Inductive trees in various proof assistants

example.agda

open import Data.Nat
open import Data.Product

module example where

  data SimpleTree (A : Set) : Set where
    empty : SimpleTree A
    leaf : A -> SimpleTree A
    node : A -> SimpleTree A -> SimpleTree A -> SimpleTree A

  record Edge : Set where
    constructor edge
    field
      fst : ℕ
      snd : ℕ

  test1 = node (edge 5 0) empty (leaf (edge 3 1))

  test2 = node (edge 147 74) (node (edge 110 2) (node (edge 85 13) (node (edge 60 36) (node (edge 43 33) (node (edge 29 20) (node (edge 8 3) (node (edge 4 0) (node (edge 2 1) (node (edge 2 0) (leaf (edge 1 0)) (empty)) (leaf (edge 3 0))) (node (edge 7 0) (node (edge 6 0) (leaf (edge 5 0)) (empty)) (leaf (edge 8 0)))) (node (edge 11 0) (node (edge 10 0) (node (edge 9 7) (leaf (edge 9 0)) (empty)) (leaf (edge 10 6))) (node (edge 12 4) (node (edge 12 0) (leaf (edge 11 5)) (empty)) (leaf (edge 28 18))))) (node (edge 38 28) (node (edge 34 21) (node (edge 32 18) (node (edge 31 19) (leaf (edge 30 19)) (empty)) (leaf (edge 33 22))) (node (edge 37 22) (node (edge 36 20) (leaf (edge 35 21)) (empty)) (leaf (edge 38 18)))) (node (edge 41 18) (node (edge 40 19) (node (edge 39 30) (leaf (edge 39 19)) (empty)) (leaf (edge 40 31))) (node (edge 42 36) (node (edge 42 20) (leaf (edge 41 32)) (empty)) (leaf (edge 43 22)))))) (node (edge 52 41) (node (edge 48 47) (node (edge 46 21) (node (edge 45 20) (node (edge 44 34) (leaf (edge 44 21)) (empty)) (leaf (edge 45 29))) (node (edge 47 37) (node (edge 47 22) (leaf (edge 46 35)) (empty)) (leaf (edge 48 27)))) (node (edge 50 49) (node (edge 50 25) (node (edge 49 46) (leaf (edge 49 25)) (empty)) (leaf (edge 50 44))) (node (edge 51 48) (node (edge 51 43) (leaf (edge 51 27)) (empty)) (leaf (edge 52 26))))) (node (edge 56 54) (node (edge 55 26) (node (edge 54 24) (node (edge 53 42) (leaf (edge 53 23)) (empty)) (leaf (edge 54 39))) (node (edge 56 24) (node (edge 55 52) (leaf (edge 55 38)) (empty)) (leaf (edge 56 40)))) (node (edge 58 28) (node (edge 57 53) (node (edge 57 45) (leaf (edge 57 23)) (empty)) (leaf (edge 58 26))) (node (edge 59 29) (leaf (edge 59 23)) (leaf (edge 60 23))))))) (node (edge 74 34) (node (edge 68 14) (node (edge 64 62) (node (edge 62 31) (node (edge 61 37) (node (edge 61 27) (leaf (edge 60 59)) (empty)) (leaf (edge 62 24))) (node (edge 64 24) (node (edge 63 35) (leaf (edge 63 25)) (empty)) (leaf (edge 64 30)))) (node (edge 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(empty)) (leaf (edge 204 71))) (node (edge 204 127) (leaf (edge 204 109)) (leaf (edge 204 129)))))) (node (edge 206 76) (node (edge 205 126) (node (edge 205 30) (node (edge 205 4) (node (edge 204 166) (leaf (edge 204 139)) (empty)) (leaf (edge 205 15))) (node (edge 205 74) (node (edge 205 68) (leaf (edge 205 37)) (empty)) (leaf (edge 205 112)))) (node (edge 206 7) (node (edge 205 142) (node (edge 205 137) (leaf (edge 205 131)) (empty)) (leaf (edge 205 164))) (node (edge 206 33) (node (edge 206 32) (leaf (edge 206 16)) (empty)) (leaf (edge 206 72))))) (node (edge 207 35) (node (edge 206 140) (node (edge 206 130) (node (edge 206 128) (leaf (edge 206 110)) (empty)) (leaf (edge 206 136))) (node (edge 207 14) (node (edge 207 5) (leaf (edge 206 167)) (empty)) (leaf (edge 207 31)))) (node (edge 207 132) (node (edge 207 111) (node (edge 207 75) (leaf (edge 207 73)) (empty)) (leaf (edge 207 125))) (node (edge 207 141) (leaf (edge 207 133)) (leaf (edge 207 165))))))))))

example.fst

(* This F* version was contributed by Danel Ahman.
   The performance of F* is closed to that of OCaml. *)

module example

type tree (a : Type) =
  | Empty : tree a
  | Leaf  : a -> tree a
  | Node  : a -> tree a -> tree a -> tree a

type edge_t = {
  fst : nat;
  snd : nat
}

let edge (x y : nat) : edge_t = 
  { fst = x; snd = y }

let test1 = Node (edge 5 0) Empty (Leaf (edge 3 1)) 

let test2 = Node (edge 147 74) (Node (edge 110 2) (Node (edge 85 13) (Node (edge 60 36) (Node (edge 43 33) (Node (edge 29 20) (Node (edge 8 3) (Node (edge 4 0) (Node (edge 2 1) (Node (edge 2 0) (Leaf (edge 1 0)) (Empty)) (Leaf (edge 3 0))) (Node (edge 7 0) (Node (edge 6 0) (Leaf (edge 5 0)) (Empty)) (Leaf (edge 8 0)))) (Node (edge 11 0) (Node (edge 10 0) (Node (edge 9 7) (Leaf (edge 9 0)) (Empty)) (Leaf (edge 10 6))) (Node (edge 12 4) (Node (edge 12 0) (Leaf (edge 11 5)) (Empty)) (Leaf (edge 28 18))))) (Node (edge 38 28) (Node (edge 34 21) (Node (edge 32 18) (Node (edge 31 19) (Leaf (edge 30 19)) (Empty)) (Leaf (edge 33 22))) (Node (edge 37 22) (Node (edge 36 20) (Leaf (edge 35 21)) (Empty)) (Leaf (edge 38 18)))) (Node (edge 41 18) (Node (edge 40 19) (Node (edge 39 30) (Leaf (edge 39 19)) (Empty)) (Leaf (edge 40 31))) (Node (edge 42 36) (Node (edge 42 20) (Leaf (edge 41 32)) (Empty)) (Leaf (edge 43 22)))))) (Node (edge 52 41) (Node (edge 48 47) (Node (edge 46 21) (Node (edge 45 20) (Node (edge 44 34) (Leaf (edge 44 21)) (Empty)) (Leaf (edge 45 29))) (Node (edge 47 37) (Node (edge 47 22) (Leaf (edge 46 35)) (Empty)) (Leaf (edge 48 27)))) (Node (edge 50 49) (Node (edge 50 25) (Node (edge 49 46) (Leaf (edge 49 25)) (Empty)) (Leaf (edge 50 44))) (Node (edge 51 48) (Node (edge 51 43) (Leaf (edge 51 27)) (Empty)) (Leaf (edge 52 26))))) (Node (edge 56 54) (Node (edge 55 26) (Node (edge 54 24) (Node (edge 53 42) (Leaf (edge 53 23)) (Empty)) (Leaf (edge 54 39))) (Node (edge 56 24) (Node (edge 55 52) (Leaf (edge 55 38)) (Empty)) (Leaf (edge 56 40)))) (Node (edge 58 28) (Node (edge 57 53) (Node (edge 57 45) (Leaf (edge 57 23)) (Empty)) (Leaf (edge 58 26))) (Node (edge 59 29) (Leaf (edge 59 23)) (Leaf (edge 60 23))))))) (Node (edge 74 34) (Node (edge 68 14) (Node (edge 64 62) (Node (edge 62 31) (Node (edge 61 37) (Node (edge 61 27) (Leaf (edge 60 59)) (Empty)) (Leaf (edge 62 24))) (Node (edge 64 24) (Node (edge 63 35) (Leaf (edge 63 25)) (Empty)) (Leaf (edge 64 30)))) (Node 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158 100) (Leaf (edge 158 82)) (Empty)) (Leaf (edge 158 150))))) (Node (edge 160 46) (Node (edge 159 87) (Node (edge 159 65) (Node (edge 159 54) (Leaf (edge 159 41)) (Empty)) (Leaf (edge 159 75))) (Node (edge 159 149) (Node (edge 159 138) (Leaf (edge 159 99)) (Empty)) (Leaf (edge 160 6)))) (Node (edge 160 100) (Node (edge 160 76) (Node (edge 160 58) (Leaf (edge 160 48)) (Empty)) (Leaf (edge 160 81))) (Node (edge 160 147) (Leaf (edge 160 135)) (Leaf (edge 161 3)))))) (Node (edge 163 49) (Node (edge 162 53) (Node (edge 161 100) (Node (edge 161 74) (Node (edge 161 67) (Leaf (edge 161 56)) (Empty)) (Leaf (edge 161 83))) (Node (edge 162 4) (Node (edge 161 146) (Leaf (edge 161 136)) (Empty)) (Leaf (edge 162 40)))) (Node (edge 162 140) (Node (edge 162 86) (Node (edge 162 70) (Leaf (edge 162 66)) (Empty)) (Leaf (edge 162 99))) (Node (edge 163 19) (Node (edge 163 3) (Leaf (edge 162 143)) (Empty)) (Leaf (edge 163 48))))) (Node (edge 164 75) (Node (edge 163 154) (Node (edge 163 89) (Node (edge 163 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(Empty)) (Leaf (edge 204 71))) (Node (edge 204 127) (Leaf (edge 204 109)) (Leaf (edge 204 129)))))) (Node (edge 206 76) (Node (edge 205 126) (Node (edge 205 30) (Node (edge 205 4) (Node (edge 204 166) (Leaf (edge 204 139)) (Empty)) (Leaf (edge 205 15))) (Node (edge 205 74) (Node (edge 205 68) (Leaf (edge 205 37)) (Empty)) (Leaf (edge 205 112)))) (Node (edge 206 7) (Node (edge 205 142) (Node (edge 205 137) (Leaf (edge 205 131)) (Empty)) (Leaf (edge 205 164))) (Node (edge 206 33) (Node (edge 206 32) (Leaf (edge 206 16)) (Empty)) (Leaf (edge 206 72))))) (Node (edge 207 35) (Node (edge 206 140) (Node (edge 206 130) (Node (edge 206 128) (Leaf (edge 206 110)) (Empty)) (Leaf (edge 206 136))) (Node (edge 207 14) (Node (edge 207 5) (Leaf (edge 206 167)) (Empty)) (Leaf (edge 207 31)))) (Node (edge 207 132) (Node (edge 207 111) (Node (edge 207 75) (Leaf (edge 207 73)) (Empty)) (Leaf (edge 207 125))) (Node (edge 207 141) (Leaf (edge 207 133)) (Leaf (edge 207 165))))))))))

example.lean

structure Edge : Type :=
  edge::
  fst : Nat
  snd : Nat

inductive Tree (α : Type) : Type
  | empty : Tree α
  | leaf : α → Tree α
  | node : α → Tree α → Tree α → Tree α

def test1 : Tree Edge := .node (.edge 5 0) .empty (.leaf (.edge 3 1))

