="Courier,monospace" font-size="14.00">has_edist</text>
</a>
</g>
</g>
<!-- pseudo_metric_space&#45;&gt;has_edist -->
<g id="edge295" class="edge">
<title>pseudo_metric_space&#45;&gt;has_edist</title>
<g id="a_edge295"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/pseudo_metric_space.to_has_edist" xlink:title="pseudo_metric_space.to_has_edist">
<path fill="none" stroke="black" d="M6596.21,-2649.8C6508.11,-2637.4 6379.91,-2613.1 6350.01,-2574.5 6328.41,-2546.7 6352.11,-2506.3 6371.11,-2481.7"/>
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<!-- pseudo_emetric_space -->
<g id="node155" class="node">
<title>pseudo_emetric_space</title>
<g id="a_node155"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/pseudo_emetric_space" xlink:title="pseudo_emetric_space">
<polygon fill="none" stroke="black" points="6540.01,-2576 6358.01,-2576 6358.01,-2545 6540.01,-2545 6540.01,-2576"/>
<text text-anchor="middle" x="6449.01" y="-2556.8" font-family="Courier,monospace" font-size="14.00">pseudo_emetric_space</text>
</a>
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</g>
<!-- pseudo_metric_space&#45;&gt;pseudo_emetric_space -->
<g id="edge296" class="edge">
<title>pseudo_metric_space&#45;&gt;pseudo_emetric_space</title>
<g id="a_edge296"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/pseudo_metric_space.to_pseudo_emetric_space" xlink:title="pseudo_metric_space.to_pseudo_emetric_space">
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<!-- bornology -->
<g id="node156" class="node">
<title>bornology</title>
<g id="a_node156"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/bornology" xlink:title="bornology">
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<text text-anchor="middle" x="6717.01" y="-2556.8" font-family="Courier,monospace" font-size="14.00">bornology</text>
</a>
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</g>
<!-- pseudo_metric_space&#45;&gt;bornology -->
<g id="edge297" class="edge">
<title>pseudo_metric_space&#45;&gt;bornology</title>
<g id="a_edge297"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/pseudo_metric_space.to_bornology" xlink:title="pseudo_metric_space.to_bornology">
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<!-- has_dist -->
<g id="node157" class="node">
<title>has_dist</title>
<g id="a_node157"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/has_dist" xlink:title="has_dist">
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<text text-anchor="middle" x="6820.01" y="-2556.8" font-family="Courier,monospace" font-size="14.00">has_dist</text>
</a>
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</g>
<!-- pseudo_metric_space&#45;&gt;has_dist -->
<g id="edge298" class="edge">
<title>pseudo_metric_space&#45;&gt;has_dist</title>
<g id="a_edge298"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/pseudo_metric_space.to_has_dist" xlink:title="pseudo_metric_space.to_has_dist">
<path fill="none" stroke="black" d="M6700.91,-2646.4C6724.61,-2629.4 6765.51,-2600.1 6792.61,-2580.7"/>
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<!-- emetric_space&#45;&gt;pseudo_emetric_space -->
<g id="edge299" class="edge">
<title>emetric_space&#45;&gt;pseudo_emetric_space</title>
<g id="a_edge299"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/emetric_space.to_pseudo_emetric_space" xlink:title="emetric_space.to_pseudo_emetric_space">
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<!-- linear_ordered_add_comm_group&#45;&gt;linear_order -->
<g id="edge300" class="edge">
<title>linear_ordered_add_comm_group&#45;&gt;linear_order</title>
<g id="a_edge300"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/linear_ordered_add_comm_group.to_linear_order" xlink:title="linear_ordered_add_comm_group.to_linear_order">
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<!-- ordered_add_comm_group -->
<g id="node158" class="node">
<title>ordered_add_comm_group</title>
<g id="a_node158"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/ordered_add_comm_group" xlink:title="ordered_add_comm_group">
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</g>
<!-- linear_ordered_add_comm_group&#45;&gt;ordered_add_comm_group -->
<g id="edge301" class="edge">
<title>linear_ordered_add_comm_group&#45;&gt;ordered_add_comm_group</title>
<g id="a_edge301"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/linear_ordered_add_comm_group.to_ordered_add_comm_group" xlink:title="linear_ordered_add_comm_group.to_ordered_add_comm_group">
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<!-- linear_ordered_cancel_add_comm_monoid -->
<g id="node159" class="node">
<title>linear_ordered_cancel_add_comm_monoid</title>
<g id="a_node159"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/linear_ordered_cancel_add_comm_monoid" xlink:title="linear_ordered_cancel_add_comm_monoid">
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</g>
<!-- linear_ordered_add_comm_group&#45;&gt;linear_ordered_cancel_add_comm_monoid -->
<g id="edge302" class="edge">
<title>linear_ordered_add_comm_group&#45;&gt;linear_ordered_cancel_add_comm_monoid</title>
<g id="a_edge302"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/linear_ordered_add_comm_group.to_linear_ordered_cancel_add_comm_monoid" xlink:title="linear_ordered_add_comm_group.to_linear_ordered_cancel_add_comm_monoid">
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</g>
<!-- normed_group&#45;&gt;has_norm -->
<g id="edge303" class="edge">
<title>normed_group&#45;&gt;has_norm</title>
<g id="a_edge303"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/normed_group.to_has_norm" xlink:title="normed_group.to_has_norm">
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<!-- normed_group&#45;&gt;metric_space -->
<g id="edge304" class="edge">
<title>normed_group&#45;&gt;metric_space</title>
<g id="a_edge304"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/normed_group.to_metric_space" xlink:title="normed_group.to_metric_space">
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<g id="node160" class="node">
<title>semi_normed_group</title>
<g id="a_node160"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/semi_normed_group" xlink:title="semi_normed_group">
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<text text-anchor="middle" x="7051.01" y="-2758.8" font-family="Courier,monospace" font-size="14.00">semi_normed_group</text>
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</g>
<!-- normed_group&#45;&gt;semi_normed_group -->
<g id="edge305" class="edge">
<title>normed_group&#45;&gt;semi_normed_group</title>
<g id="a_edge305"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/normed_group.to_semi_normed_group" xlink:title="normed_group.to_semi_normed_group">
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<!-- add_comm_group -->
<g id="node161" class="node">
<title>add_comm_group</title>
<g id="a_node161"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/add_comm_group" xlink:title="add_comm_group">
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</g>
<!-- normed_group&#45;&gt;add_comm_group -->
<g id="edge306" class="edge">
<title>normed_group&#45;&gt;add_comm_group</title>
<g id="a_edge306"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/normed_group.to_add_comm_group" xlink:title="normed_group.to_add_comm_group">
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<!-- linear_ordered_semifield&#45;&gt;semifield -->
<g id="edge307" class="edge">
<title>linear_ordered_semifield&#45;&gt;semifield</title>
<g id="a_edge307"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/linear_ordered_semifield.to_semifield" xlink:title="linear_ordered_semifield.to_semifield">
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<!-- linear_ordered_semiring -->
<g id="node162" class="node">
<title>linear_ordered_semiring</title>
<g id="a_node162"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/linear_ordered_semiring" xlink:title="linear_ordered_semiring">
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<text text-anchor="middle" x="10323.01" y="-2959.8" font-family="Courier,monospace" font-size="14.00">linear_ordered_semiring</text>
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</g>
<!-- linear_ordered_semifield&#45;&gt;linear_ordered_semiring -->
<g id="edge308" class="edge">
<title>linear_ordered_semifield&#45;&gt;linear_ordered_semiring</title>
<g id="a_edge308"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/linear_ordered_semifield.to_linear_ordered_semiring" xlink:title="linear_ordered_semifield.to_linear_ordered_semiring">
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<!-- linear_ordered_comm_ring&#45;&gt;comm_monoid -->
<g id="edge309" class="edge">
<title>linear_ordered_comm_ring&#45;&gt;comm_monoid</title>
<g id="a_edge309"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/linear_ordered_comm_ring.to_comm_monoid" xlink:title="linear_ordered_comm_ring.to_comm_monoid">
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<!-- linear_ordered_comm_ring&#45;&gt;linear_ordered_semiring -->
<g id="edge311" class="edge">
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<g id="a_edge311"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/linear_ordered_comm_ring.to_linear_ordered_semiring" xlink:title="linear_ordered_comm_ring.to_linear_ordered_semiring">
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<!-- linear_ordered_ring -->
<g id="node163" class="node">
<title>linear_ordered_ring</title>