def test2 : Tree Edge := .node (.edge 147 74) (.node (.edge 110 2) (.node (.edge 85 13) (.node (.edge 60 36) (.node (.edge 43 33) (.node (.edge 29 20) (.node (.edge 8 3) (.node (.edge 4 0) (.node (.edge 2 1) (.node (.edge 2 0) (.leaf (.edge 1 0)) (.empty)) (.leaf (.edge 3 0))) (.node (.edge 7 0) (.node (.edge 6 0) (.leaf (.edge 5 0)) (.empty)) (.leaf (.edge 8 0)))) (.node (.edge 11 0) (.node (.edge 10 0) (.node (.edge 9 7) (.leaf (.edge 9 0)) (.empty)) (.leaf (.edge 10 6))) (.node (.edge 12 4) (.node (.edge 12 0) (.leaf (.edge 11 5)) (.empty)) (.leaf (.edge 28 18))))) (.node (.edge 38 28) (.node (.edge 34 21) (.node (.edge 32 18) (.node (.edge 31 19) (.leaf (.edge 30 19)) (.empty)) (.leaf (.edge 33 22))) (.node (.edge 37 22) (.node (.edge 36 20) (.leaf (.edge 35 21)) (.empty)) (.leaf (.edge 38 18)))) (.node (.edge 41 18) (.node (.edge 40 19) (.node (.edge 39 30) (.leaf (.edge 39 19)) (.empty)) (.leaf (.edge 40 31))) (.node (.edge 42 36) (.node (.edge 42 20) (.leaf (.edge 41 32)) (.empty)) (.leaf (.edge 43 22)))))) (.node (.edge 52 41) (.node (.edge 48 47) (.node (.edge 46 21) (.node (.edge 45 20) (.node (.edge 44 34) (.leaf (.edge 44 21)) (.empty)) (.leaf (.edge 45 29))) (.node (.edge 47 37) (.node (.edge 47 22) (.leaf (.edge 46 35)) (.empty)) (.leaf (.edge 48 27)))) (.node (.edge 50 49) (.node (.edge 50 25) (.node (.edge 49 46) (.leaf (.edge 49 25)) (.empty)) (.leaf (.edge 50 44))) (.node (.edge 51 48) (.node (.edge 51 43) (.leaf (.edge 51 27)) (.empty)) (.leaf (.edge 52 26))))) (.node (.edge 56 54) (.node (.edge 55 26) (.node (.edge 54 24) (.node (.edge 53 42) (.leaf (.edge 53 23)) (.empty)) (.leaf (.edge 54 39))) (.node (.edge 56 24) (.node (.edge 55 52) (.leaf (.edge 55 38)) (.empty)) (.leaf (.edge 56 40)))) (.node (.edge 58 28) (.node (.edge 57 53) (.node (.edge 57 45) (.leaf (.edge 57 23)) (.empty)) (.leaf (.edge 58 26))) (.node (.edge 59 29) (.leaf (.edge 59 23)) (.leaf (.edge 60 23))))))) (.node (.edge 74 34) (.node (.edge 68 14) (.node (.edge 64 62) (.node (.edge 62 31) (.node (.edge 61 37) (.node (.edge 61 27) (.leaf (.edge 60 59)) (.empty)) (.leaf (.edge 62 24))) (.node (.edge 64 24) (.node (.edge 63 35) (.leaf (.edge 63 25)) (.empty)) (.leaf (.edge 64 30)))) (.node (.edge 66 32) (.node (.edge 65 63) (.node (.edge 65 34) (.leaf (.edge 65 25)) (.empty)) (.leaf (.edge 66 26))) (.node (.edge 67 33) (.node (.edge 67 27) (.leaf (.edge 66 58)) (.empty)) (.leaf (.edge 67 61))))) (.node (.edge 71 32) (.node (.edge 69 61) (.node (.edge 69 17) (.node (.edge 68 58) (.leaf (.edge 68 28)) (.empty)) (.leaf (.edge 69 37))) (.node (.edge 70 63) (.node (.edge 70 35) (.leaf (.edge 70 16)) (.empty)) (.leaf (.edge 71 14)))) (.node (.edge 73 15) (.node (.edge 72 36) (.node (.edge 72 15) (.leaf (.edge 71 66)) (.empty)) (.leaf (.edge 72 60))) (.node (.edge 73 59) (.leaf (.edge 73 29)) (.leaf (.edge 74 16)))))) (.node (.edge 80 38) (.node (.edge 77 64) (.node (.edge 76 13) (.node (.edge 75 33) (.node (.edge 75 17) (.leaf (.edge 74 65)) (.empty)) (.leaf (.edge 75 67))) (.node (.edge 77 13) (.node (.edge 76 62) (.leaf (.edge 76 31)) (.empty)) (.leaf (.edge 77 30)))) (.node (.edge 79 16) (.node (.edge 78 48) (.node (.edge 78 47) (.leaf (.edge 78 17)) (.empty)) (.leaf (.edge 78 75))) (.node (.edge 79 74) (.node (.edge 79 49) (.leaf (.edge 79 46)) (.empty)) (.leaf (.edge 80 14))))) (.node (.edge 82 70) (.node (.edge 81 57) (.node (.edge 81 15) (.node (.edge 80 71) (.leaf (.edge 80 55)) (.empty)) (.leaf (.edge 81 45))) (.node (.edge 82 44) (.node (.edge 82 16) (.leaf (.edge 81 72)) (.empty)) (.leaf (.edge 82 50)))) (.node (.edge 84 13) (.node (.edge 83 52) (.node (.edge 83 41) (.leaf (.edge 83 14)) (.empty)) (.leaf (.edge 83 68))) (.node (.edge 84 56) (.leaf (.edge 84 40)) (.leaf (.edge 84 77)))))))) (.node (.edge 97 96) (.node (.edge 92 9) (.node (.edge 89 19) (.node (.edge 87 53) (.node (.edge 86 43) (.node (.edge 85 76) (.node (.edge 85 54) (.leaf (.edge 85 39)) (.empty)) (.leaf (.edge 86 17))) (.node (.edge 87 15) (.node (.edge 86 69) (.leaf (.edge 86 51)) (.empty)) (.leaf (.edge 87 42)))) (.node (.edge 88 15) (.node (.edge 88 13) (.node (.edge 88 1) (.leaf (.edge 87 73)) (.empty)) (.leaf (.edge 88 14))) (.node (.edge 89 1) (.node (.edge 88 17) (.leaf (.edge 88 16)) (.empty)) (.leaf (.edge 89 18))))) (.node (.edge 90 59) (.node (.edge 90 8) (.node (.edge 89 22) (.node (.edge 89 21) (.leaf (.edge 89 20)) (.empty)) (.leaf (.edge 89 88))) (.node (.edge 90 44) (.node (.edge 90 43) (.leaf (.edge 90 13)) (.empty)) (.leaf (.edge 90 58)))) (.node (.edge 91 46) (.node (.edge 91 15) (.node (.edge 91 12) (.leaf (.edge 90 88)) (.empty)) (.leaf (.edge 91 41))) (.node (.edge 91 64) (.leaf (.edge 91 61)) (.leaf (.edge 91 88)))))) (.node (.edge 94 88) (.node (.edge 93 47) (.node (.edge 92 67) (.node (.edge 92 45) (.node (.edge 92 39) (.leaf (.edge 92 16)) (.empty)) (.leaf (.edge 92 66))) (.node (.edge 93 14) (.node (.edge 93 11) (.leaf (.edge 92 88)) (.empty)) (.leaf (.edge 93 42)))) (.node (.edge 94 17) (.node (.edge 93 88) (.node (.edge 93 63) (.leaf (.edge 93 62)) (.empty)) (.leaf (.edge 94 10))) (.node (.edge 94 60) (.node (.edge 94 40) (.leaf (.edge 94 38)) (.empty)) (.leaf (.edge 94 65))))) (.node (.edge 96 32) (.node (.edge 95 35) (.node (.edge 95 30) (.node (.edge 95 28) (.leaf (.edge 95 1)) (.empty)) (.leaf (.edge 95 33))) (.node (.edge 96 29) (.node (.edge 96 1) (.leaf (.edge 95 36)) (.empty)) (.leaf (.edge 96 31)))) (.node (.edge 97 51) (.node (.edge 97 1) (.node (.edge 96 37) (.leaf (.edge 96 34)) (.empty)) (.leaf (.edge 97 49))) (.node (.edge 97 54) (.leaf (.edge 97 53)) (.leaf (.edge 97 55))))))) (.node (.edge 103 67) (.node (.edge 101 1) (.node (.edge 99 61) (.node (.edge 98 56) (.node (.edge 98 50) (.node (.edge 98 48) (.leaf (.edge 98 1)) (.empty)) (.leaf (.edge 98 52))) (.node (.edge 99 1) (.node (.edge 98 95) (.leaf (.edge 98 57)) (.empty)) (.leaf (.edge 99 59)))) (.node (.edge 100 58) (.node (.edge 99 66) (.node (.edge 99 65) (.leaf (.edge 99 62)) (.empty)) (.leaf (.edge 100 1))) (.node (.edge 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example.ml

type 'a tree =
  | Empty
  | Leaf of 'a
  | Node of 'a * 'a tree * 'a tree

type edge = int * int

let edge (x, y) = (x, y)

let empty = Empty
let node x l r = Node (x, l, r)
let leaf x = Leaf x


let test1 = node (edge (5,0)) empty (leaf (edge (3,1)))

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(192,43)) (node (edge (192,29)) (leaf (edge (192,24))) (empty)) (leaf (edge (192,83)))) (node (edge (192,153)) (node (edge (192,148)) (leaf (edge (192,113))) (empty)) (leaf (edge (192,183)))))) (node (edge (193,191)) (node (edge (193,68)) (node (edge (193,49)) (node (edge (193,23)) (leaf (edge (193,17))) (empty)) (leaf (edge (193,64)))) (node (edge (193,163)) (node (edge (193,149)) (leaf (edge (193,107))) (empty)) (leaf (edge (193,180))))) (node (edge (194,62)) (node (edge (194,26)) (node (edge (194,16)) (leaf (edge (194,10))) (empty)) (leaf (edge (194,48)))) (node (edge (194,103)) (leaf (edge (194,73))) (leaf (edge (194,146))))))))) (node (edge (201,71)) (node (edge (198,13)) (node (edge (196,106)) (node (edge (195,144)) (node (edge (195,24)) (node (edge (195,9)) (node (edge (194,187)) (leaf (edge (194,177))) (empty)) (leaf (edge (195,14)))) (node (edge (195,69)) (node (edge (195,59)) (leaf (edge (195,50))) (empty)) (leaf (edge (195,105))))) (node (edge (196,15)) (node (edge 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example.v

Inductive simpleTree (A : Set) : Set :=
| empty : simpleTree A
| leaf : A -> simpleTree A
| node : A -> simpleTree A -> simpleTree A -> simpleTree A.

Arguments empty {_}.
Arguments leaf {_} _.
Arguments node {_} _ _ _.

Definition edge (p : nat * nat) := p.

Definition test1 := node (edge (5 , 0)) empty (leaf (edge (3 , 1))).