<g id="a_node163"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/linear_ordered_ring" xlink:title="linear_ordered_ring">
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<text text-anchor="middle" x="10388.01" y="-3061.8" font-family="Courier,monospace" font-size="14.00">linear_ordered_ring</text>
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</g>
<!-- linear_ordered_comm_ring&#45;&gt;linear_ordered_ring -->
<g id="edge310" class="edge">
<title>linear_ordered_comm_ring&#45;&gt;linear_ordered_ring</title>
<g id="a_edge310"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/linear_ordered_comm_ring.to_linear_ordered_ring" xlink:title="linear_ordered_comm_ring.to_linear_ordered_ring">
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<g id="node164" class="node">
<title>ordered_comm_ring</title>
<g id="a_node164"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/ordered_comm_ring" xlink:title="ordered_comm_ring">
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<text text-anchor="middle" x="8423.01" y="-3061.8" font-family="Courier,monospace" font-size="14.00">ordered_comm_ring</text>
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</g>
<!-- linear_ordered_comm_ring&#45;&gt;ordered_comm_ring -->
<g id="edge312" class="edge">
<title>linear_ordered_comm_ring&#45;&gt;ordered_comm_ring</title>
<g id="a_edge312"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/linear_ordered_comm_ring.to_ordered_comm_ring" xlink:title="linear_ordered_comm_ring.to_ordered_comm_ring">
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<!-- division_semiring -->
<g id="node282" class="node">
<title>division_semiring</title>
<g id="a_node282"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/division_semiring" xlink:title="division_semiring">
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</a>
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</g>
<!-- division_ring&#45;&gt;division_semiring -->
<g id="edge1333" class="edge">
<title>division_ring&#45;&gt;division_semiring</title>
<g id="a_edge1333"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/division_ring.to_division_semiring" xlink:title="division_ring.to_division_semiring">
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<!-- nontrivial -->
<g id="node286" class="node">
<title>nontrivial</title>
<g id="a_node286"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/nontrivial" xlink:title="nontrivial">
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</a>
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</g>
<!-- division_ring&#45;&gt;nontrivial -->
<g id="edge1335" class="edge">
<title>division_ring&#45;&gt;nontrivial</title>
<g id="a_edge1335"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/division_ring.to_nontrivial" xlink:title="division_ring.to_nontrivial">
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<!-- div_inv_monoid -->
<g id="node288" class="node">
<title>div_inv_monoid</title>
<g id="a_node288"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/div_inv_monoid" xlink:title="div_inv_monoid">
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</a>
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</g>
<!-- division_ring&#45;&gt;div_inv_monoid -->
<g id="edge1336" class="edge">
<title>division_ring&#45;&gt;div_inv_monoid</title>
<g id="a_edge1336"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/division_ring.to_div_inv_monoid" xlink:title="division_ring.to_div_inv_monoid">
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<g id="node343" class="node">
<title>ring</title>
<g id="a_node343"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/ring" xlink:title="ring">
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<text text-anchor="middle" x="8063.01" y="-2858.8" font-family="Courier,monospace" font-size="14.00">ring</text>
</a>
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</g>
<!-- division_ring&#45;&gt;ring -->
<g id="edge1334" class="edge">
<title>division_ring&#45;&gt;ring</title>
<g id="a_edge1334"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/division_ring.to_ring" xlink:title="division_ring.to_ring">
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<!-- normed_ring&#45;&gt;has_norm -->
<g id="edge1337" class="edge">
<title>normed_ring&#45;&gt;has_norm</title>
<g id="a_edge1337"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/normed_ring.to_has_norm" xlink:title="normed_ring.to_has_norm">
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<!-- normed_ring&#45;&gt;metric_space -->
<g id="edge1338" class="edge">
<title>normed_ring&#45;&gt;metric_space</title>
<g id="a_edge1338"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/normed_ring.to_metric_space" xlink:title="normed_ring.to_metric_space">
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<!-- semi_normed_ring -->
<g id="node342" class="node">
<title>semi_normed_ring</title>
<g id="a_node342"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/semi_normed_ring" xlink:title="semi_normed_ring">
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</g>
<!-- normed_ring&#45;&gt;semi_normed_ring -->
<g id="edge1339" class="edge">
<title>normed_ring&#45;&gt;semi_normed_ring</title>
<g id="a_edge1339"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/normed_ring.to_semi_normed_ring" xlink:title="normed_ring.to_semi_normed_ring">
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<!-- normed_ring&#45;&gt;ring -->
<g id="edge1340" class="edge">
<title>normed_ring&#45;&gt;ring</title>
<g id="a_edge1340"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/normed_ring.to_ring" xlink:title="normed_ring.to_ring">
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<!-- non_unital_normed_ring -->
<g id="node656" class="node">
<title>non_unital_normed_ring</title>
<g id="a_node656"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/non_unital_normed_ring" xlink:title="non_unital_normed_ring">
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</g>
<!-- normed_ring&#45;&gt;non_unital_normed_ring -->
<g id="edge1341" class="edge">
<title>normed_ring&#45;&gt;non_unital_normed_ring</title>
<g id="a_edge1341"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/normed_ring.to_non_unital_normed_ring" xlink:title="normed_ring.to_non_unital_normed_ring">
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<g id="node274" class="node">
<title>comm_semiring</title>
<g id="a_node274"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/comm_semiring" xlink:title="comm_semiring">
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</g>
<!-- semifield&#45;&gt;comm_semiring -->
<g id="edge508" class="edge">
<title>semifield&#45;&gt;comm_semiring</title>
<g id="a_edge508"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/semifield.to_comm_semiring" xlink:title="semifield.to_comm_semiring">
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<!-- comm_group_with_zero -->
<g id="node281" class="node">
<title>comm_group_with_zero</title>
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<!-- semifield&#45;&gt;comm_group_with_zero -->
<g id="edge509" class="edge">
<title>semifield&#45;&gt;comm_group_with_zero</title>
<g id="a_edge509"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/semifield.to_comm_group_with_zero" xlink:title="semifield.to_comm_group_with_zero">
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</g>
<!-- semifield&#45;&gt;division_semiring -->
<g id="edge510" class="edge">
<title>semifield&#45;&gt;division_semiring</title>
<g id="a_edge510"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/semifield.to_division_semiring" xlink:title="semifield.to_division_semiring">
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</g>
<!-- comm_ring&#45;&gt;comm_monoid -->
<g id="edge1342" class="edge">
<title>comm_ring&#45;&gt;comm_monoid</title>
<g id="a_edge1342"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/comm_ring.to_comm_monoid" xlink:title="comm_ring.to_comm_monoid">
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</g>
<!-- comm_ring&#45;&gt;comm_semiring -->
<g id="edge1343" class="edge">
<title>comm_ring&#45;&gt;comm_semiring</title>
<g id="a_edge1343"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/comm_ring.to_comm_semiring" xlink:title="comm_ring.to_comm_semiring">
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</g>
<!-- comm_ring&#45;&gt;ring -->
<g id="edge1344" class="edge">
<title>comm_ring&#45;&gt;ring</title>
<g id="a_edge1344"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/comm_ring.to_ring" xlink:title="comm_ring.to_ring">
<path fill="none" stroke="black" d="M8075.11,-2949.2C8072.81,-2933.3 8069.11,-2907 8066.41,-2887.7"/>
<polygon fill="black" stroke="black" points="8069.85,-2886.98 8064.91,-2877.6 8062.92,-2888.01 8069.85,-2886.98"/>
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</g>
<!-- non_unital_comm_ring -->
<g id="node501" class="node">
<title>non_unital_comm_ring</title>
<g id="a_node501"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/non_unital_comm_ring" xlink:title="non_unital_comm_ring">
<polygon fill="none" stroke="black" points="7692.01,-2878 7510.01,-2878 7510.01,-2847 7692.01,-2847 7692.01,-2878"/>
<text text-anchor="middle" x="7601.01" y="-2858.8" font-family="Courier,monospace" font-size="14.00">non_unital_comm_ring</text>
</a>
</g>
</g>
<!-- comm_ring&#45;&gt;non_unital_comm_ring -->
<g id="edge1345" class="edge">
<title>comm_ring&#45;&gt;non_unital_comm_ring</title>
<g id="a_edge1345"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/comm_ring.to_non_unital_comm_ring" xlink:title="comm_ring.to_non_unital_comm_ring">
<path fill="none" stroke="black" d="M8032.21,-2953.7C7950.41,-2936.7 7776.11,-2900.4 7676.01,-2879.6"/>
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</g>
<!-- euclidean_domain&#45;&gt;comm_ring -->
<g id="edge1348" class="edge">
<title>euclidean_domain&#45;&gt;comm_ring</title>
<g id="a_edge1348"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/euclidean_domain.to_comm_ring" xlink:title="euclidean_domain.to_comm_ring">
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</g>
<!-- euclidean_domain&#45;&gt;nontrivial -->
<g id="edge1346" class="edge">
<title>euclidean_domain&#45;&gt;nontrivial</title>
<g id="a_edge1346"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/euclidean_domain.to_nontrivial" xlink:title="euclidean_domain.to_nontrivial">
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</g>
<!-- has_div -->
<g id="node420" class="node">
<title>has_div</title>
<g id="a_node420"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/has_div" xlink:title="has_div">
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</a>
</g>
</g>
<!-- euclidean_domain&#45;&gt;has_div -->
<g id="edge1347" class="edge">
<title>euclidean_domain&#45;&gt;has_div</title>
<g id="a_edge1347"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/euclidean_domain.has_div" xlink:title="euclidean_domain.has_div">
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</g>
<!-- has_mod -->
<g id="node657" class="node">
<title>has_mod</title>
<g id="a_node657"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/has_mod" xlink:title="has_mod">
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</a>
</g>
</g>
<!-- euclidean_domain&#45;&gt;has_mod -->
<g id="edge1349" class="edge">
<title>euclidean_domain&#45;&gt;has_mod</title>
<g id="a_edge1349"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/euclidean_domain.has_mod" xlink:title="euclidean_domain.has_mod">
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<polygon fill="black" stroke="black" points="8217.51,-2988.6 8214.01,-2978.6 8210.51,-2988.6 8217.51,-2988.6"/>
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</g>
<!-- semi_normed_comm_ring&#45;&gt;comm_ring -->
<g id="edge1351" class="edge">
<title>semi_normed_comm_ring&#45;&gt;comm_ring</title>
<g id="a_edge1351"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/semi_normed_comm_ring.to_comm_ring" xlink:title="semi_normed_comm_ring.to_comm_ring">
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</g>
<!-- semi_normed_comm_ring&#45;&gt;semi_normed_ring -->
<g id="edge1350" class="edge">
<title>semi_normed_comm_ring&#45;&gt;semi_normed_ring</title>
<g id="a_edge1350"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/semi_normed_comm_ring.to_semi_normed_ring" xlink:title="semi_normed_comm_ring.to_semi_normed_ring">
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</g>
<!-- topological_space -->
<g id="node341" class="node">
<title>topological_space</title>
<g id="a_node341"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/topological_space" xlink:title="topological_space">
<polygon fill="none" stroke="black" points="7050.51,-2374 6893.51,-2374 6893.51,-2343 7050.51,-2343 7050.51,-2374"/>
<text text-anchor="middle" x="6972.01" y="-2354.8" font-family="Courier,monospace" font-size="14.00">topological_space</text>
</a>
</g>
</g>
<!-- uniform_space&#45;&gt;topological_space -->
<g id="edge635" class="edge">
<title>uniform_space&#45;&gt;topological_space</title>
<g id="a_edge635"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/uniform_space.to_topological_space" xlink:title="uniform_space.to_topological_space">
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</g>
<!-- pseudo_emetric_space&#45;&gt;uniform_space -->
<g id="edge636" class="edge">
<title>pseudo_emetric_space&#45;&gt;uniform_space</title>
<g id="a_edge636"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/pseudo_emetric_space.to_uniform_space" xlink:title="pseudo_emetric_space.to_uniform_space">
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</g>
<!-- pseudo_emetric_space&#45;&gt;has_edist -->
<g id="edge637" class="edge">
<title>pseudo_emetric_space&#45;&gt;has_edist</title>
<g id="a_edge637"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/pseudo_emetric_space.to_has_edist" xlink:title="pseudo_emetric_space.to_has_edist">
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</g>
<!-- ordered_add_comm_group&#45;&gt;partial_order -->
<g id="edge755" class="edge">
<title>ordered_add_comm_group&#45;&gt;partial_order</title>
<g id="a_edge755"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/ordered_add_comm_group.to_partial_order" xlink:title="ordered_add_comm_group.to_partial_order">
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</g>
<!-- ordered_add_comm_group&#45;&gt;add_comm_group -->
<g id="edge754" class="edge">
<title>ordered_add_comm_group&#45;&gt;add_comm_group</title>
<g id="a_edge754"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/ordered_add_comm_group.to_add_comm_group" xlink:title="ordered_add_comm_group.to_add_comm_group">
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<!-- ordered_cancel_add_comm_monoid -->
<g id="node397" class="node">
<title>ordered_cancel_add_comm_monoid</title>
<g id="a_node397"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/ordered_cancel_add_comm_monoid" xlink:title="ordered_cancel_add_comm_monoid">
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</a>
</g>
</g>
<!-- ordered_add_comm_group&#45;&gt;ordered_cancel_add_comm_monoid -->
<g id="edge756" class="edge">
<title>ordered_add_comm_group&#45;&gt;ordered_cancel_add_comm_monoid</title>
<g id="a_edge756"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/ordered_add_comm_group.to_ordered_cancel_add_comm_monoid" xlink:title="ordered_add_comm_group.to_ordered_cancel_add_comm_monoid">
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</g>
<!-- linear_ordered_add_comm_monoid -->
<g id="node396" class="node">
<title>linear_ordered_add_comm_monoid</title>
<g id="a_node396"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/linear_ordered_add_comm_monoid" xlink:title="linear_ordered_add_comm_monoid">
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</a>
</g>
</g>
<!-- linear_ordered_cancel_add_comm_monoid&#45;&gt;linear_ordered_add_comm_monoid -->
<g id="edge757" class="edge">
<title>linear_ordered_cancel_add_comm_monoid&#45;&gt;linear_ordered_add_comm_monoid</title>
<g id="a_edge757"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/linear_ordered_cancel_add_comm_monoid.to_linear_ordered_add_comm_monoid" xlink:title="linear_ordered_cancel_add_comm_monoid.to_linear_ordered_add_comm_monoid">
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</g>
<!-- linear_ordered_cancel_add_comm_monoid&#45;&gt;ordered_cancel_add_comm_monoid -->
<g id="edge758" class="edge">
<title>linear_ordered_cancel_add_comm_monoid&#45;&gt;ordered_cancel_add_comm_monoid</title>
<g id="a_edge758"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/linear_ordered_cancel_add_comm_monoid.to_ordered_cancel_add_comm_monoid" xlink:title="linear_ordered_cancel_add_comm_monoid.to_ordered_cancel_add_comm_monoid">
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<!-- semi_normed_group&#45;&gt;has_norm -->
<g id="edge623" class="edge">
<title>semi_normed_group&#45;&gt;has_norm</title>
<g id="a_edge623"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/semi_normed_group.to_has_norm" xlink:title="semi_normed_group.to_has_norm">
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<!-- semi_normed_group&#45;&gt;pseudo_metric_space -->
<g id="edge624" class="edge">
<title>semi_normed_group&#45;&gt;pseudo_metric_space</title>
<g id="a_edge624"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/semi_normed_group.to_pseudo_metric_space" xlink:title="semi_normed_group.to_pseudo_metric_space">
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<!-- semi_normed_group&#45;&gt;add_comm_group -->
<g id="edge625" class="edge">
<title>semi_normed_group&#45;&gt;add_comm_group</title>
<g id="a_edge625"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/semi_normed_group.to_add_comm_group" xlink:title="semi_normed_group.to_add_comm_group">
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<g id="node333" class="node">
<title>has_nnnorm</title>
<g id="a_node333"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/has_nnnorm" xlink:title="has_nnnorm">
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</g>
<!-- semi_normed_group&#45;&gt;has_nnnorm -->
<g id="edge626" class="edge">
<title>semi_normed_group&#45;&gt;has_nnnorm</title>
<g id="a_edge626"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/semi_normed_group.to_has_nnnorm" xlink:title="semi_normed_group.to_has_nnnorm">
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<!-- add_cancel_comm_monoid -->
<g id="node335" class="node">
<title>add_cancel_comm_monoid</title>
<g id="a_node335"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/add_cancel_comm_monoid" xlink:title="add_cancel_comm_monoid">
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</a>
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</g>
<!-- add_comm_group&#45;&gt;add_cancel_comm_monoid -->
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<g id="edge358" class="edge">