Definition test5 := node (edge (147 , 74)) (node (edge (110 , 2)) (node (edge (85 , 13)) (node (edge (60 , 36)) (node (edge (43 , 33)) (node (edge (29 , 20)) (node (edge (8 , 3)) (node (edge (4 , 0)) (node (edge (2 , 1)) (node (edge (2 , 0)) (leaf (edge (1 , 0))) (empty)) (leaf (edge (3 , 0)))) (node (edge (7 , 0)) (node (edge (6 , 0)) (leaf (edge (5 , 0))) (empty)) (leaf (edge (8 , 0))))) (node (edge (11 , 0)) (node (edge (10 , 0)) (node (edge (9 , 7)) (leaf (edge (9 , 0))) (empty)) (leaf (edge (10 , 6)))) (node (edge (12 , 4)) (node (edge (12 , 0)) (leaf (edge (11 , 5))) (empty)) (leaf (edge (28 , 18)))))) (node (edge (38 , 28)) (node (edge (34 , 21)) (node (edge (32 , 18)) (node (edge (31 , 19)) (leaf (edge (30 , 19))) (empty)) (leaf (edge (33 , 22)))) (node (edge (37 , 22)) (node (edge (36 , 20)) (leaf (edge (35 , 21))) (empty)) (leaf (edge (38 , 18))))) (node (edge (41 , 18)) (node (edge (40 , 19)) (node (edge (39 , 30)) (leaf (edge (39 , 19))) (empty)) (leaf (edge (40 , 31)))) (node (edge (42 , 36)) (node (edge (42 , 20)) (leaf (edge (41 , 32))) (empty)) (leaf (edge (43 , 22))))))) (node (edge (52 , 41)) (node (edge (48 , 47)) (node (edge (46 , 21)) (node (edge (45 , 20)) (node (edge (44 , 34)) (leaf (edge (44 , 21))) (empty)) (leaf (edge (45 , 29)))) (node (edge (47 , 37)) (node (edge (47 , 22)) (leaf (edge (46 , 35))) (empty)) (leaf (edge (48 , 27))))) (node (edge (50 , 49)) (node (edge (50 , 25)) (node (edge (49 , 46)) (leaf (edge (49 , 25))) (empty)) (leaf (edge (50 , 44)))) (node (edge (51 , 48)) (node (edge (51 , 43)) (leaf (edge (51 , 27))) (empty)) (leaf (edge (52 , 26)))))) (node (edge (56 , 54)) (node (edge (55 , 26)) (node (edge (54 , 24)) (node (edge (53 , 42)) (leaf (edge (53 , 23))) (empty)) (leaf (edge (54 , 39)))) (node (edge (56 , 24)) (node (edge (55 , 52)) (leaf (edge (55 , 38))) (empty)) (leaf (edge (56 , 40))))) (node (edge (58 , 28)) (node (edge (57 , 53)) (node (edge (57 , 45)) (leaf (edge (57 , 23))) (empty)) (leaf (edge (58 , 26)))) (node (edge (59 , 29)) (leaf (edge (59 , 23))) (leaf (edge (60 , 23)))))))) (node (edge (74 , 34)) (node (edge (68 , 14)) (node (edge (64 , 62)) (node (edge (62 , 31)) (node (edge (61 , 37)) (node (edge (61 , 27)) (leaf (edge (60 , 59))) (empty)) (leaf (edge (62 , 24)))) (node (edge (64 , 24)) (node (edge (63 , 35)) (leaf (edge (63 , 25))) (empty)) (leaf (edge (64 , 30))))) (node (edge (66 , 32)) (node (edge (65 , 63)) (node (edge (65 , 34)) (leaf (edge (65 , 25))) (empty)) (leaf (edge (66 , 26)))) (node (edge (67 , 33)) (node (edge (67 , 27)) (leaf (edge (66 , 58))) (empty)) (leaf (edge (67 , 61)))))) (node (edge (71 , 32)) (node (edge (69 , 61)) (node (edge (69 , 17)) (node (edge (68 , 58)) (leaf (edge (68 , 28))) (empty)) (leaf (edge (69 , 37)))) (node (edge (70 , 63)) (node (edge (70 , 35)) (leaf (edge (70 , 16))) (empty)) (leaf (edge (71 , 14))))) (node (edge (73 , 15)) (node (edge (72 , 36)) (node (edge (72 , 15)) (leaf (edge (71 , 66))) (empty)) (leaf (edge (72 , 60)))) (node (edge (73 , 59)) (leaf (edge (73 , 29))) (leaf (edge (74 , 16))))))) (node (edge (80 , 38)) (node (edge (77 , 64)) (node (edge (76 , 13)) (node (edge (75 , 33)) (node (edge (75 , 17)) (leaf (edge (74 , 65))) (empty)) (leaf (edge (75 , 67)))) (node (edge (77 , 13)) (node (edge (76 , 62)) (leaf (edge (76 , 31))) (empty)) (leaf (edge (77 , 30))))) (node (edge (79 , 16)) (node (edge (78 , 48)) (node (edge (78 , 47)) (leaf (edge (78 , 17))) (empty)) (leaf (edge (78 , 75)))) (node (edge (79 , 74)) (node (edge (79 , 49)) (leaf (edge (79 , 46))) (empty)) (leaf (edge (80 , 14)))))) (node (edge (82 , 70)) (node (edge (81 , 57)) (node (edge (81 , 15)) (node (edge (80 , 71)) (leaf (edge (80 , 55))) (empty)) (leaf (edge (81 , 45)))) (node (edge (82 , 44)) (node (edge (82 , 16)) (leaf (edge (81 , 72))) (empty)) (leaf (edge (82 , 50))))) (node (edge (84 , 13)) (node (edge (83 , 52)) (node (edge (83 , 41)) (leaf (edge (83 , 14))) (empty)) (leaf (edge (83 , 68)))) (node (edge (84 , 56)) (leaf (edge (84 , 40))) (leaf (edge (84 , 77))))))))) (node (edge (97 , 96)) (node (edge (92 , 9)) (node (edge (89 , 19)) (node (edge (87 , 53)) (node (edge (86 , 43)) (node (edge (85 , 76)) (node (edge (85 , 54)) (leaf (edge (85 , 39))) (empty)) (leaf (edge (86 , 17)))) (node (edge (87 , 15)) (node (edge (86 , 69)) (leaf (edge (86 , 51))) (empty)) (leaf (edge (87 , 42))))) (node (edge (88 , 15)) (node (edge (88 , 13)) (node (edge (88 , 1)) (leaf (edge (87 , 73))) (empty)) (leaf (edge (88 , 14)))) (node (edge (89 , 1)) (node (edge (88 , 17)) (leaf (edge (88 , 16))) (empty)) (leaf (edge (89 , 18)))))) (node (edge (90 , 59)) (node (edge (90 , 8)) (node (edge (89 , 22)) (node (edge (89 , 21)) (leaf (edge (89 , 20))) (empty)) (leaf (edge (89 , 88)))) (node (edge (90 , 44)) (node (edge (90 , 43)) (leaf (edge (90 , 13))) (empty)) (leaf (edge (90 , 58))))) (node (edge (91 , 46)) (node (edge (91 , 15)) (node (edge (91 , 12)) (leaf (edge (90 , 88))) (empty)) (leaf (edge (91 , 41)))) (node (edge (91 , 64)) (leaf (edge (91 , 61))) (leaf (edge (91 , 88))))))) (node (edge (94 , 88)) (node (edge (93 , 47)) (node (edge (92 , 67)) (node (edge (92 , 45)) (node (edge (92 , 39)) (leaf (edge (92 , 16))) (empty)) (leaf (edge (92 , 66)))) (node (edge (93 , 14)) (node (edge (93 , 11)) (leaf (edge (92 , 88))) (empty)) (leaf (edge (93 , 42))))) (node (edge (94 , 17)) (node (edge (93 , 88)) (node (edge (93 , 63)) (leaf (edge (93 , 62))) (empty)) (leaf (edge (94 , 10)))) (node (edge (94 , 60)) (node (edge (94 , 40)) (leaf (edge (94 , 38))) (empty)) (leaf (edge (94 , 65)))))) (node (edge (96 , 32)) (node (edge (95 , 35)) (node (edge (95 , 30)) (node (edge (95 , 28)) (leaf (edge (95 , 1))) (empty)) (leaf (edge (95 , 33)))) (node (edge (96 , 29)) (node (edge (96 , 1)) (leaf (edge (95 , 36))) (empty)) (leaf (edge (96 , 31))))) (node (edge (97 , 51)) (node (edge (97 , 1)) (node (edge (96 , 37)) (leaf (edge (96 , 34))) (empty)) (leaf (edge (97 , 49)))) (node (edge (97 , 54)) (leaf (edge (97 , 53))) (leaf (edge 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exampleDependent.agda

open import Data.Nat
open import Data.Bool hiding (_<_)
open import Relation.Binary.PropositionalEquality
open import Data.Product

module exampleDependent where

  data Tree (A : Set) : Set where
    empty : Tree A
    leaf : A -> Tree A
    node : A -> Tree A -> Tree A -> Tree A

  record Fin (n : ℕ) : Set where
    constructor fin
    field
      val : ℕ
      lt : (val <ᵇ n) ≡ true

  record Edge (n : ℕ) : Set where
    constructor edge
    field
      fst : Fin n
      snd : Fin (Fin.val fst)

  test1 : Tree (Edge 30)
  test1 = node (edge (fin 5 refl) (fin 0 refl)) empty (leaf (edge (fin 3 refl) (fin 1 refl)))

  test2 : Tree (Edge 666)
  test2 = node (edge (fin 147 refl) (fin 74 refl)) (node (edge (fin 110 refl) (fin 2 refl)) (node (edge (fin 85 refl) (fin 13 refl)) (node (edge (fin 60 refl) (fin 36 refl)) (node (edge (fin 43 refl) (fin 33 refl)) (node (edge (fin 29 refl) (fin 20 refl)) (node (edge (fin 8 refl) (fin 3 refl)) (node (edge (fin 4 refl) (fin 0 refl)) (node (edge (fin 2 refl) (fin 1 refl)) (node (edge (fin 2 refl) (fin 0 refl)) (leaf (edge (fin 1 refl) (fin 0 refl))) (empty)) (leaf (edge (fin 3 refl) (fin 0 refl)))) (node (edge (fin 7 refl) (fin 0 refl)) (node (edge (fin 6 refl) (fin 0 refl)) (leaf (edge (fin 5 refl) (fin 0 refl))) (empty)) (leaf (edge (fin 8 refl) (fin 0 refl))))) (node (edge (fin 11 refl) (fin 0 refl)) (node (edge (fin 10 refl) (fin 0 refl)) (node (edge (fin 9 refl) (fin 7 refl)) (leaf (edge (fin 9 refl) (fin 0 refl))) (empty)) (leaf (edge (fin 10 refl) (fin 6 refl)))) (node (edge (fin 12 refl) (fin 4 refl)) (node (edge (fin 12 refl) (fin 0 refl)) (leaf (edge (fin 11 refl) (fin 5 refl))) (empty)) (leaf (edge (fin 28 refl) (fin 18 refl)))))) (node (edge (fin 38 refl) (fin 28 refl)) (node (edge (fin 34 refl) (fin 21 refl)) (node (edge (fin 32 refl) (fin 18 refl)) (node (edge (fin 31 refl) (fin 19 refl)) (leaf (edge (fin 30 refl) (fin 19 refl))) (empty)) (leaf (edge (fin 33 refl) (fin 22 refl)))) (node (edge (fin 37 refl) (fin 22 refl)) (node (edge (fin 36 refl) (fin 20 refl)) (leaf (edge (fin 35 refl) (fin 21 refl))) (empty)) (leaf (edge (fin 38 refl) (fin 18 refl))))) (node (edge (fin 41 refl) (fin 18 refl)) (node (edge (fin 40 refl) (fin 19 refl)) (node (edge (fin 39 refl) (fin 30 refl)) (leaf (edge (fin 39 refl) (fin 19 refl))) (empty)) (leaf (edge (fin 40 refl) (fin 31 refl)))) (node (edge (fin 42 refl) (fin 36 refl)) (node (edge (fin 42 refl) (fin 20 refl)) (leaf (edge (fin 41 refl) (fin 32 refl))) (empty)) (leaf (edge (fin 43 refl) (fin 22 refl))))))) (node (edge (fin 52 refl) (fin 41 refl)) (node (edge (fin 48 refl) (fin 47 refl)) (node (edge (fin 46 refl) (fin 21 refl)) (node (edge (fin 45 refl) (fin 20 refl)) (node (edge (fin 44 refl) (fin 34 refl)) (leaf (edge (fin 44 refl) (fin 21 refl))) (empty)) (leaf (edge (fin 45 refl) (fin 29 refl)))) (node (edge (fin 47 refl) (fin 37 refl)) (node (edge (fin 47 refl) (fin 22 refl)) (leaf (edge (fin 46 refl) (fin 35 refl))) (empty)) (leaf (edge (fin 48 refl) (fin 27 refl))))) (node (edge (fin 50 refl) (fin 49 refl)) (node (edge (fin 50 refl) (fin 25 refl)) (node (edge (fin 49 refl) (fin 46 refl)) (leaf (edge (fin 49 refl) (fin 25 refl))) (empty)) (leaf (edge (fin 50 refl) (fin 44 refl)))) (node (edge (fin 51 refl) (fin 48 refl)) (node (edge (fin 51 refl) (fin 43 refl)) (leaf (edge (fin 51 refl) (fin 27 refl))) (empty)) (leaf (edge (fin 52 refl) (fin 26 refl)))))) (node (edge (fin 56 refl) (fin 54 refl)) (node (edge (fin 55 refl) (fin 26 refl)) (node (edge (fin 54 refl) (fin 24 refl)) (node (edge (fin 53 refl) (fin 42 refl)) (leaf (edge (fin 53 refl) (fin 23 refl))) (empty)) (leaf (edge (fin 54 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(fin 65 refl)))))))) (node (edge (fin 204 refl) (fin 138 refl)) (node (edge (fin 203 refl) (fin 28 refl)) (node (edge (fin 202 refl) (fin 60 refl)) (node (edge (fin 201 refl) (fin 190 refl)) (node (edge (fin 201 refl) (fin 167 refl)) (node (edge (fin 201 refl) (fin 152 refl)) (leaf (edge (fin 201 refl) (fin 107 refl))) (empty)) (leaf (edge (fin 201 refl) (fin 173 refl)))) (node (edge (fin 202 refl) (fin 27 refl)) (node (edge (fin 202 refl) (fin 16 refl)) (leaf (edge (fin 202 refl) (fin 11 refl))) (empty)) (leaf (edge (fin 202 refl) (fin 55 refl))))) (node (edge (fin 202 refl) (fin 182 refl)) (node (edge (fin 202 refl) (fin 143 refl)) (node (edge (fin 202 refl) (fin 104 refl)) (leaf (edge (fin 202 refl) (fin 77 refl))) (empty)) (leaf (edge (fin 202 refl) (fin 164 refl)))) (node (edge (fin 203 refl) (fin 3 refl)) (node (edge (fin 202 refl) (fin 201 refl)) (leaf (edge (fin 202 refl) (fin 192 refl))) (empty)) (leaf (edge (fin 203 refl) (fin 13 refl)))))) (node (edge (fin 204 refl) (fin 6 refl)) (node (edge (fin 203 refl) (fin 123 refl)) (node (edge (fin 203 refl) (fin 70 refl)) (node (edge (fin 203 refl) (fin 69 refl)) (leaf (edge (fin 203 refl) (fin 29 refl))) (empty)) (leaf (edge (fin 203 refl) (fin 108 refl)))) (node (edge (fin 203 refl) (fin 135 refl)) (node (edge (fin 203 refl) (fin 134 refl)) (leaf (edge (fin 203 refl) (fin 124 refl))) (empty)) (leaf (edge (fin 203 refl) (fin 163 refl))))) (node (edge (fin 204 refl) (fin 77 refl)) (node (edge (fin 204 refl) (fin 36 refl)) (node (edge (fin 204 refl) (fin 34 refl)) (leaf (edge (fin 204 refl) (fin 17 refl))) (empty)) (leaf (edge (fin 204 refl) (fin 71 refl)))) (node (edge (fin 204 refl) (fin 127 refl)) (leaf (edge (fin 204 refl) (fin 109 refl))) (leaf (edge (fin 204 refl) (fin 129 refl))))))) (node (edge (fin 206 refl) (fin 76 refl)) (node (edge (fin 205 refl) (fin 126 refl)) (node (edge (fin 205 refl) (fin 30 refl)) (node (edge (fin 205 refl) (fin 4 refl)) (node (edge (fin 204 refl) (fin 166 refl)) (leaf (edge (fin 204 refl) (fin 139 refl))) (empty)) (leaf (edge (fin 205 refl) (fin 15 refl)))) (node (edge (fin 205 refl) (fin 74 refl)) (node (edge (fin 205 refl) (fin 68 refl)) (leaf (edge (fin 205 refl) (fin 37 refl))) (empty)) (leaf (edge (fin 205 refl) (fin 112 refl))))) (node (edge (fin 206 refl) (fin 7 refl)) (node (edge (fin 205 refl) (fin 142 refl)) (node (edge (fin 205 refl) (fin 137 refl)) (leaf (edge (fin 205 refl) (fin 131 refl))) (empty)) (leaf (edge (fin 205 refl) (fin 164 refl)))) (node (edge (fin 206 refl) (fin 33 refl)) (node (edge (fin 206 refl) (fin 32 refl)) (leaf (edge (fin 206 refl) (fin 16 refl))) (empty)) (leaf (edge (fin 206 refl) (fin 72 refl)))))) (node (edge (fin 207 refl) (fin 35 refl)) (node (edge (fin 206 refl) (fin 140 refl)) (node (edge (fin 206 refl) (fin 130 refl)) (node (edge (fin 206 refl) (fin 128 refl)) (leaf (edge (fin 206 refl) (fin 110 refl))) (empty)) (leaf (edge (fin 206 refl) (fin 136 refl)))) (node (edge (fin 207 refl) (fin 14 refl)) (node (edge (fin 207 refl) (fin 5 refl)) (leaf (edge (fin 206 refl) (fin 167 refl))) (empty)) (leaf (edge (fin 207 refl) (fin 31 refl))))) (node (edge (fin 207 refl) (fin 132 refl)) (node (edge (fin 207 refl) (fin 111 refl)) (node (edge (fin 207 refl) (fin 75 refl)) (leaf (edge (fin 207 refl) (fin 73 refl))) (empty)) (leaf (edge (fin 207 refl) (fin 125 refl)))) (node (edge (fin 207 refl) (fin 141 refl)) (leaf (edge (fin 207 refl) (fin 133 refl))) (leaf (edge (fin 207 refl) (fin 165 refl)))))))))))

exampleDependent.v

Require Import Coq.Init.Nat.

Inductive Tree (A : Set) : Set :=
| empty : Tree A
| leaf : A -> Tree A
| node : A -> Tree A -> Tree A -> Tree A.

Arguments empty {_}.
Arguments leaf {_} _.
Arguments node {_} _ _ _.

Structure Fin (n : nat) : Type := fin {
  val : nat ;
  lt : true = (val <? n)%nat
}.

Arguments val {_} _.

Structure Edge (n : nat) : Type := edge {
  fst : Fin n ;
  snd : Fin (val fst)
}.

Arguments edge {_} _ _.

Notation "'F[' i ',' j ']'" := (fin i j eq_refl) (at level 5).

Definition test1 := node (edge F[10,5] (fin 5 2 eq_refl)) empty (leaf (edge (fin 10 3 eq_refl) (fin 3 1 eq_refl))).

Definition test5 := node (edge F[666,147] F[147,74]) (node (edge F[666,110] F[110,2]) (node (edge F[666,85] F[85,13]) (node (edge F[666,60] F[60,36]) (node (edge F[666,43] F[43,33]) (node (edge F[666,29] F[29,20]) (node (edge F[666,8] F[8,3]) (node (edge F[666,4] F[4,0]) (node (edge F[666,2] F[2,1]) (node (edge F[666,2] F[2,0]) (leaf (edge F[666,1] F[1,0])) (empty)) (leaf (edge F[666,3] F[3,0]))) (node (edge F[666,7] F[7,0]) (node (edge F[666,6] F[6,0]) (leaf (edge F[666,5] F[5,0])) (empty)) (leaf (edge F[666,8] F[8,0])))) (node (edge F[666,11] F[11,0]) (node (edge F[666,10] F[10,0]) (node (edge F[666,9] F[9,7]) (leaf (edge F[666,9] F[9,0])) (empty)) (leaf (edge F[666,10] F[10,6]))) (node (edge F[666,12] F[12,4]) (node (edge F[666,12] F[12,0]) (leaf (edge F[666,11] F[11,5])) (empty)) (leaf (edge F[666,28] F[28,18]))))) (node (edge F[666,38] F[38,28]) (node (edge F[666,34] F[34,21]) (node (edge F[666,32] F[32,18]) (node (edge F[666,31] F[31,19]) (leaf (edge F[666,30] F[30,19])) (empty)) (leaf (edge F[666,33] F[33,22]))) (node (edge F[666,37] F[37,22]) (node (edge F[666,36] F[36,20]) (leaf (edge F[666,35] F[35,21])) (empty)) (leaf (edge F[666,38] F[38,18])))) (node (edge F[666,41] F[41,18]) (node (edge F[666,40] F[40,19]) (node (edge F[666,39] F[39,30]) (leaf (edge F[666,39] F[39,19])) (empty)) (leaf (edge F[666,40] F[40,31]))) (node (edge F[666,42] F[42,36]) (node (edge F[666,42] F[42,20]) (leaf (edge F[666,41] F[41,32])) (empty)) (leaf (edge F[666,43] F[43,22])))))) (node (edge F[666,52] F[52,41]) (node (edge F[666,48] F[48,47]) (node (edge F[666,46] F[46,21]) (node (edge F[666,45] F[45,20]) (node (edge F[666,44] F[44,34]) (leaf (edge F[666,44] F[44,21])) (empty)) (leaf (edge F[666,45] F[45,29]))) (node (edge F[666,47] F[47,37]) (node (edge F[666,47] F[47,22]) (leaf (edge F[666,46] F[46,35])) (empty)) (leaf (edge F[666,48] F[48,27])))) (node (edge F[666,50] F[50,49]) (node (edge F[666,50] F[50,25]) (node (edge F[666,49] F[49,46]) (leaf (edge F[666,49] F[49,25])) (empty)) (leaf (edge F[666,50] F[50,44]))) (node (edge F[666,51] F[51,48]) (node (edge F[666,51] F[51,43]) (leaf (edge F[666,51] F[51,27])) (empty)) (leaf (edge F[666,52] F[52,26]))))) (node (edge F[666,56] F[56,54]) (node (edge F[666,55] F[55,26]) (node (edge F[666,54] F[54,24]) (node (edge F[666,53] F[53,42]) (leaf (edge F[666,53] F[53,23])) (empty)) (leaf (edge F[666,54] F[54,39]))) (node (edge F[666,56] F[56,24]) (node (edge F[666,55] F[55,52]) (leaf (edge F[666,55] F[55,38])) (empty)) (leaf (edge F[666,56] F[56,40])))) (node (edge F[666,58] F[58,28]) (node (edge F[666,57] F[57,53]) (node (edge F[666,57] F[57,45]) (leaf (edge F[666,57] F[57,23])) (empty)) (leaf (edge F[666,58] F[58,26]))) (node (edge F[666,59] F[59,29]) (leaf (edge F[666,59] F[59,23])) (leaf (edge F[666,60] F[60,23]))))))) (node (edge F[666,74] F[74,34]) (node (edge F[666,68] F[68,14]) (node (edge F[666,64] F[64,62]) (node (edge F[666,62] F[62,31]) (node (edge F[666,61] F[61,37]) (node (edge F[666,61] F[61,27]) (leaf (edge F[666,60] F[60,59])) (empty)) (leaf (edge F[666,62] F[62,24]))) (node (edge F[666,64] F[64,24]) (node (edge F[666,63] F[63,35]) (leaf (edge F[666,63] F[63,25])) (empty)) (leaf (edge F[666,64] F[64,30])))) (node (edge F[666,66] F[66,32]) (node (edge F[666,65] F[65,63]) (node (edge F[666,65] F[65,34]) (leaf (edge F[666,65] F[65,25])) (empty)) (leaf (edge F[666,66] F[66,26]))) (node (edge F[666,67] F[67,33]) (node (edge F[666,67] F[67,27]) (leaf (edge F[666,66] F[66,58])) (empty)) (leaf (edge F[666,67] F[67,61]))))) (node (edge F[666,71] F[71,32]) (node (edge F[666,69] F[69,61]) (node (edge F[666,69] F[69,17]) (node (edge F[666,68] F[68,58]) (leaf (edge F[666,68] F[68,28])) (empty)) (leaf (edge F[666,69] F[69,37]))) (node (edge F[666,70] F[70,63]) (node (edge F[666,70] F[70,35]) (leaf (edge F[666,70] F[70,16])) (empty)) (leaf (edge F[666,71] F[71,14])))) (node (edge F[666,73] F[73,15]) (node (edge F[666,72] F[72,36]) (node (edge F[666,72] F[72,15]) (leaf (edge F[666,71] F[71,66])) (empty)) (leaf (edge F[666,72] F[72,60]))) (node (edge F[666,73] F[73,59]) (leaf (edge F[666,73] F[73,29])) (leaf (edge F[666,74] F[74,16])))))) (node (edge F[666,80] F[80,38]) (node (edge F[666,77] F[77,64]) (node (edge F[666,76] F[76,13]) (node (edge F[666,75] F[75,33]) (node (edge F[666,75] F[75,17]) (leaf (edge F[666,74] F[74,65])) (empty)) (leaf (edge F[666,75] F[75,67]))) (node (edge F[666,77] F[77,13]) (node (edge F[666,76] F[76,62]) (leaf (edge F[666,76] F[76,31])) (empty)) (leaf (edge F[666,77] F[77,30])))) (node (edge F[666,79] F[79,16]) (node (edge F[666,78] F[78,48]) (node (edge F[666,78] F[78,47]) (leaf (edge F[666,78] F[78,17])) (empty)) (leaf (edge F[666,78] F[78,75]))) (node (edge F[666,79] F[79,74]) (node (edge F[666,79] F[79,49]) (leaf (edge F[666,79] F[79,46])) (empty)) (leaf (edge F[666,80] F[80,14]))))) (node (edge F[666,82] F[82,70]) (node (edge F[666,81] F[81,57]) (node (edge F[666,81] F[81,15]) (node (edge F[666,80] F[80,71]) (leaf (edge F[666,80] F[80,55])) (empty)) (leaf (edge F[666,81] F[81,45]))) (node (edge F[666,82] F[82,44]) (node (edge F[666,82] F[82,16]) (leaf (edge F[666,81] F[81,72])) (empty)) (leaf (edge F[666,82] F[82,50])))) (node (edge F[666,84] F[84,13]) (node (edge F[666,83] F[83,52]) (node (edge F[666,83] F[83,41]) (leaf (edge F[666,83] F[83,14])) (empty)) (leaf (edge F[666,83] F[83,68]))) (node (edge F[666,84] F[84,56]) (leaf (edge F[666,84] F[84,40])) (leaf (edge F[666,84] F[84,77])))))))) (node (edge F[666,97] F[97,96]) (node (edge F[666,92] F[92,9]) (node (edge F[666,89] F[89,19]) (node (edge F[666,87] F[87,53]) (node (edge F[666,86] F[86,43]) (node (edge F[666,85] F[85,76]) (node (edge F[666,85] F[85,54]) (leaf (edge F[666,85] F[85,39])) (empty)) (leaf (edge F[666,86] F[86,17]))) (node (edge F[666,87] F[87,15]) (node (edge F[666,86] F[86,69]) (leaf (edge F[666,86] F[86,51])) (empty)) (leaf (edge F[666,87] F[87,42])))) (node (edge F[666,88] F[88,15]) (node (edge F[666,88] F[88,13]) (node (edge F[666,88] F[88,1]) (leaf (edge F[666,87] F[87,73])) (empty)) (leaf (edge F[666,88] F[88,14]))) (node (edge F[666,89] F[89,1]) (node (edge F[666,88] F[88,17]) (leaf (edge F[666,88] F[88,16])) (empty)) (leaf (edge F[666,89] F[89,18]))))) (node (edge F[666,90] F[90,59]) (node (edge F[666,90] F[90,8]) (node (edge F[666,89] F[89,22]) (node (edge F[666,89] F[89,21]) (leaf (edge F[666,89] F[89,20])) (empty)) (leaf (edge F[666,89] F[89,88]))) (node (edge F[666,90] F[90,44]) (node (edge F[666,90] F[90,43]) (leaf (edge F[666,90] F[90,13])) (empty)) (leaf (edge F[666,90] F[90,58])))) (node (edge F[666,91] F[91,46]) (node (edge F[666,91] F[91,15]) (node (edge F[666,91] F[91,12]) (leaf (edge F[666,90] F[90,88])) (empty)) (leaf (edge F[666,91] F[91,41]))) (node (edge F[666,91] F[91,64]) (leaf (edge F[666,91] F[91,61])) (leaf (edge F[666,91] F[91,88])))))) (node (edge F[666,94] F[94,88]) (node (edge F[666,93] F[93,47]) (node (edge F[666,92] F[92,67]) (node (edge F[666,92] F[92,45]) (node (edge F[666,92] F[92,39]) (leaf (edge F[666,92] F[92,16])) (empty)) (leaf (edge F[666,92] F[92,66]))) (node (edge F[666,93] F[93,14]) (node (edge F[666,93] F[93,11]) (leaf (edge F[666,92] F[92,88])) (empty)) (leaf (edge F[666,93] F[93,42])))) (node (edge F[666,94] F[94,17]) (node (edge F[666,93] F[93,88]) (node (edge F[666,93] F[93,63]) (leaf (edge F[666,93] F[93,62])) (empty)) (leaf (edge F[666,94] F[94,10]))) (node (edge F[666,94] F[94,60]) (node (edge F[666,94] F[94,40]) (leaf (edge F[666,94] F[94,38])) (empty)) (leaf (edge F[666,94] F[94,65]))))) (node (edge F[666,96] F[96,32]) (node (edge F[666,95] F[95,35]) (node (edge F[666,95] F[95,30]) (node (edge F[666,95] F[95,28]) (leaf (edge F[666,95] F[95,1])) (empty)) (leaf (edge F[666,95] F[95,33]))) (node (edge F[666,96] F[96,29]) (node (edge F[666,96] F[96,1]) (leaf (edge F[666,95] F[95,36])) (empty)) (leaf (edge F[666,96] F[96,31])))) (node (edge F[666,97] F[97,51]) (node (edge F[666,97] F[97,1]) (node (edge F[666,96] F[96,37]) (leaf (edge F[666,96] F[96,34])) (empty)) (leaf (edge F[666,97] F[97,49]))) (node (edge F[666,97] F[97,54]) (leaf (edge F[666,97] F[97,53])) (leaf (edge F[666,97] F[97,55]))))))) (node (edge F[666,103] F[103,67]) (node (edge F[666,101] F[101,1]) (node (edge F[666,99] F[99,61]) (node (edge F[666,98] F[98,56]) (node (edge F[666,98] F[98,50]) (node (edge F[666,98] F[98,48]) (leaf (edge F[666,98] F[98,1])) (empty)) (leaf (edge F[666,98] F[98,52]))) (node (edge F[666,99] F[99,1]) (node (edge F[666,98] F[98,95]) (leaf (edge F[666,98] F[98,57])) (empty)) (leaf (edge F[666,99] F[99,59])))) (node (edge F[666,100] F[100,58]) (node (edge F[666,99] F[99,66]) (node (edge F[666,99] F[99,65]) (leaf (edge F[666,99] F[99,62])) (empty)) (leaf (edge F[666,100] F[100,1]))) (node (edge F[666,100] F[100,64]) (node (edge F[666,100] F[100,63]) (leaf (edge F[666,100] F[100,60])) (empty)) (leaf (edge F[666,100] F[100,67]))))) (node (edge F[666,102] F[102,85]) (node (edge F[666,101] F[101,84]) (node (edge F[666,101] F[101,82]) (node (edge F[666,101] F[101,81]) (leaf (edge F[666,101] F[101,78])) (empty)) (leaf (edge F[666,101] F[101,83]))) (node (edge F[666,102] F[102,79]) (node (edge F[666,102] F[102,1]) (leaf (edge F[666,101] F[101,99])) (empty)) (leaf (edge F[666,102] F[102,80])))) (node (edge F[666,103] F[103,20]) (node (edge F[666,102] F[102,100]) (node (edge F[666,102] F[102,87]) (leaf (edge F[666,102] F[102,86])) (empty)) (leaf (edge F[666,103] F[103,2]))) (node (edge F[666,103] F[103,34]) (leaf (edge F[666,103] F[103,28])) (leaf (edge F[666,103] F[103,62])))))) (node (edge F[666,107] F[107,18]) (node (edge F[666,105] F[105,32]) (node (edge F[666,104] F[104,60]) (node (edge F[666,104] F[104,35]) (node (edge F[666,104] F[104,19]) (leaf (edge F[666,104] F[104,2])) (empty)) (leaf (edge F[666,104] F[104,37]))) (node (edge F[666,105] F[105,22]) (node (edge F[666,105] F[105,2]) (leaf (edge F[666,104] F[104,66])) (empty)) (leaf (edge F[666,105] F[105,30])))) (node (edge F[666,106] F[106,31]) (node (edge F[666,106] 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F[666,200] F[200,25]))) (node (edge F[666,200] F[200,103]) (node (edge F[666,200] F[200,72]) (leaf (edge F[666,200] F[200,67])) (empty)) (leaf (edge F[666,200] F[200,151])))) (node (edge F[666,201] F[201,15]) (node (edge F[666,200] F[200,199]) (node (edge F[666,200] F[200,189]) (leaf (edge F[666,200] F[200,181])) (empty)) (leaf (edge F[666,201] F[201,8]))) (node (edge F[666,201] F[201,56]) (leaf (edge F[666,201] F[201,27])) (leaf (edge F[666,201] F[201,65]))))))) (node (edge F[666,204] F[204,138]) (node (edge F[666,203] F[203,28]) (node (edge F[666,202] F[202,60]) (node (edge F[666,201] F[201,190]) (node (edge F[666,201] F[201,167]) (node (edge F[666,201] F[201,152]) (leaf (edge F[666,201] F[201,107])) (empty)) (leaf (edge F[666,201] F[201,173]))) (node (edge F[666,202] F[202,27]) (node (edge F[666,202] F[202,16]) (leaf (edge F[666,202] F[202,11])) (empty)) (leaf (edge F[666,202] F[202,55])))) (node (edge F[666,202] F[202,182]) (node (edge F[666,202] F[202,143]) (node (edge F[666,202] F[202,104]) (leaf (edge F[666,202] F[202,77])) (empty)) (leaf (edge F[666,202] F[202,164]))) (node (edge F[666,203] F[203,3]) (node (edge F[666,202] F[202,201]) (leaf (edge F[666,202] F[202,192])) (empty)) (leaf (edge F[666,203] F[203,13]))))) (node (edge F[666,204] F[204,6]) (node (edge F[666,203] F[203,123]) (node (edge F[666,203] F[203,70]) (node (edge F[666,203] F[203,69]) (leaf (edge F[666,203] F[203,29])) (empty)) (leaf (edge F[666,203] F[203,108]))) (node (edge F[666,203] F[203,135]) (node (edge F[666,203] F[203,134]) (leaf (edge F[666,203] F[203,124])) (empty)) (leaf (edge F[666,203] F[203,163])))) (node (edge F[666,204] F[204,77]) (node (edge F[666,204] F[204,36]) (node (edge F[666,204] F[204,34]) (leaf (edge F[666,204] F[204,17])) (empty)) (leaf (edge F[666,204] F[204,71]))) (node (edge F[666,204] F[204,127]) (leaf (edge F[666,204] F[204,109])) (leaf (edge F[666,204] F[204,129])))))) (node (edge F[666,206] F[206,76]) (node (edge F[666,205] F[205,126]) (node (edge F[666,205] F[205,30]) (node (edge F[666,205] F[205,4]) (node (edge F[666,204] F[204,166]) (leaf (edge F[666,204] F[204,139])) (empty)) (leaf (edge F[666,205] F[205,15]))) (node (edge F[666,205] F[205,74]) (node (edge F[666,205] F[205,68]) (leaf (edge F[666,205] F[205,37])) (empty)) (leaf (edge F[666,205] F[205,112])))) (node (edge F[666,206] F[206,7]) (node (edge F[666,205] F[205,142]) (node (edge F[666,205] F[205,137]) (leaf (edge F[666,205] F[205,131])) (empty)) (leaf (edge F[666,205] F[205,164]))) (node (edge F[666,206] F[206,33]) (node (edge F[666,206] F[206,32]) (leaf (edge F[666,206] F[206,16])) (empty)) (leaf (edge F[666,206] F[206,72]))))) (node (edge F[666,207] F[207,35]) (node (edge F[666,206] F[206,140]) (node (edge F[666,206] F[206,130]) (node (edge F[666,206] F[206,128]) (leaf (edge F[666,206] F[206,110])) (empty)) (leaf (edge F[666,206] F[206,136]))) (node (edge F[666,207] F[207,14]) (node (edge F[666,207] F[207,5]) (leaf (edge F[666,206] F[206,167])) (empty)) (leaf (edge F[666,207] F[207,31])))) (node (edge F[666,207] F[207,132]) (node (edge F[666,207] F[207,111]) (node (edge F[666,207] F[207,75]) (leaf (edge F[666,207] F[207,73])) (empty)) (leaf (edge F[666,207] F[207,125]))) (node (edge F[666,207] F[207,141]) (leaf (edge F[666,207] F[207,133])) (leaf (edge F[666,207] F[207,165])))))))))).