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<g id="a_edge358"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/has_continuous_mul.has_measurable_mul₂" xlink:title="has_continuous_mul.has_measurable_mul₂">
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<g id="node195" class="node">
<title>is_scalar_tower.has_continuous_const_smul</title>
<g id="a_node195"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/is_scalar_tower.has_continuous_const_smul" xlink:title="is_scalar_tower.has_continuous_const_smul">
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<!-- has_continuous_mul&#45;&gt;is_scalar_tower.has_continuous_const_smul -->
<g id="edge359" class="edge">
<title>has_continuous_mul&#45;&gt;is_scalar_tower.has_continuous_const_smul</title>
<g id="a_edge359"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/is_scalar_tower.has_continuous_const_smul" xlink:title="is_scalar_tower.has_continuous_const_smul">
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<!-- smul_comm_class.has_continuous_const_smul -->
<g id="node196" class="node">
<title>smul_comm_class.has_continuous_const_smul</title>
<g id="a_node196"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/smul_comm_class.has_continuous_const_smul" xlink:title="smul_comm_class.has_continuous_const_smul">
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<!-- has_continuous_mul&#45;&gt;smul_comm_class.has_continuous_const_smul -->
<g id="edge360" class="edge">
<title>has_continuous_mul&#45;&gt;smul_comm_class.has_continuous_const_smul</title>
<g id="a_edge360"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/smul_comm_class.has_continuous_const_smul" xlink:title="smul_comm_class.has_continuous_const_smul">
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<!-- has_continuous_mul.has_measurable_mul -->
<g id="node197" class="node">
<title>has_continuous_mul.has_measurable_mul</title>
<g id="a_node197"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/has_continuous_mul.has_measurable_mul" xlink:title="has_continuous_mul.has_measurable_mul">
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<!-- has_continuous_mul&#45;&gt;has_continuous_mul.has_measurable_mul -->
<g id="edge361" class="edge">
<title>has_continuous_mul&#45;&gt;has_continuous_mul.has_measurable_mul</title>
<g id="a_edge361"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/has_continuous_mul.has_measurable_mul" xlink:title="has_continuous_mul.has_measurable_mul">
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</g>
<!-- compact_space&#45;&gt;locally_compact_of_compact -->
<g id="edge362" class="edge">
<title>compact_space&#45;&gt;locally_compact_of_compact</title>
<g id="a_edge362"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/locally_compact_of_compact" xlink:title="locally_compact_of_compact">
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<!-- compact_space&#45;&gt;paracompact_space -->
<g id="edge365" class="edge">
<title>compact_space&#45;&gt;paracompact_space</title>
<g id="a_edge365"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/paracompact_of_compact" xlink:title="paracompact_of_compact">
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<!-- proper_space -->
<g id="node198" class="node">
<title>proper_space</title>
<g id="a_node198"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/proper_space" xlink:title="proper_space">
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</a>
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</g>
<!-- compact_space&#45;&gt;proper_space -->
<g id="edge363" class="edge">
<title>compact_space&#45;&gt;proper_space</title>
<g id="a_edge363"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/proper_of_compact" xlink:title="proper_of_compact">
<path fill="none" stroke="black" d="M14290.01,-1939.4C14312.01,-1922.5 14350.01,-1893.4 14375.01,-1873.9"/>
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<!-- first_countable_topology.seq_compact_of_compact -->
<g id="node199" class="node">
<title>first_countable_topology.seq_compact_of_compact</title>
<g id="a_node199"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/first_countable_topology.seq_compact_of_compact" xlink:title="first_countable_topology.seq_compact_of_compact">
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</g>
<!-- compact_space&#45;&gt;first_countable_topology.seq_compact_of_compact -->
<g id="edge364" class="edge">
<title>compact_space&#45;&gt;first_countable_topology.seq_compact_of_compact</title>
<g id="a_edge364"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/first_countable_topology.seq_compact_of_compact" xlink:title="first_countable_topology.seq_compact_of_compact">
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<!-- sigma_compact_space -->
<g id="node200" class="node">
<title>sigma_compact_space</title>
<g id="a_node200"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/sigma_compact_space" xlink:title="sigma_compact_space">
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<text text-anchor="middle" x="16282.01" y="-1040.8" font-family="Courier,monospace" font-size="14.00">sigma_compact_space</text>
</a>
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</g>
<!-- compact_space&#45;&gt;sigma_compact_space -->
<g id="edge366" class="edge">
<title>compact_space&#45;&gt;sigma_compact_space</title>
<g id="a_edge366"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/compact_space.sigma_compact" xlink:title="compact_space.sigma_compact">
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<!-- complete_space -->
<g id="node201" class="node">
<title>complete_space</title>
<g id="a_node201"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/complete_space" xlink:title="complete_space">
<polygon fill="none" stroke="black" points="14072.01,-1767 13940.01,-1767 13940.01,-1736 14072.01,-1736 14072.01,-1767"/>
<text text-anchor="middle" x="14006.01" y="-1747.8" font-family="Courier,monospace" font-size="14.00">complete_space</text>
</a>
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</g>
<!-- compact_space&#45;&gt;complete_space -->
<g id="edge367" class="edge">
<title>compact_space&#45;&gt;complete_space</title>
<g id="a_edge367"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/complete_of_compact" xlink:title="complete_of_compact">
<path fill="none" stroke="black" d="M14211.01,-1940.5C14110.01,-1919.8 13920.01,-1879.4 13911.01,-1867.5 13884.01,-1833.2 13934.01,-1794.1 13971.01,-1771.7"/>
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<!-- topological_ring -->
<g id="node202" class="node">
<title>topological_ring</title>
<g id="a_node202"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/topological_ring" xlink:title="topological_ring">
<polygon fill="none" stroke="black" points="12685.01,-1868 12537.01,-1868 12537.01,-1837 12685.01,-1837 12685.01,-1868"/>
<text text-anchor="middle" x="12611.01" y="-1848.8" font-family="Courier,monospace" font-size="14.00">topological_ring</text>
</a>
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</g>
<!-- topological_division_ring&#45;&gt;topological_ring -->
<g id="edge368" class="edge">
<title>topological_division_ring&#45;&gt;topological_ring</title>
<g id="a_edge368"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/topological_division_ring.to_topological_ring" xlink:title="topological_division_ring.to_topological_ring">
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<polygon fill="black" stroke="black" points="12658.61,-1867.86 12648.01,-1867.6 12656.13,-1874.41 12658.61,-1867.86"/>
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<!-- has_continuous_inv₀ -->
<g id="node203" class="node">
<title>has_continuous_inv₀</title>
<g id="a_node203"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/has_continuous_inv₀" xlink:title="has_continuous_inv₀">
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<text text-anchor="middle" x="12923.01" y="-1747.8" font-family="Courier,monospace" font-size="14.00">has_continuous_inv₀</text>
</a>
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</g>
<!-- topological_division_ring&#45;&gt;has_continuous_inv₀ -->
<g id="edge369" class="edge">
<title>topological_division_ring&#45;&gt;has_continuous_inv₀</title>
<g id="a_edge369"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/topological_division_ring.to_has_continuous_inv₀" xlink:title="topological_division_ring.to_has_continuous_inv₀">
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<!-- filter.ne_bot -->
<g id="node204" class="node">
<title>filter.ne_bot</title>
<g id="a_node204"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/filter.ne_bot" xlink:title="filter.ne_bot">
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</a>
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<!-- nhds_within.filter.ne_bot&#45;&gt;filter.ne_bot -->
<g id="edge370" class="edge">
<title>nhds_within.filter.ne_bot&#45;&gt;filter.ne_bot</title>
<g id="a_edge370"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/nhds_within.filter.ne_bot" xlink:title="nhds_within.filter.ne_bot">
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<!-- nhds_within_Ioi_self_ne_bot&#45;&gt;filter.ne_bot -->
<g id="edge371" class="edge">
<title>nhds_within_Ioi_self_ne_bot&#45;&gt;filter.ne_bot</title>
<g id="a_edge371"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/nhds_within_Ioi_self_ne_bot" xlink:title="nhds_within_Ioi_self_ne_bot">
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<!-- preconnected_space -->
<g id="node205" class="node">
<title>preconnected_space</title>