exampleDependentNoTactic.lean

structure Fine (n : Nat) : Type :=
  fine::
  val : Nat
  lt : ↑ (val < n) = true

structure Edge (n : Nat) : Type :=
  edge::
  fst : Fine n
  snd : Fine fst.val

inductive Tree (α : Type) : Type
  | empty : Tree α
  | leaf : α → Tree α
  | node : α → Tree α → Tree α → Tree α

def test1 : Tree (Edge 100) := .node (.edge (.fine 5 rfl) (.fine 2 rfl)) .empty (.leaf (.edge (.fine 3 rfl) (.fine 1 rfl)))

def test2 : Tree (Edge 666) := .node (.edge (.fine 147 rfl) (.fine 74 rfl)) (.node (.edge (.fine 110 rfl) (.fine 2 rfl)) (.node (.edge (.fine 85 rfl) (.fine 13 rfl)) (.node (.edge (.fine 60 rfl) (.fine 36 rfl)) (.node (.edge (.fine 43 rfl) (.fine 33 rfl)) (.node (.edge (.fine 29 rfl) (.fine 20 rfl)) (.node (.edge (.fine 8 rfl) (.fine 3 rfl)) (.node (.edge (.fine 4 rfl) (.fine 0 rfl)) (.node (.edge (.fine 2 rfl) (.fine 1 rfl)) (.node (.edge (.fine 2 rfl) (.fine 0 rfl)) (.leaf (.edge (.fine 1 rfl) (.fine 0 rfl))) (.empty)) (.leaf (.edge (.fine 3 rfl) (.fine 0 rfl)))) (.node (.edge (.fine 7 rfl) (.fine 0 rfl)) (.node (.edge (.fine 6 rfl) (.fine 0 rfl)) (.leaf (.edge (.fine 5 rfl) (.fine 0 rfl))) (.empty)) (.leaf (.edge (.fine 8 rfl) (.fine 0 rfl))))) (.node (.edge (.fine 11 rfl) (.fine 0 rfl)) (.node (.edge (.fine 10 rfl) (.fine 0 rfl)) (.node (.edge (.fine 9 rfl) (.fine 7 rfl)) (.leaf (.edge (.fine 9 rfl) (.fine 0 rfl))) (.empty)) (.leaf (.edge (.fine 10 rfl) (.fine 6 rfl)))) (.node (.edge (.fine 12 rfl) (.fine 4 rfl)) (.node (.edge (.fine 12 rfl) (.fine 0 rfl)) (.leaf (.edge (.fine 11 rfl) (.fine 5 rfl))) (.empty)) (.leaf (.edge (.fine 28 rfl) (.fine 18 rfl)))))) (.node (.edge (.fine 38 rfl) (.fine 28 rfl)) (.node (.edge (.fine 34 rfl) (.fine 21 rfl)) (.node (.edge (.fine 32 rfl) (.fine 18 rfl)) (.node (.edge (.fine 31 rfl) (.fine 19 rfl)) (.leaf (.edge (.fine 30 rfl) (.fine 19 rfl))) (.empty)) (.leaf (.edge (.fine 33 rfl) (.fine 22 rfl)))) (.node (.edge (.fine 37 rfl) (.fine 22 rfl)) (.node (.edge (.fine 36 rfl) (.fine 20 rfl)) (.leaf (.edge (.fine 35 rfl) (.fine 21 rfl))) (.empty)) (.leaf (.edge (.fine 38 rfl) (.fine 18 rfl))))) (.node (.edge (.fine 41 rfl) (.fine 18 rfl)) (.node (.edge (.fine 40 rfl) (.fine 19 rfl)) (.node (.edge (.fine 39 rfl) (.fine 30 rfl)) (.leaf (.edge (.fine 39 rfl) (.fine 19 rfl))) (.empty)) (.leaf (.edge (.fine 40 rfl) (.fine 31 rfl)))) (.node (.edge (.fine 42 rfl) (.fine 36 rfl)) (.node (.edge (.fine 42 rfl) (.fine 20 rfl)) (.leaf (.edge (.fine 41 rfl) (.fine 32 rfl))) (.empty)) (.leaf (.edge (.fine 43 rfl) (.fine 22 rfl))))))) (.node (.edge (.fine 52 rfl) (.fine 41 rfl)) (.node (.edge (.fine 48 rfl) (.fine 47 rfl)) (.node (.edge (.fine 46 rfl) (.fine 21 rfl)) (.node (.edge (.fine 45 rfl) (.fine 20 rfl)) (.node (.edge (.fine 44 rfl) (.fine 34 rfl)) (.leaf (.edge (.fine 44 rfl) (.fine 21 rfl))) (.empty)) (.leaf (.edge (.fine 45 rfl) (.fine 29 rfl)))) (.node (.edge (.fine 47 rfl) (.fine 37 rfl)) (.node (.edge (.fine 47 rfl) (.fine 22 rfl)) (.leaf (.edge (.fine 46 rfl) (.fine 35 rfl))) (.empty)) (.leaf (.edge (.fine 48 rfl) (.fine 27 rfl))))) (.node (.edge (.fine 50 rfl) (.fine 49 rfl)) (.node (.edge (.fine 50 rfl) (.fine 25 rfl)) (.node (.edge (.fine 49 rfl) (.fine 46 rfl)) (.leaf (.edge (.fine 49 rfl) (.fine 25 rfl))) (.empty)) (.leaf (.edge (.fine 50 rfl) (.fine 44 rfl)))) (.node (.edge (.fine 51 rfl) (.fine 48 rfl)) (.node (.edge (.fine 51 rfl) (.fine 43 rfl)) (.leaf (.edge (.fine 51 rfl) (.fine 27 rfl))) (.empty)) (.leaf (.edge (.fine 52 rfl) (.fine 26 rfl)))))) (.node (.edge (.fine 56 rfl) (.fine 54 rfl)) (.node (.edge (.fine 55 rfl) (.fine 26 rfl)) (.node (.edge (.fine 54 rfl) (.fine 24 rfl)) (.node (.edge (.fine 53 rfl) (.fine 42 rfl)) (.leaf (.edge (.fine 53 rfl) (.fine 23 rfl))) (.empty)) (.leaf (.edge (.fine 54 rfl) (.fine 39 rfl)))) (.node (.edge (.fine 56 rfl) (.fine 24 rfl)) (.node (.edge (.fine 55 rfl) (.fine 52 rfl)) (.leaf (.edge (.fine 55 rfl) (.fine 38 rfl))) (.empty)) (.leaf (.edge (.fine 56 rfl) (.fine 40 rfl))))) (.node (.edge (.fine 58 rfl) (.fine 28 rfl)) (.node (.edge (.fine 57 rfl) (.fine 53 rfl)) (.node (.edge (.fine 57 rfl) (.fine 45 rfl)) (.leaf (.edge (.fine 57 rfl) (.fine 23 rfl))) (.empty)) (.leaf (.edge (.fine 58 rfl) (.fine 26 rfl)))) (.node (.edge (.fine 59 rfl) (.fine 29 rfl)) (.leaf (.edge (.fine 59 rfl) (.fine 23 rfl))) (.leaf (.edge (.fine 60 rfl) (.fine 23 rfl)))))))) (.node (.edge (.fine 74 rfl) (.fine 34 rfl)) (.node (.edge (.fine 68 rfl) (.fine 14 rfl)) (.node (.edge (.fine 64 rfl) (.fine 62 rfl)) (.node (.edge (.fine 62 rfl) (.fine 31 rfl)) (.node (.edge (.fine 61 rfl) (.fine 37 rfl)) (.node (.edge (.fine 61 rfl) (.fine 27 rfl)) (.leaf (.edge (.fine 60 rfl) (.fine 59 rfl))) (.empty)) (.leaf (.edge (.fine 62 rfl) (.fine 24 rfl)))) (.node (.edge (.fine 64 rfl) (.fine 24 rfl)) (.node (.edge (.fine 63 rfl) (.fine 35 rfl)) (.leaf (.edge (.fine 63 rfl) (.fine 25 rfl))) (.empty)) (.leaf (.edge (.fine 64 rfl) (.fine 30 rfl))))) (.node (.edge (.fine 66 rfl) (.fine 32 rfl)) (.node (.edge (.fine 65 rfl) (.fine 63 rfl)) (.node (.edge (.fine 65 rfl) (.fine 34 rfl)) (.leaf (.edge (.fine 65 rfl) (.fine 25 rfl))) (.empty)) (.leaf (.edge (.fine 66 rfl) (.fine 26 rfl)))) (.node (.edge (.fine 67 rfl) (.fine 33 rfl)) (.node (.edge (.fine 67 rfl) (.fine 27 rfl)) (.leaf (.edge (.fine 66 rfl) (.fine 58 rfl))) (.empty)) (.leaf (.edge (.fine 67 rfl) (.fine 61 rfl)))))) (.node (.edge (.fine 71 rfl) (.fine 32 rfl)) (.node (.edge (.fine 69 rfl) (.fine 61 rfl)) (.node (.edge (.fine 69 rfl) (.fine 17 rfl)) (.node (.edge (.fine 68 rfl) (.fine 58 rfl)) (.leaf (.edge (.fine 68 rfl) (.fine 28 rfl))) (.empty)) (.leaf (.edge (.fine 69 rfl) (.fine 37 rfl)))) (.node (.edge (.fine 70 rfl) (.fine 63 rfl)) (.node (.edge (.fine 70 rfl) (.fine 35 rfl)) (.leaf (.edge (.fine 70 rfl) (.fine 16 rfl))) (.empty)) (.leaf (.edge (.fine 71 rfl) (.fine 14 rfl))))) (.node (.edge (.fine 73 rfl) (.fine 15 rfl)) (.node (.edge (.fine 72 rfl) (.fine 36 rfl)) (.node (.edge (.fine 72 rfl) (.fine 15 rfl)) (.leaf (.edge (.fine 71 rfl) (.fine 66 rfl))) (.empty)) (.leaf (.edge (.fine 72 rfl) (.fine 60 rfl)))) (.node (.edge (.fine 73 rfl) (.fine 59 rfl)) (.leaf (.edge (.fine 73 rfl) (.fine 29 rfl))) (.leaf (.edge (.fine 74 rfl) (.fine 16 rfl))))))) (.node (.edge (.fine 80 rfl) (.fine 38 rfl)) (.node (.edge (.fine 77 rfl) (.fine 64 rfl)) (.node (.edge (.fine 76 rfl) (.fine 13 rfl)) (.node (.edge (.fine 75 rfl) (.fine 33 rfl)) (.node (.edge (.fine 75 rfl) (.fine 17 rfl)) (.leaf (.edge (.fine 74 rfl) (.fine 65 rfl))) (.empty)) (.leaf (.edge (.fine 75 rfl) (.fine 67 rfl)))) (.node (.edge (.fine 77 rfl) (.fine 13 rfl)) (.node (.edge (.fine 76 rfl) (.fine 62 rfl)) (.leaf (.edge (.fine 76 rfl) (.fine 31 rfl))) (.empty)) (.leaf (.edge (.fine 77 rfl) (.fine 30 rfl))))) (.node (.edge (.fine 79 rfl) (.fine 16 rfl)) (.node (.edge (.fine 78 rfl) (.fine 48 rfl)) (.node (.edge (.fine 78 rfl) (.fine 47 rfl)) (.leaf (.edge (.fine 78 rfl) (.fine 17 rfl))) (.empty)) (.leaf (.edge (.fine 78 rfl) (.fine 75 rfl)))) (.node (.edge (.fine 79 rfl) (.fine 74 rfl)) (.node (.edge (.fine 79 rfl) (.fine 49 rfl)) (.leaf (.edge (.fine 79 rfl) (.fine 46 rfl))) (.empty)) (.leaf (.edge (.fine 80 rfl) (.fine 14 rfl)))))) (.node (.edge (.fine 82 rfl) (.fine 70 rfl)) (.node (.edge (.fine 81 rfl) (.fine 57 rfl)) (.node (.edge (.fine 81 rfl) (.fine 15 rfl)) (.node (.edge (.fine 80 rfl) (.fine 71 rfl)) (.leaf (.edge (.fine 80 rfl) (.fine 55 rfl))) (.empty)) (.leaf (.edge (.fine 81 rfl) (.fine 45 rfl)))) (.node (.edge (.fine 82 rfl) (.fine 44 rfl)) (.node (.edge (.fine 82 rfl) (.fine 16 rfl)) (.leaf (.edge (.fine 81 rfl) (.fine 72 rfl))) (.empty)) (.leaf (.edge (.fine 82 rfl) (.fine 50 rfl))))) (.node (.edge (.fine 84 rfl) (.fine 13 rfl)) (.node (.edge (.fine 83 rfl) (.fine 52 rfl)) (.node (.edge (.fine 83 rfl) (.fine 41 rfl)) (.leaf (.edge (.fine 83 rfl) (.fine 14 rfl))) (.empty)) (.leaf (.edge (.fine 83 rfl) (.fine 68 rfl)))) (.node (.edge (.fine 84 rfl) (.fine 56 rfl)) (.leaf (.edge (.fine 84 rfl) (.fine 40 rfl))) (.leaf (.edge (.fine 84 rfl) (.fine 77 rfl))))))))) (.node (.edge (.fine 97 rfl) (.fine 96 rfl)) (.node (.edge (.fine 92 rfl) (.fine 9 rfl)) (.node (.edge (.fine 89 rfl) (.fine 19 rfl)) (.node (.edge (.fine 87 rfl) (.fine 53 rfl)) (.node (.edge (.fine 86 rfl) (.fine 43 rfl)) (.node (.edge (.fine 85 rfl) (.fine 76 rfl)) (.node (.edge (.fine 85 rfl) (.fine 54 rfl)) (.leaf (.edge (.fine 85 rfl) (.fine 39 rfl))) (.empty)) (.leaf (.edge (.fine 86 rfl) (.fine 17 rfl)))) (.node (.edge (.fine 87 rfl) (.fine 15 rfl)) (.node (.edge (.fine 86 rfl) (.fine 69 rfl)) (.leaf (.edge (.fine 86 rfl) (.fine 51 rfl))) (.empty)) (.leaf (.edge (.fine 87 rfl) (.fine 42 rfl))))) (.node (.edge (.fine 88 rfl) (.fine 15 rfl)) (.node (.edge (.fine 88 rfl) (.fine 13 rfl)) (.node (.edge (.fine 88 rfl) (.fine 1 rfl)) (.leaf (.edge (.fine 87 rfl) (.fine 73 rfl))) (.empty)) (.leaf (.edge (.fine 88 rfl) (.fine 14 rfl)))) (.node (.edge (.fine 89 rfl) (.fine 1 rfl)) (.node (.edge (.fine 88 rfl) (.fine 17 rfl)) (.leaf (.edge (.fine 88 rfl) (.fine 16 rfl))) (.empty)) (.leaf (.edge (.fine 89 rfl) (.fine 18 rfl)))))) (.node (.edge (.fine 90 rfl) (.fine 59 rfl)) (.node (.edge (.fine 90 rfl) (.fine 8 rfl)) (.node (.edge (.fine 89 rfl) (.fine 22 rfl)) (.node (.edge (.fine 89 rfl) (.fine 21 rfl)) (.leaf (.edge (.fine 89 rfl) (.fine 20 rfl))) (.empty)) (.leaf (.edge (.fine 89 rfl) (.fine 88 rfl)))) (.node (.edge (.fine 90 rfl) (.fine 44 rfl)) (.node (.edge (.fine 90 rfl) (.fine 43 rfl)) (.leaf (.edge (.fine 90 rfl) (.fine 13 rfl))) (.empty)) (.leaf (.edge (.fine 90 rfl) (.fine 58 rfl))))) (.node (.edge (.fine 91 rfl) (.fine 46 rfl)) (.node (.edge (.fine 91 rfl) (.fine 15 rfl)) (.node (.edge (.fine 91 rfl) (.fine 12 rfl)) (.leaf (.edge (.fine 90 rfl) (.fine 88 rfl))) (.empty)) (.leaf (.edge (.fine 91 rfl) (.fine 41 rfl)))) (.node (.edge (.fine 91 rfl) (.fine 64 rfl)) (.leaf (.edge (.fine 91 rfl) (.fine 61 rfl))) (.leaf (.edge (.fine 91 rfl) (.fine 88 rfl))))))) (.node (.edge (.fine 94 rfl) (.fine 88 rfl)) (.node (.edge (.fine 93 rfl) (.fine 47 rfl)) (.node (.edge (.fine 92 rfl) (.fine 67 rfl)) (.node (.edge (.fine 92 rfl) (.fine 45 rfl)) (.node (.edge (.fine 92 rfl) (.fine 39 rfl)) (.leaf (.edge (.fine 92 rfl) (.fine 16 rfl))) (.empty)) (.leaf (.edge (.fine 92 rfl) (.fine 66 rfl)))) (.node (.edge (.fine 93 rfl) (.fine 14 rfl)) (.node (.edge (.fine 93 rfl) (.fine 11 rfl)) (.leaf (.edge (.fine 92 rfl) (.fine 88 rfl))) (.empty)) (.leaf (.edge (.fine 93 rfl) 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rfl)) (.node (.edge (.fine 203 rfl) (.fine 28 rfl)) (.node (.edge (.fine 202 rfl) (.fine 60 rfl)) (.node (.edge (.fine 201 rfl) (.fine 190 rfl)) (.node (.edge (.fine 201 rfl) (.fine 167 rfl)) (.node (.edge (.fine 201 rfl) (.fine 152 rfl)) (.leaf (.edge (.fine 201 rfl) (.fine 107 rfl))) (.empty)) (.leaf (.edge (.fine 201 rfl) (.fine 173 rfl)))) (.node (.edge (.fine 202 rfl) (.fine 27 rfl)) (.node (.edge (.fine 202 rfl) (.fine 16 rfl)) (.leaf (.edge (.fine 202 rfl) (.fine 11 rfl))) (.empty)) (.leaf (.edge (.fine 202 rfl) (.fine 55 rfl))))) (.node (.edge (.fine 202 rfl) (.fine 182 rfl)) (.node (.edge (.fine 202 rfl) (.fine 143 rfl)) (.node (.edge (.fine 202 rfl) (.fine 104 rfl)) (.leaf (.edge (.fine 202 rfl) (.fine 77 rfl))) (.empty)) (.leaf (.edge (.fine 202 rfl) (.fine 164 rfl)))) (.node (.edge (.fine 203 rfl) (.fine 3 rfl)) (.node (.edge (.fine 202 rfl) (.fine 201 rfl)) (.leaf (.edge (.fine 202 rfl) (.fine 192 rfl))) (.empty)) (.leaf (.edge (.fine 203 rfl) (.fine 13 rfl)))))) (.node (.edge (.fine 204 rfl) (.fine 6 rfl)) (.node (.edge (.fine 203 rfl) (.fine 123 rfl)) (.node (.edge (.fine 203 rfl) (.fine 70 rfl)) (.node (.edge (.fine 203 rfl) (.fine 69 rfl)) (.leaf (.edge (.fine 203 rfl) (.fine 29 rfl))) (.empty)) (.leaf (.edge (.fine 203 rfl) (.fine 108 rfl)))) (.node (.edge (.fine 203 rfl) (.fine 135 rfl)) (.node (.edge (.fine 203 rfl) (.fine 134 rfl)) (.leaf (.edge (.fine 203 rfl) (.fine 124 rfl))) (.empty)) (.leaf (.edge (.fine 203 rfl) (.fine 163 rfl))))) (.node (.edge (.fine 204 rfl) (.fine 77 rfl)) (.node (.edge (.fine 204 rfl) (.fine 36 rfl)) (.node (.edge (.fine 204 rfl) (.fine 34 rfl)) (.leaf (.edge (.fine 204 rfl) (.fine 17 rfl))) (.empty)) (.leaf (.edge (.fine 204 rfl) (.fine 71 rfl)))) (.node (.edge (.fine 204 rfl) (.fine 127 rfl)) (.leaf (.edge (.fine 204 rfl) (.fine 109 rfl))) (.leaf (.edge (.fine 204 rfl) (.fine 129 rfl))))))) (.node (.edge (.fine 206 rfl) (.fine 76 rfl)) (.node (.edge (.fine 205 rfl) (.fine 126 rfl)) (.node (.edge (.fine 205 rfl) (.fine 30 rfl)) (.node (.edge (.fine 205 rfl) (.fine 4 rfl)) (.node (.edge (.fine 204 rfl) (.fine 166 rfl)) (.leaf (.edge (.fine 204 rfl) (.fine 139 rfl))) (.empty)) (.leaf (.edge (.fine 205 rfl) (.fine 15 rfl)))) (.node (.edge (.fine 205 rfl) (.fine 74 rfl)) (.node (.edge (.fine 205 rfl) (.fine 68 rfl)) (.leaf (.edge (.fine 205 rfl) (.fine 37 rfl))) (.empty)) (.leaf (.edge (.fine 205 rfl) (.fine 112 rfl))))) (.node (.edge (.fine 206 rfl) (.fine 7 rfl)) (.node (.edge (.fine 205 rfl) (.fine 142 rfl)) (.node (.edge (.fine 205 rfl) (.fine 137 rfl)) (.leaf (.edge (.fine 205 rfl) (.fine 131 rfl))) (.empty)) (.leaf (.edge (.fine 205 rfl) (.fine 164 rfl)))) (.node (.edge (.fine 206 rfl) (.fine 33 rfl)) (.node (.edge (.fine 206 rfl) (.fine 32 rfl)) (.leaf (.edge (.fine 206 rfl) (.fine 16 rfl))) (.empty)) (.leaf (.edge (.fine 206 rfl) (.fine 72 rfl)))))) (.node (.edge (.fine 207 rfl) (.fine 35 rfl)) (.node (.edge (.fine 206 rfl) (.fine 140 rfl)) (.node (.edge (.fine 206 rfl) (.fine 130 rfl)) (.node (.edge (.fine 206 rfl) (.fine 128 rfl)) (.leaf (.edge (.fine 206 rfl) (.fine 110 rfl))) (.empty)) (.leaf (.edge (.fine 206 rfl) (.fine 136 rfl)))) (.node (.edge (.fine 207 rfl) (.fine 14 rfl)) (.node (.edge (.fine 207 rfl) (.fine 5 rfl)) (.leaf (.edge (.fine 206 rfl) (.fine 167 rfl))) (.empty)) (.leaf (.edge (.fine 207 rfl) (.fine 31 rfl))))) (.node (.edge (.fine 207 rfl) (.fine 132 rfl)) (.node (.edge (.fine 207 rfl) (.fine 111 rfl)) (.node (.edge (.fine 207 rfl) (.fine 75 rfl)) (.leaf (.edge (.fine 207 rfl) (.fine 73 rfl))) (.empty)) (.leaf (.edge (.fine 207 rfl) (.fine 125 rfl)))) (.node (.edge (.fine 207 rfl) (.fine 141 rfl)) (.leaf (.edge (.fine 207 rfl) (.fine 133 rfl))) (.leaf (.edge (.fine 207 rfl) (.fine 165 rfl)))))))))))