<g id="a_node205"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/preconnected_space" xlink:title="preconnected_space">
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</a>
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<!-- ordered_connected_space&#45;&gt;preconnected_space -->
<g id="edge372" class="edge">
<title>ordered_connected_space&#45;&gt;preconnected_space</title>
<g id="a_edge372"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/ordered_connected_space" xlink:title="ordered_connected_space">
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<!-- nhds_within_Iio_self_ne_bot&#45;&gt;filter.ne_bot -->
<g id="edge373" class="edge">
<title>nhds_within_Iio_self_ne_bot&#45;&gt;filter.ne_bot</title>
<g id="a_edge373"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/nhds_within_Iio_self_ne_bot" xlink:title="nhds_within_Iio_self_ne_bot">
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<g id="node206" class="node">
<title>real.punctured_nhds_module_ne_bot</title>
<g id="a_node206"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/real.punctured_nhds_module_ne_bot" xlink:title="real.punctured_nhds_module_ne_bot">
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<g id="edge374" class="edge">
<title>has_continuous_add&#45;&gt;real.punctured_nhds_module_ne_bot</title>
<g id="a_edge374"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/real.punctured_nhds_module_ne_bot" xlink:title="real.punctured_nhds_module_ne_bot">
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<g id="node207" class="node">
<title>real_topological_vector_space.contractible_space</title>
<g id="a_node207"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/real_topological_vector_space.contractible_space" xlink:title="real_topological_vector_space.contractible_space">
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<g id="edge375" class="edge">
<title>has_continuous_add&#45;&gt;real_topological_vector_space.contractible_space</title>
<g id="a_edge375"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/real_topological_vector_space.contractible_space" xlink:title="real_topological_vector_space.contractible_space">
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<g id="a_edge377"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/has_continuous_add.has_measurable_add" xlink:title="has_continuous_add.has_measurable_add">
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<g id="a_edge402"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/polish_space_of_complete_second_countable" xlink:title="polish_space_of_complete_second_countable">
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<g id="a_edge411"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/filter.map_ne_bot" xlink:title="filter.map_ne_bot">
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<g id="a_edge700"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/real.punctured_nhds_module_ne_bot" xlink:title="real.punctured_nhds_module_ne_bot">
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<!-- topological_space.second_countable_topology&#45;&gt;measure_theory.sigma_finite -->
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<!-- topological_space.second_countable_topology&#45;&gt;topological_space.first_countable_topology -->
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<g id="a_edge584"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/topological_space.second_countable_topology.to_first_countable_topology" xlink:title="topological_space.second_countable_topology.to_first_countable_topology">
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<g id="a_edge498"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/non_unital_comm_semiring.to_comm_semigroup" xlink:title="non_unital_comm_semiring.to_comm_semigroup">
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<!-- semiring&#45;&gt;monoid_with_zero -->
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<g id="a_edge500"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/semiring.to_monoid_with_zero" xlink:title="semiring.to_monoid_with_zero">
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<!-- semiring&#45;&gt;non_assoc_semiring -->
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<!-- non_unital_semiring&#45;&gt;non_unital_non_assoc_semiring -->
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<!-- non_assoc_semiring&#45;&gt;mul_zero_one_class -->
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<g id="a_edge506"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/non_assoc_semiring.to_non_unital_non_assoc_semiring" xlink:title="non_assoc_semiring.to_non_unital_non_assoc_semiring">
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<!-- add_comm_monoid_with_one -->
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<!-- non_assoc_semiring&#45;&gt;add_comm_monoid_with_one -->
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<g id="a_edge507"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/non_assoc_semiring.to_add_comm_monoid_with_one" xlink:title="non_assoc_semiring.to_add_comm_monoid_with_one">
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<!-- non_unital_non_assoc_semiring&#45;&gt;mul_zero_class -->
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<g id="a_edge966"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/non_unital_non_assoc_semiring.to_mul_zero_class" xlink:title="non_unital_non_assoc_semiring.to_mul_zero_class">
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<!-- non_unital_non_assoc_semiring&#45;&gt;distrib -->
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<g id="a_edge964"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/non_unital_non_assoc_semiring.to_distrib" xlink:title="non_unital_non_assoc_semiring.to_distrib">
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<g id="a_edge1524"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/add_comm_monoid_with_one.to_add_comm_monoid" xlink:title="add_comm_monoid_with_one.to_add_comm_monoid">
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<!-- add_comm_monoid_with_one&#45;&gt;add_monoid_with_one -->
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<g id="a_edge1525"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/add_comm_monoid_with_one.to_add_monoid_with_one" xlink:title="add_comm_monoid_with_one.to_add_monoid_with_one">
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<g id="a_edge514"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/comm_group_with_zero.cancel_comm_monoid_with_zero" xlink:title="comm_group_with_zero.cancel_comm_monoid_with_zero">
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<!-- group_with_zero&#45;&gt;monoid_with_zero -->
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<title>group_with_zero&#45;&gt;monoid_with_zero</title>
<g id="a_edge517"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/group_with_zero.to_monoid_with_zero" xlink:title="group_with_zero.to_monoid_with_zero">
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<!-- group_with_zero&#45;&gt;nontrivial -->
<g id="edge518" class="edge">
<title>group_with_zero&#45;&gt;nontrivial</title>
<g id="a_edge518"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/group_with_zero.to_nontrivial" xlink:title="group_with_zero.to_nontrivial">
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<!-- division_monoid -->
<g id="node287" class="node">
<title>division_monoid</title>
<g id="a_node287"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/division_monoid" xlink:title="division_monoid">
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</g>
<!-- group_with_zero&#45;&gt;division_monoid -->
<g id="edge519" class="edge">
<title>group_with_zero&#45;&gt;division_monoid</title>
<g id="a_edge519"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/group_with_zero.to_division_monoid" xlink:title="group_with_zero.to_division_monoid">
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<!-- group_with_zero&#45;&gt;div_inv_monoid -->
<g id="edge520" class="edge">
<title>group_with_zero&#45;&gt;div_inv_monoid</title>
<g id="a_edge520"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/group_with_zero.to_div_inv_monoid" xlink:title="group_with_zero.to_div_inv_monoid">
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<!-- cancel_monoid_with_zero -->
<g id="node289" class="node">
<title>cancel_monoid_with_zero</title>
<g id="a_node289"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/cancel_monoid_with_zero" xlink:title="cancel_monoid_with_zero">
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<text text-anchor="middle" x="9371.01" y="-2758.8" font-family="Courier,monospace" font-size="14.00">cancel_monoid_with_zero</text>
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<!-- group_with_zero&#45;&gt;cancel_monoid_with_zero -->
<g id="edge521" class="edge">
<title>group_with_zero&#45;&gt;cancel_monoid_with_zero</title>
<g id="a_edge521"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/group_with_zero.cancel_monoid_with_zero" xlink:title="group_with_zero.cancel_monoid_with_zero">
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<!-- division_comm_monoid&#45;&gt;comm_monoid -->
<g id="edge522" class="edge">
<title>division_comm_monoid&#45;&gt;comm_monoid</title>
<g id="a_edge522"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/division_comm_monoid.to_comm_monoid" xlink:title="division_comm_monoid.to_comm_monoid">
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</g>