exampleDependentTactic.lean

structure Edge (n : Nat) : Type :=
  edge::
  fst : Fin n
  snd : Fin fst

-- smart constructor for edges
macro "E[" i:term "," j:term "]" : term =>
 `(.edge $i (Fin.mk $j (by trivial)))

inductive Tree (α : Type) : Type
  | empty : Tree α
  | leaf : α → Tree α
  | node : α → Tree α → Tree α → Tree α

def test1 : Tree (Edge 100) := .node E[5,0] .empty (.leaf E[3,1])

def test2 : Tree (Edge 666) := .node E[147,74] (.node E[110,2] (.node E[85,13] (.node E[60,36] (.node E[43,33] (.node E[29,20] (.node E[8,3] (.node E[4,0] (.node E[2,1] (.node E[2,0] (.leaf E[1,0]) (.empty)) (.leaf E[3,0])) (.node E[7,0] (.node E[6,0] (.leaf E[5,0]) (.empty)) (.leaf E[8,0]))) (.node E[11,0] (.node E[10,0] (.node E[9,7] (.leaf E[9,0]) (.empty)) (.leaf E[10,6])) (.node E[12,4] (.node E[12,0] (.leaf E[11,5]) (.empty)) (.leaf E[28,18])))) (.node E[38,28] (.node E[34,21] (.node E[32,18] (.node E[31,19] (.leaf E[30,19]) (.empty)) (.leaf E[33,22])) (.node E[37,22] (.node E[36,20] (.leaf E[35,21]) (.empty)) (.leaf E[38,18]))) (.node E[41,18] (.node E[40,19] (.node E[39,30] (.leaf E[39,19]) (.empty)) (.leaf E[40,31])) (.node E[42,36] (.node E[42,20] (.leaf E[41,32]) (.empty)) (.leaf E[43,22]))))) (.node E[52,41] (.node E[48,47] (.node E[46,21] (.node E[45,20] (.node E[44,34] (.leaf E[44,21]) (.empty)) (.leaf E[45,29])) (.node E[47,37] (.node E[47,22] (.leaf E[46,35]) (.empty)) (.leaf E[48,27]))) (.node E[50,49] (.node E[50,25] (.node E[49,46] (.leaf E[49,25]) (.empty)) (.leaf E[50,44])) (.node E[51,48] (.node E[51,43] (.leaf E[51,27]) (.empty)) (.leaf E[52,26])))) (.node E[56,54] (.node E[55,26] (.node E[54,24] (.node E[53,42] (.leaf E[53,23]) (.empty)) (.leaf E[54,39])) (.node E[56,24] (.node E[55,52] (.leaf E[55,38]) (.empty)) (.leaf E[56,40]))) (.node E[58,28] (.node E[57,53] (.node E[57,45] (.leaf E[57,23]) (.empty)) (.leaf E[58,26])) (.node E[59,29] (.leaf E[59,23]) (.leaf E[60,23])))))) (.node E[74,34] (.node E[68,14] (.node E[64,62] (.node E[62,31] (.node E[61,37] (.node E[61,27] (.leaf E[60,59]) (.empty)) (.leaf E[62,24])) (.node E[64,24] (.node E[63,35] (.leaf E[63,25]) (.empty)) (.leaf E[64,30]))) (.node E[66,32] (.node E[65,63] (.node E[65,34] (.leaf E[65,25]) (.empty)) (.leaf E[66,26])) (.node E[67,33] (.node E[67,27] (.leaf E[66,58]) (.empty)) (.leaf E[67,61])))) (.node E[71,32] (.node E[69,61] (.node E[69,17] (.node E[68,58] (.leaf E[68,28]) (.empty)) (.leaf E[69,37])) (.node E[70,63] (.node E[70,35] (.leaf E[70,16]) (.empty)) (.leaf E[71,14]))) (.node E[73,15] (.node E[72,36] (.node E[72,15] (.leaf E[71,66]) (.empty)) (.leaf E[72,60])) (.node E[73,59] (.leaf E[73,29]) (.leaf E[74,16]))))) (.node E[80,38] (.node E[77,64] (.node E[76,13] (.node E[75,33] (.node E[75,17] (.leaf E[74,65]) (.empty)) (.leaf E[75,67])) (.node E[77,13] (.node E[76,62] (.leaf E[76,31]) (.empty)) (.leaf E[77,30]))) (.node E[79,16] (.node E[78,48] (.node E[78,47] (.leaf E[78,17]) (.empty)) (.leaf E[78,75])) (.node E[79,74] (.node E[79,49] (.leaf E[79,46]) (.empty)) (.leaf E[80,14])))) (.node E[82,70] (.node E[81,57] (.node E[81,15] (.node E[80,71] (.leaf E[80,55]) (.empty)) (.leaf E[81,45])) (.node E[82,44] (.node E[82,16] (.leaf E[81,72]) (.empty)) (.leaf E[82,50]))) (.node E[84,13] (.node E[83,52] (.node E[83,41] (.leaf E[83,14]) (.empty)) (.leaf E[83,68])) (.node E[84,56] (.leaf E[84,40]) (.leaf E[84,77]))))))) (.node E[97,96] (.node E[92,9] (.node E[89,19] (.node E[87,53] (.node E[86,43] (.node E[85,76] (.node E[85,54] (.leaf E[85,39]) (.empty)) (.leaf E[86,17])) (.node E[87,15] (.node E[86,69] (.leaf E[86,51]) (.empty)) (.leaf E[87,42]))) (.node E[88,15] (.node E[88,13] (.node E[88,1] (.leaf E[87,73]) (.empty)) (.leaf E[88,14])) (.node E[89,1] (.node E[88,17] (.leaf E[88,16]) (.empty)) (.leaf E[89,18])))) (.node E[90,59] (.node E[90,8] (.node E[89,22] (.node E[89,21] (.leaf E[89,20]) (.empty)) (.leaf E[89,88])) (.node E[90,44] (.node E[90,43] (.leaf E[90,13]) (.empty)) (.leaf E[90,58]))) (.node E[91,46] (.node E[91,15] (.node E[91,12] (.leaf E[90,88]) (.empty)) (.leaf E[91,41])) (.node E[91,64] (.leaf E[91,61]) (.leaf E[91,88]))))) (.node E[94,88] (.node E[93,47] (.node E[92,67] (.node E[92,45] (.node E[92,39] (.leaf E[92,16]) (.empty)) (.leaf E[92,66])) (.node E[93,14] (.node E[93,11] (.leaf E[92,88]) (.empty)) (.leaf E[93,42]))) (.node E[94,17] (.node E[93,88] (.node E[93,63] (.leaf E[93,62]) (.empty)) (.leaf E[94,10])) (.node E[94,60] (.node E[94,40] (.leaf E[94,38]) (.empty)) (.leaf E[94,65])))) (.node E[96,32] (.node E[95,35] (.node E[95,30] (.node E[95,28] (.leaf E[95,1]) (.empty)) (.leaf E[95,33])) (.node E[96,29] (.node E[96,1] (.leaf E[95,36]) (.empty)) (.leaf E[96,31]))) (.node E[97,51] (.node E[97,1] (.node E[96,37] (.leaf E[96,34]) (.empty)) (.leaf E[97,49])) (.node E[97,54] (.leaf E[97,53]) (.leaf E[97,55])))))) (.node E[103,67] (.node E[101,1] (.node E[99,61] (.node E[98,56] (.node E[98,50] (.node E[98,48] (.leaf E[98,1]) (.empty)) (.leaf E[98,52])) (.node E[99,1] (.node E[98,95] (.leaf E[98,57]) (.empty)) (.leaf E[99,59]))) (.node E[100,58] (.node E[99,66] (.node E[99,65] (.leaf E[99,62]) (.empty)) (.leaf E[100,1])) (.node E[100,64] (.node E[100,63] (.leaf E[100,60]) (.empty)) (.leaf E[100,67])))) (.node E[102,85] (.node E[101,84] (.node E[101,82] (.node E[101,81] (.leaf E[101,78]) (.empty)) (.leaf E[101,83])) (.node E[102,79] (.node E[102,1] (.leaf E[101,99]) (.empty)) (.leaf E[102,80]))) (.node E[103,20] (.node E[102,100] (.node E[102,87] (.leaf E[102,86]) (.empty)) (.leaf E[103,2])) (.node E[103,34] (.leaf E[103,28]) (.leaf E[103,62]))))) (.node E[107,18] (.node E[105,32] (.node E[104,60] (.node E[104,35] (.node E[104,19] (.leaf E[104,2]) (.empty)) (.leaf E[104,37])) (.node E[105,22] (.node E[105,2] (.leaf E[104,66]) (.empty)) (.leaf E[105,30]))) (.node E[106,31] (.node E[106,2] (.node E[105,63] (.leaf E[105,59]) (.empty)) (.leaf E[106,21])) (.node E[106,61] (.node E[106,58] (.leaf E[106,36]) (.empty)) (.leaf E[107,2])))) (.node E[108,87] (.node E[108,2] (.node E[107,64] (.node E[107,33] (.leaf E[107,29]) (.empty)) (.leaf E[107,65])) (.node E[108,51] (.node E[108,50] (.leaf E[108,13]) (.empty)) (.leaf E[108,83]))) (.node E[109,56] (.node E[109,17] (.node E[109,2] (.leaf E[108,104]) (.empty)) (.leaf E[109,55])) (.node E[109,81] (.leaf E[109,79]) (.leaf E[109,105])))))))) (.node E[129,41] (.node E[119,112] (.node E[115,27] (.node E[112,103] (.node E[111,53] (.node E[110,80] (.node E[110,57] (.node E[110,54] (.leaf E[110,16]) (.empty)) (.leaf E[110,78])) (.node E[111,14] (.node E[111,2] (.leaf E[110,106]) (.empty)) (.leaf E[111,48]))) (.node E[112,15] (.node E[111,107] (.node E[111,85] (.leaf E[111,82]) (.empty)) (.leaf E[112,2])) (.node E[112,84] (.node E[112,52] (.leaf E[112,49]) (.empty)) (.leaf E[112,86])))) (.node E[114,19] (.node E[113,53] (.node E[113,25] (.node E[113,19] (.leaf E[113,6]) (.empty)) (.leaf E[113,38])) (.node E[113,111] (.node E[113,91] (.leaf E[113,61]) (.empty)) (.leaf E[114,7]))) (.node E[114,93] (.node E[114,52] (.node E[114,45] (.leaf E[114,27]) (.empty)) (.leaf E[114,63])) (.node E[115,4] (.leaf E[114,112]) (.leaf E[115,18]))))) (.node E[117,55] (.node E[116,47] (.node E[115,110] (.node E[115,59] (.node E[115,54] (.leaf E[115,46]) (.empty)) (.leaf E[115,90])) (.node E[116,20] (.node E[116,5] (.leaf E[115,114]) (.empty)) (.leaf E[116,25]))) (.node E[116,113] (.node E[116,90] (.node E[116,58] (.leaf E[116,56]) (.empty)) (.leaf E[116,109])) (.node E[117,23] (.node E[117,21] (.leaf E[117,3]) (.empty)) (.leaf E[117,43])))) (.node E[118,94] (.node E[118,21] (.node E[117,109] (.node E[117,93] (.leaf E[117,62]) (.empty)) (.leaf E[118,4])) (.node E[118,48] (.node E[118,41] (.leaf E[118,24]) (.empty)) (.leaf E[118,60]))) (.node E[119,42] (.node E[119,22] (.node E[119,5] (.leaf E[118,111]) (.empty)) (.leaf E[119,24])) (.node E[119,66] (.leaf E[119,49]) (.leaf E[119,92])))))) (.node E[124,56] (.node E[122,18] (.node E[121,7] (.node E[120,44] (.node E[120,22] (.node E[120,3] (.leaf E[119,118]) (.empty)) (.leaf E[120,26])) (.node E[120,91] (.node E[120,64] (.leaf E[120,57]) (.empty)) (.leaf E[120,110]))) (.node E[121,65] (.node E[121,39] (.node E[121,26] (.leaf E[121,20]) (.empty)) (.leaf E[121,51])) (.node E[121,120] (.node E[121,108] (.leaf E[121,94]) (.empty)) (.leaf E[122,6])))) (.node E[123,47] (.node E[122,92] (.node E[122,50] (.node E[122,40] (.leaf E[122,23]) (.empty)) (.leaf E[122,67])) (.node E[123,12] (.node E[122,117] (.leaf E[122,108]) (.empty)) (.leaf E[123,28]))) (.node E[123,97] (.node E[123,74] (.node E[123,60] (.leaf E[123,54]) (.empty)) (.leaf E[123,93])) (.node E[124,29] (.leaf E[124,11]) (.leaf E[124,46]))))) (.node E[126,97] (.node E[125,72] (.node E[125,9] (.node E[124,91] (.node E[124,75] (.leaf E[124,66]) (.empty)) (.leaf E[124,98])) (.node E[125,52] (.node E[125,43] (.leaf E[125,31]) (.empty)) (.leaf E[125,65]))) (.node E[126,44] (.node E[126,10] (.node E[125,98] (.leaf E[125,90]) (.empty)) (.leaf E[126,30])) (.node E[126,71] (.node E[126,67] (.leaf E[126,53]) (.empty)) (.leaf E[126,90])))) (.node E[128,32] (.node E[127,59] (.node E[127,39] (.node E[127,34] (.leaf E[127,12]) (.empty)) (.leaf E[127,48])) (.node E[127,98] (.node E[127,92] (.leaf E[127,68]) (.empty)) (.leaf E[128,10]))) (.node E[128,93] (.node E[128,61] (.node E[128,50] (.leaf E[128,42]) (.empty)) (.leaf E[128,77])) (.node E[129,9] (.leaf E[128,98]) (.leaf E[129,36]))))))) (.node E[138,58] (.node E[134,7] (.node E[131,94] (.node E[130,58] (.node E[129,97] (.node E[129,76] (.node E[129,63] (.leaf E[129,51]) (.empty)) (.leaf E[129,91])) (.node E[130,40] (.node E[130,33] (.leaf E[130,11]) (.empty)) (.leaf E[130,49]))) (.node E[131,37] (.node E[130,97] (.node E[130,94] (.leaf E[130,73]) (.empty)) (.leaf E[131,8])) (.node E[131,62] (.node E[131,57] (.leaf E[131,38]) (.empty)) (.leaf E[131,70])))) (.node E[133,4] (.node E[132,55] (.node E[132,35] (.node E[132,8] (.leaf E[131,98]) (.empty)) (.leaf E[132,45])) (.node E[132,92] (.node E[132,69] (.leaf E[132,64]) (.empty)) (.leaf E[132,97]))) (.node E[133,79] (.node E[133,61] (.node E[133,39] (.leaf E[133,28]) (.empty)) (.leaf E[133,73])) (.node E[133,121] (.leaf E[133,109]) (.leaf E[133,128]))))) (.node E[136,38] (.node E[135,30] (.node E[134,81] (.node E[134,67] (.node E[134,41] (.leaf E[134,31]) (.empty)) (.leaf E[134,70])) (.node E[134,126] (.node E[134,118] (.leaf E[134,109]) (.empty)) (.leaf E[135,6]))) (.node E[135,110] (.node E[135,69] (.node E[135,65] (.leaf E[135,42]) (.empty)) (.leaf E[135,80])) (.node E[136,3] (.node E[135,125] (.leaf E[135,119]) (.empty)) (.leaf E[136,35])))) (.node E[137,63] (.node E[136,113] (.node E[136,86] (.node E[136,76] (.leaf E[136,59]) (.empty)) (.leaf E[136,112])) (.node E[137,29] (.node E[137,5] (.leaf E[136,127]) (.empty)) (.leaf E[137,40]))) (.node E[137,129] (.node E[137,110] (.node E[137,78] (.leaf E[137,68]) (.empty)) (.leaf E[137,122])) (.node E[138,37] (.leaf E[138,3]) (.leaf E[138,45])))))) (.node E[142,111] (.node E[140,83] (.node E[139,71] (.node E[138,130] (.node E[138,111] (.node E[138,82] (.leaf E[138,77]) (.empty)) (.leaf E[138,114])) (.node E[139,46] (.node E[139,33] (.leaf E[139,5]) (.empty)) (.leaf E[139,62]))) (.node E[140,4] (.node E[139,115] (.node E[139,108] (.leaf E[139,87]) (.empty)) (.leaf E[139,131])) (.node E[140,64] (.node E[140,47] (.leaf E[140,34]) (.empty)) (.leaf E[140,72])))) (.node E[141,112] (.node E[141,32] (.node E[140,132] (.node 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exampleJson.lean