<!-- division_comm_monoid&#45;&gt;division_monoid -->
<g id="edge523" class="edge">
<title>division_comm_monoid&#45;&gt;division_monoid</title>
<g id="a_edge523"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/division_comm_monoid.to_division_monoid" xlink:title="division_comm_monoid.to_division_monoid">
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<!-- cancel_comm_monoid_with_zero&#45;&gt;comm_monoid_with_zero -->
<g id="edge524" class="edge">
<title>cancel_comm_monoid_with_zero&#45;&gt;comm_monoid_with_zero</title>
<g id="a_edge524"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/cancel_comm_monoid_with_zero.to_comm_monoid_with_zero" xlink:title="cancel_comm_monoid_with_zero.to_comm_monoid_with_zero">
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<!-- cancel_comm_monoid_with_zero&#45;&gt;cancel_monoid_with_zero -->
<g id="edge525" class="edge">
<title>cancel_comm_monoid_with_zero&#45;&gt;cancel_monoid_with_zero</title>
<g id="a_edge525"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/cancel_comm_monoid_with_zero.to_cancel_monoid_with_zero" xlink:title="cancel_comm_monoid_with_zero.to_cancel_monoid_with_zero">
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<!-- nontrivial&#45;&gt;nhds_within.filter.ne_bot -->
<g id="edge661" class="edge">
<title>nontrivial&#45;&gt;nhds_within.filter.ne_bot</title>
<g id="a_edge661"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/nhds_within.filter.ne_bot" xlink:title="nhds_within.filter.ne_bot">
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<!-- nontrivial&#45;&gt;real.punctured_nhds_module_ne_bot -->
<g id="edge674" class="edge">
<title>nontrivial&#45;&gt;real.punctured_nhds_module_ne_bot</title>
<g id="a_edge674"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/real.punctured_nhds_module_ne_bot" xlink:title="real.punctured_nhds_module_ne_bot">
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<!-- nonempty -->
<g id="node352" class="node">
<title>nonempty</title>
<g id="a_node352"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/nonempty" xlink:title="nonempty">
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<text text-anchor="middle" x="11117.01" y="-1040.8" font-family="Courier,monospace" font-size="14.00">nonempty</text>
</a>
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</g>
<!-- nontrivial&#45;&gt;nonempty -->
<g id="edge662" class="edge">
<title>nontrivial&#45;&gt;nonempty</title>
<g id="a_edge662"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/nontrivial.to_nonempty" xlink:title="nontrivial.to_nonempty">
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<!-- char_zero_of_exp_char_one&#39; -->
<g id="node353" class="node">
<title>char_zero_of_exp_char_one&#39;</title>
<g id="a_node353"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/char_zero_of_exp_char_one'" xlink:title="char_zero_of_exp_char_one&#39;">
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</g>
<!-- nontrivial&#45;&gt;char_zero_of_exp_char_one&#39; -->
<g id="edge663" class="edge">
<title>nontrivial&#45;&gt;char_zero_of_exp_char_one&#39;</title>
<g id="a_edge663"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/char_zero_of_exp_char_one'" xlink:title="char_zero_of_exp_char_one&#39;">
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<!-- strong_rank_condition -->
<g id="node354" class="node">
<title>strong_rank_condition</title>
<g id="a_node354"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/strong_rank_condition" xlink:title="strong_rank_condition">
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</a>
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<!-- nontrivial&#45;&gt;strong_rank_condition -->
<g id="edge664" class="edge">
<title>nontrivial&#45;&gt;strong_rank_condition</title>
<g id="a_edge664"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/comm_ring_strong_rank_condition" xlink:title="comm_ring_strong_rank_condition">
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<!-- no_min_order -->
<g id="node355" class="node">
<title>no_min_order</title>
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<text text-anchor="middle" x="12387.01" y="-2252.8" font-family="Courier,monospace" font-size="14.00">no_min_order</text>
</a>
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<!-- nontrivial&#45;&gt;no_min_order -->
<g id="edge665" class="edge">
<title>nontrivial&#45;&gt;no_min_order</title>
<g id="a_edge665"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/linear_ordered_comm_group.to_no_min_order" xlink:title="linear_ordered_comm_group.to_no_min_order">
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<!-- nontrivial&#45;&gt;no_min_order -->
<g id="edge666" class="edge">
<title>nontrivial&#45;&gt;no_min_order</title>
<g id="a_edge666"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/linear_ordered_add_comm_group.to_no_min_order" xlink:title="linear_ordered_add_comm_group.to_no_min_order">
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<!-- ne_zero.invertible -->
<g id="node356" class="node">
<title>ne_zero.invertible</title>
<g id="a_node356"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/ne_zero.invertible" xlink:title="ne_zero.invertible">
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<!-- nontrivial&#45;&gt;ne_zero.invertible -->
<g id="edge667" class="edge">
<title>nontrivial&#45;&gt;ne_zero.invertible</title>
<g id="a_edge667"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/ne_zero.invertible" xlink:title="ne_zero.invertible">
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<!-- valuation.supp.ideal.is_prime -->
<g id="node357" class="node">
<title>valuation.supp.ideal.is_prime</title>
<g id="a_node357"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/valuation.supp.ideal.is_prime" xlink:title="valuation.supp.ideal.is_prime">
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<!-- nontrivial&#45;&gt;valuation.supp.ideal.is_prime -->
<g id="edge668" class="edge">
<title>nontrivial&#45;&gt;valuation.supp.ideal.is_prime</title>
<g id="a_edge668"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/valuation.supp.ideal.is_prime" xlink:title="valuation.supp.ideal.is_prime">
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<g id="node358" class="node">
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<!-- nontrivial&#45;&gt;has_faithful_smul -->
<g id="edge669" class="edge">
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<g id="a_edge669"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/cancel_monoid_with_zero.to_has_faithful_smul" xlink:title="cancel_monoid_with_zero.to_has_faithful_smul">
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<!-- no_max_order -->
<g id="node359" class="node">
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<g id="edge670" class="edge">
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<g id="a_edge621"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/non_unital_semi_normed_ring.to_semi_normed_group" xlink:title="non_unital_semi_normed_ring.to_semi_normed_group">
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<text text-anchor="middle" x="8713.01" y="-2354.8" font-family="Courier,monospace" font-size="14.00">subtraction_monoid</text>
</a>
</g>
</g>
<!-- add_group&#45;&gt;subtraction_monoid -->
<g id="edge892" class="edge">
<title>add_group&#45;&gt;subtraction_monoid</title>
<g id="a_edge892"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/add_group.to_division_add_monoid" xlink:title="add_group.to_division_add_monoid">
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<polygon fill="black" stroke="black" points="8666.83,-2379.21 8675.11,-2372.6 8664.52,-2372.6 8666.83,-2379.21"/>
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</g>
<!-- subtraction_comm_monoid&#45;&gt;add_comm_monoid -->
<g id="edge893" class="edge">
<title>subtraction_comm_monoid&#45;&gt;add_comm_monoid</title>
<g id="a_edge893"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/subtraction_comm_monoid.to_add_comm_monoid" xlink:title="subtraction_comm_monoid.to_add_comm_monoid">
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<polygon fill="black" stroke="black" points="8496.42,-2375.88 8486.31,-2372.7 8492.23,-2381.49 8496.42,-2375.88"/>
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</g>
<!-- subtraction_comm_monoid&#45;&gt;subtraction_monoid -->
<g id="edge894" class="edge">
<title>subtraction_comm_monoid&#45;&gt;subtraction_monoid</title>
<g id="a_edge894"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/subtraction_comm_monoid.to_subtraction_monoid" xlink:title="subtraction_comm_monoid.to_subtraction_monoid">
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<polygon fill="black" stroke="black" points="8692.23,-2381.84 8697.41,-2372.6 8687.6,-2376.59 8692.23,-2381.84"/>
</a>
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</g>
<!-- semi_normed_ring&#45;&gt;has_norm -->
<g id="edge640" class="edge">
<title>semi_normed_ring&#45;&gt;has_norm</title>
<g id="a_edge640"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/semi_normed_ring.to_has_norm" xlink:title="semi_normed_ring.to_has_norm">
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</g>
<!-- semi_normed_ring&#45;&gt;pseudo_metric_space -->
<g id="edge641" class="edge">
<title>semi_normed_ring&#45;&gt;pseudo_metric_space</title>
<g id="a_edge641"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/semi_normed_ring.to_pseudo_metric_space" xlink:title="semi_normed_ring.to_pseudo_metric_space">
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</g>
<!-- semi_normed_ring&#45;&gt;non_unital_semi_normed_ring -->
<g id="edge642" class="edge">
<title>semi_normed_ring&#45;&gt;non_unital_semi_normed_ring</title>
<g id="a_edge642"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/semi_normed_ring.to_non_unital_semi_normed_ring" xlink:title="semi_normed_ring.to_non_unital_semi_normed_ring">
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<polygon fill="black" stroke="black" points="7206.36,-2883.11 7197.31,-2877.6 7200.95,-2887.55 7206.36,-2883.11"/>
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</g>
<!-- semi_normed_ring&#45;&gt;ring -->
<g id="edge643" class="edge">
<title>semi_normed_ring&#45;&gt;ring</title>
<g id="a_edge643"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/semi_normed_ring.to_ring" xlink:title="semi_normed_ring.to_ring">
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<polygon fill="black" stroke="black" points="8029.24,-2871.75 8038.71,-2867 8028.35,-2864.81 8029.24,-2871.75"/>
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</g>
<!-- ring&#45;&gt;monoid -->
<g id="edge644" class="edge">
<title>ring&#45;&gt;monoid</title>
<g id="a_edge644"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/ring.to_monoid" xlink:title="ring.to_monoid">
<path fill="none" stroke="black" d="M8087.11,-2856.9C8188.91,-2835.2 8579.61,-2752.3 8606.01,-2747.5 8709.71,-2728.6 9006.31,-2755.5 9075.01,-2675.5 9103.81,-2641.9 9032.61,-2606.2 9022.01,-2574.5 9012.01,-2544.5 9014.01,-2507.7 9017.01,-2484"/>
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</g>
<!-- ring&#45;&gt;semiring -->
<g id="edge645" class="edge">
<title>ring&#45;&gt;semiring</title>
<g id="a_edge645"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/ring.to_semiring" xlink:title="ring.to_semiring">
<path fill="none" stroke="black" d="M8087.41,-2857.9C8176.01,-2843.1 8482.51,-2792 8604.91,-2771.5"/>
<polygon fill="black" stroke="black" points="8605.92,-2774.88 8615.21,-2769.8 8604.78,-2767.98 8605.92,-2774.88"/>
</a>
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</g>
<!-- ring&#45;&gt;non_unital_ring -->
<g id="edge646" class="edge">
<title>ring&#45;&gt;non_unital_ring</title>
<g id="a_edge646"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/ring.to_non_unital_ring" xlink:title="ring.to_non_unital_ring">
<path fill="none" stroke="black" d="M8038.91,-2858.5C7960.01,-2847.1 7702.01,-2809.7 7489.01,-2776.5 7487.71,-2776.3 7486.51,-2776.1 7485.21,-2775.9"/>
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</a>
</g>
</g>
<!-- lie_ring -->
<g id="node344" class="node">
<title>lie_ring</title>
<g id="a_node344"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/lie_ring" xlink:title="lie_ring">
<polygon fill="none" stroke="black" points="8368.51,-2778 8287.51,-2778 8287.51,-2747 8368.51,-2747 8368.51,-2778"/>
<text text-anchor="middle" x="8328.01" y="-2758.8" font-family="Courier,monospace" font-size="14.00">lie_ring</text>
</a>
</g>
</g>
<!-- ring&#45;&gt;lie_ring -->
<g id="edge647" class="edge">
<title>ring&#45;&gt;lie_ring</title>
<g id="a_edge647"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/lie_ring.of_associative_ring" xlink:title="lie_ring.of_associative_ring">
<path fill="none" stroke="black" d="M8087.51,-2852.9C8131.71,-2836.3 8225.51,-2801.3 8282.01,-2780.2"/>
<polygon fill="black" stroke="black" points="8283.4,-2783.42 8291.51,-2776.6 8280.92,-2776.87 8283.4,-2783.42"/>
</a>
</g>
</g>
<!-- has_bracket -->
<g id="node345" class="node">
<title>has_bracket</title>
<g id="a_node345"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/has_bracket" xlink:title="has_bracket">
<polygon fill="none" stroke="black" points="8346.01,-2677 8240.01,-2677 8240.01,-2646 8346.01,-2646 8346.01,-2677"/>
<text text-anchor="middle" x="8293.01" y="-2657.8" font-family="Courier,monospace" font-size="14.00">has_bracket</text>
</a>
</g>
</g>
<!-- ring&#45;&gt;has_bracket -->
<g id="edge648" class="edge">
<title>ring&#45;&gt;has_bracket</title>
<g id="a_edge648"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/ring.has_bracket" xlink:title="ring.has_bracket">
<path fill="none" stroke="black" d="M8038.91,-2860.6C7960.41,-2855.1 7720.91,-2831.2 7792.01,-2747.5 7854.11,-2674.4 8117.31,-2692.8 8230.21,-2675.4"/>
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</g>
<!-- ring&#45;&gt;distrib -->
<g id="edge649" class="edge">
<title>ring&#45;&gt;distrib</title>
<g id="a_edge649"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/ring.to_distrib" xlink:title="ring.to_distrib">
<path fill="none" stroke="black" d="M8038.91,-2862.4C7960.71,-2862.9 7708.41,-2857.6 7522.01,-2776.5 7519.91,-2775.6 7394.51,-2677.2 7393.01,-2675.5 7357.01,-2636.1 7343.11,-2625.7 7328.01,-2574.5 7324.41,-2562.1 7322.91,-2557.3 7328.01,-2545.5 7340.11,-2517.5 7366.41,-2494.5 7387.61,-2479.4"/>
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</g>
</g>
<!-- add_comm_group_with_one -->
<g id="node347" class="node">
<title>add_comm_group_with_one</title>
<g id="a_node347"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/add_comm_group_with_one" xlink:title="add_comm_group_with_one">
<polygon fill="none" stroke="black" points="8845.51,-2677 8638.51,-2677 8638.51,-2646 8845.51,-2646 8845.51,-2677"/>
<text text-anchor="middle" x="8742.01" y="-2657.8" font-family="Courier,monospace" font-size="14.00">add_comm_group_with_one</text>
</a>
</g>
</g>
<!-- ring&#45;&gt;add_comm_group_with_one -->
<g id="edge650" class="edge">
<title>ring&#45;&gt;add_comm_group_with_one</title>
<g id="a_edge650"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/ring.to_add_comm_group_with_one" xlink:title="ring.to_add_comm_group_with_one">
<path fill="none" stroke="black" d="M8087.31,-2856.8C8144.21,-2844.6 8290.81,-2812 8411.01,-2776.5 8425.01,-2772.4 8605.21,-2709.7 8693.61,-2678.9"/>
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</a>
</g>
</g>
<!-- non_assoc_ring -->
<g id="node348" class="node">
<title>non_assoc_ring</title>
<g id="a_node348"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/non_assoc_ring" xlink:title="non_assoc_ring">
<polygon fill="none" stroke="black" points="8114.01,-2778 7982.01,-2778 7982.01,-2747 8114.01,-2747 8114.01,-2778"/>
<text text-anchor="middle" x="8048.01" y="-2758.8" font-family="Courier,monospace" font-size="14.00">non_assoc_ring</text>
</a>
</g>
</g>
<!-- ring&#45;&gt;non_assoc_ring -->
<g id="edge651" class="edge">
<title>ring&#45;&gt;non_assoc_ring</title>
<g id="a_edge651"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/ring.to_non_assoc_ring" xlink:title="ring.to_non_assoc_ring">
<path fill="none" stroke="black" d="M8060.91,-2848.2C8058.51,-2832.3 8054.51,-2806 8051.61,-2786.7"/>
<polygon fill="black" stroke="black" points="8055.05,-2785.98 8050.11,-2776.6 8048.12,-2787.01 8055.05,-2785.98"/>
</a>
</g>
</g>
<!-- lie_ring&#45;&gt;add_comm_group -->
<g id="edge652" class="edge">
<title>lie_ring&#45;&gt;add_comm_group</title>
<g id="a_edge652"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/lie_ring.to_add_comm_group" xlink:title="lie_ring.to_add_comm_group">
<path fill="none" stroke="black" d="M8332.41,-2747.3C8341.01,-2723.1 8362.31,-2672.7 8398.01,-2646.5 8419.71,-2630.6 8572.61,-2596.4 8667.11,-2576.5"/>
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</g>
<!-- lie_ring&#45;&gt;has_bracket -->
<g id="edge653" class="edge">
<title>lie_ring&#45;&gt;has_bracket</title>
<g id="a_edge653"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/lie_ring.to_has_bracket" xlink:title="lie_ring.to_has_bracket">
<path fill="none" stroke="black" d="M8323.11,-2747.2C8317.51,-2731.2 8308.01,-2704.5 8301.21,-2685.2"/>
<polygon fill="black" stroke="black" points="8304.45,-2683.86 8297.81,-2675.6 8297.85,-2686.19 8304.45,-2683.86"/>
</a>
</g>
</g>
<!-- has_add -->
<g id="node349" class="node">
<title>has_add</title>
<g id="a_node349"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/has_add" xlink:title="has_add">
<polygon fill="none" stroke="black" points="8749.51,-1970 8676.51,-1970 8676.51,-1939 8749.51,-1939 8749.51,-1970"/>
<text text-anchor="middle" x="8713.01" y="-1950.8" font-family="Courier,monospace" font-size="14.00">has_add</text>
</a>
</g>
</g>
<!-- distrib&#45;&gt;has_add -->
<g id="edge654" class="edge">
<title>distrib&#45;&gt;has_add</title>
<g id="a_edge654"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/distrib.to_has_add" xlink:title="distrib.to_has_add">
<path fill="none" stroke="black" d="M7442.71,-2444.4C7542.91,-2386.7 7929.61,-2164.7 7988.01,-2141.5 8277.41,-2026.4 8366.71,-2050.8 8667.01,-1968.5 8667.11,-1968.5 8667.21,-1968.4 8667.31,-1968.4"/>
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</g>
</g>
<!-- distrib&#45;&gt;has_mul -->
<g id="edge655" class="edge">
<title>distrib&#45;&gt;has_mul</title>
<g id="a_edge655"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/distrib.to_has_mul" xlink:title="distrib.to_has_mul">
<path fill="none" stroke="black" d="M7455.01,-2446.2C7457.41,-2445.6 7459.71,-2445 7462.01,-2444.5 7672.21,-2396 7744.81,-2459.9 7942.01,-2372.5 7967.91,-2361 8027.01,-2308.7 8059.51,-2278.9"/>
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</g>
<!-- add_comm_group_with_one&#45;&gt;add_comm_group -->
<g id="edge656" class="edge">
<title>add_comm_group_with_one&#45;&gt;add_comm_group</title>
<g id="a_edge656"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/add_comm_group_with_one.to_add_comm_group" xlink:title="add_comm_group_with_one.to_add_comm_group">
<path fill="none" stroke="black" d="M8742.01,-2646.2C8742.01,-2630.3 8742.01,-2604 8742.01,-2584.7"/>
<polygon fill="black" stroke="black" points="8745.51,-2584.6 8742.01,-2574.6 8738.51,-2584.6 8745.51,-2584.6"/>
</a>
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</g>
<!-- add_group_with_one -->
<g id="node351" class="node">
<title>add_group_with_one</title>
<g id="a_node351"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/add_group_with_one" xlink:title="add_group_with_one">
<polygon fill="none" stroke="black" points="8431.51,-2576 8266.51,-2576 8266.51,-2545 8431.51,-2545 8431.51,-2576"/>
<text text-anchor="middle" x="8349.01" y="-2556.8" font-family="Courier,monospace" font-size="14.00">add_group_with_one</text>
</a>
</g>
</g>
<!-- add_comm_group_with_one&#45;&gt;add_group_with_one -->
<g id="edge657" class="edge">
<title>add_comm_group_with_one&#45;&gt;add_group_with_one</title>
<g id="a_edge657"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/add_comm_group_with_one.to_add_group_with_one" xlink:title="add_comm_group_with_one.to_add_group_with_one">
<path fill="none" stroke="black" d="M8688.21,-2646.4C8616.41,-2628.3 8489.41,-2596.4 8412.81,-2577.1"/>
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</a>
</g>
</g>
<!-- non_assoc_ring&#45;&gt;non_assoc_semiring -->
<g id="edge658" class="edge">
<title>non_assoc_ring&#45;&gt;non_assoc_semiring</title>
<g id="a_edge658"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/non_assoc_ring.to_non_assoc_semiring" xlink:title="non_assoc_ring.to_non_assoc_semiring">
<path fill="none" stroke="black" d="M8060.91,-2747.2C8076.51,-2730.6 8103.01,-2702.5 8121.21,-2683.1"/>
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</a>
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</g>
<!-- non_assoc_ring&#45;&gt;non_unital_non_assoc_ring -->
<g id="edge659" class="edge">
<title>non_assoc_ring&#45;&gt;non_unital_non_assoc_ring</title>
<g id="a_edge659"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/non_assoc_ring.to_non_unital_non_assoc_ring" xlink:title="non_assoc_ring.to_non_unital_non_assoc_ring">
<path fill="none" stroke="black" d="M8026.61,-2747.4C7999.51,-2730.2 7952.61,-2700.5 7921.91,-2681"/>
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</g>
<!-- non_assoc_ring&#45;&gt;add_group_with_one -->
<g id="edge660" class="edge">
<title>non_assoc_ring&#45;&gt;add_group_with_one</title>
<g id="a_edge660"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/non_assoc_ring.to_add_group_with_one" xlink:title="non_assoc_ring.to_add_group_with_one">
<path fill="none" stroke="black" d="M8043.51,-2747.3C8036.81,-2724 8027.21,-2676.1 8050.01,-2646.5 8075.41,-2613.4 8179.21,-2589.1 8257.41,-2575"/>
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</g>
<!-- has_vadd -->
<g id="node465" class="node">
<title>has_vadd</title>
<g id="a_node465"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/has_vadd" xlink:title="has_vadd">
<polygon fill="none" stroke="black" points="8682.51,-1868 8601.51,-1868 8601.51,-1837 8682.51,-1837 8682.51,-1868"/>
<text text-anchor="middle" x="8642.01" y="-1848.8" font-family="Courier,monospace" font-size="14.00">has_vadd</text>
</a>
</g>
</g>
<!-- has_add&#45;&gt;has_vadd -->
<g id="edge886" class="edge">
<title>has_add&#45;&gt;has_vadd</title>
<g id="a_edge886"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/has_add.to_has_vadd" xlink:title="has_add.to_has_vadd">
<path fill="none" stroke="black" d="M8703.11,-1939.2C8691.41,-1922.8 8671.61,-1895.2 8657.71,-1875.9"/>
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</g>
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<!-- infinite -->
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</g>
<!-- char_zero&#45;&gt;infinite -->
<g id="edge717" class="edge">
<title>char_zero&#45;&gt;infinite</title>
<g id="a_edge717"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/char_zero.infinite" xlink:title="char_zero.infinite">
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<!-- is_alg_closed_of_char_zero.is_cyclotomic_extension -->
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<title>is_alg_closed_of_char_zero.is_cyclotomic_extension</title>
<g id="a_node389"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/is_alg_closed_of_char_zero.is_cyclotomic_extension" xlink:title="is_alg_closed_of_char_zero.is_cyclotomic_extension">
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<!-- char_zero&#45;&gt;is_alg_closed_of_char_zero.is_cyclotomic_extension -->
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<g id="a_edge718"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/is_alg_closed_of_char_zero.is_cyclotomic_extension" xlink:title="is_alg_closed_of_char_zero.is_cyclotomic_extension">
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<!-- char_p -->
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<!-- char_zero&#45;&gt;char_p -->
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<!-- char_zero&#45;&gt;ne_zero.char_zero -->
<g id="edge720" class="edge">
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<!-- invertible_of_pos -->
<g id="node392" class="node">
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<!-- char_zero&#45;&gt;invertible_of_pos -->
<g id="edge721" class="edge">
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<!-- rank_condition&#45;&gt;invariant_basis_number -->
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<g id="edge723" class="edge">
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<g id="a_edge723"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/discrete_topology.order_topology_of_pred_succ'" xlink:title="discrete_topology.order_topology_of_pred_succ&#39;">
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<!-- first_order.language.model_DLO -->
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<!-- no_bot_order&#45;&gt;first_order.language.model_DLO -->
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<g id="a_edge724"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/first_order.language.model_DLO" xlink:title="first_order.language.model_DLO">
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<!-- noncompact_space&#45;&gt;filter.ne_bot -->
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<g id="a_edge821"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/algebraic_geometry.Scheme.restrict.is_integral" xlink:title="algebraic_geometry.Scheme.restrict.is_integral">
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<g id="a_edge822"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/algebraic_geometry.is_reduced_of_is_integral" xlink:title="algebraic_geometry.is_reduced_of_is_integral">
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<!-- invertible&#45;&gt;invertible -->
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<!-- invertible&#45;&gt;invertible -->
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<!-- infinite&#45;&gt;filter.ne_bot -->
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<g id="edge1068" class="edge">
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<!-- subsingleton -->
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<g id="a_edge1318"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/char_p.subsingleton" xlink:title="char_p.subsingleton">
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<g id="edge1542" class="edge">
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<g id="a_edge1542"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/first_order.language.model_DLO" xlink:title="first_order.language.model_DLO">
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<g id="edge741" class="edge">
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<g id="a_edge741"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/ordered_ring.to_ordered_add_comm_group" xlink:title="ordered_ring.to_ordered_add_comm_group">
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<g id="a_edge739"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/ordered_ring.to_ring" xlink:title="ordered_ring.to_ring">
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<g id="edge742" class="edge">
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<g id="edge743" class="edge">
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<g id="a_edge743"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/ordered_semiring.to_ordered_cancel_add_comm_monoid" xlink:title="ordered_semiring.to_ordered_cancel_add_comm_monoid">
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<g id="edge745" class="edge">
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<!-- ordered_cancel_add_comm_monoid&#45;&gt;partial_order -->
<g id="edge777" class="edge">
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<g id="a_edge778"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/ordered_cancel_add_comm_monoid.to_add_cancel_comm_monoid" xlink:title="ordered_cancel_add_comm_monoid.to_add_cancel_comm_monoid">
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<g id="a_edge779"><a xlink:href="https://leanprover-community.github.io/mathlib_docs/find/ordered_cancel_add_comm_monoid.to_ordered_add_comm_monoid" xlink:title="ordered_cancel_add_comm_monoid.to_ordered_add_comm_monoid">
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out-small.svg

Some variants at https://github.com/leanprover-community/mathlib/pull/new/eric-wieser/hierarchy-graph