-- This solution resolves all issues. It was proposed by Mario Carneiro at
-- https://proofassistants.stackexchange.com/a/2102/169

-- The idea is to load the data from a JSON file and circumvent elaboration
-- and the linter by creating the required objects more directly.
-- Note that the solution depends on mathlib4, and more precisely the
-- Qq library.

import Lean
import Qq

structure Edge (n : Nat) : Type :=
  edge ::
  fst : Fin n
  snd : Fin fst
open Edge

inductive Tree (α : Type) : Type
  | empty : Tree α
  | leaf : α → Tree α
  | node : α → Tree α → Tree α → Tree α

def Edge.mk' (n a b : Nat) (H : Nat.blt a n = true) (H2 : Nat.blt b a = true) : Edge n :=
  ⟨⟨a, by simp_all⟩, ⟨b, (by simp_all : b < a)⟩⟩

open Qq Lean Meta Elab

def mkEdge (n : Q(Nat)) (j : Json) : Except String Q(Edge $n) := do
  let arr ← j.getArr?
  have a : Q(Nat) := mkRawNatLit (← arr[0]!.getNat?)
  have b : Q(Nat) := mkRawNatLit (← arr[1]!.getNat?)
  have H : Q(Nat.blt $a $n = true) := (q(Eq.refl true) : Expr)
  have H2 : Q(Nat.blt $b $a = true) := (q(Eq.refl true) : Expr)
  pure q(Edge.mk' $n $a $b $H $H2)

partial def mkTree (n : Q(Nat)) (j : Json) : Except String Q(Tree (Edge $n)) := do
  let arr ← j.getArr?
  match arr with
  | #[e, l, r] => pure q(Tree.node $(← mkEdge n e) $(← mkTree n l) $(← mkTree n r))
  | #[] => pure q(Tree.empty)
  | _ => pure q(Tree.leaf $(← mkEdge n j))

elab "tree_from_file" name:ident " from " file:str : command => do
  let file ← IO.FS.readFile file.getString
  let result : Except String (Q(Nat) × Expr) := do
    let .arr #[n, tree] ← Json.parse file | throw "bad format"
    let n : Q(Nat) := mkRawNatLit (← n.getNat?)
    pure (n, ← mkTree n tree)
  let .ok (n, value) := result | throwError "failed to parse"
  Elab.Command.liftCoreM <| addDecl <| .defnDecl {
    name := name.getId
    levelParams := []
    type := q(Tree (Edge $n))
    value
    hints := .regular 0
    safety := .safe
  }

tree_from_file test from "test.json"
#check test -- test : Tree (Edge 666)

test.json

[666, [[147, 74], [[110, 2], [[85, 13], [[60, 36], [[43, 33], [[29, 20], [[8, 3], [[4, 0], [[2, 1], [[2, 0], [1, 0], []], [3, 0]], [[7, 0], [[6, 0], [5, 0], []], [8, 0]]], [[11, 0], [[10, 0], [[9, 7], [9, 0], []], [10, 6]], [[12, 4], [[12, 0], [11, 5], []], [28, 18]]]], [[38, 28], [[34, 21], [[32, 18], [[31, 19], [30, 19], []], [33, 22]], [[37, 22], [[36, 20], [35, 21], []], [38, 18]]], [[41, 18], [[40, 19], [[39, 30], [39, 19], []], [40, 31]], [[42, 36], [[42, 20], [41, 32], []], [43, 22]]]]], [[52, 41], [[48, 47], [[46, 21], [[45, 20], [[44, 34], [44, 21], []], [45, 29]], [[47, 37], [[47, 22], [46, 35], []], [48, 27]]], [[50, 49], [[50, 25], [[49, 46], [49, 25], []], [50, 44]], [[51, 48], [[51, 43], [51, 27], []], [52, 26]]]], [[56, 54], [[55, 26], [[54, 24], [[53, 42], [53, 23], []], [54, 39]], [[56, 24], [[55, 52], [55, 38], []], [56, 40]]], [[58, 28], [[57, 53], [[57, 45], [57, 23], []], [58, 26]], [[59, 29], [59, 23], [60, 23]]]]]], [[74, 34], [[68, 14], [[64, 62], [[62, 31], [[61, 37], [[61, 27], [60, 59], []], [62, 24]], [[64, 24], [[63, 35], [63, 25], []], [64, 30]]], [[66, 32], [[65, 63], [[65, 34], [65, 25], []], [66, 26]], [[67, 33], [[67, 27], [66, 58], []], [67, 61]]]], [[71, 32], [[69, 61], [[69, 17], [[68, 58], [68, 28], []], [69, 37]], [[70, 63], [[70, 35], [70, 16], []], [71, 14]]], [[73, 15], [[72, 36], [[72, 15], [71, 66], []], [72, 60]], [[73, 59], [73, 29], [74, 16]]]]], [[80, 38], [[77, 64], [[76, 13], [[75, 33], [[75, 17], [74, 65], []], [75, 67]], [[77, 13], [[76, 62], [76, 31], []], [77, 30]]], [[79, 16], [[78, 48], [[78, 47], [78, 17], []], [78, 75]], [[79, 74], [[79, 49], [79, 46], []], [80, 14]]]], [[82, 70], [[81, 57], [[81, 15], [[80, 71], [80, 55], []], [81, 45]], [[82, 44], [[82, 16], [81, 72], []], [82, 50]]], [[84, 13], [[83, 52], [[83, 41], [83, 14], []], [83, 68]], [[84, 56], [84, 40], [84, 77]]]]]]], [[97, 96], [[92, 9], [[89, 19], [[87, 53], [[86, 43], [[85, 76], [[85, 54], [85, 39], []], [86, 17]], [[87, 15], [[86, 69], [86, 51], []], [87, 42]]], [[88, 15], [[88, 13], [[88, 1], [87, 73], []], [88, 14]], [[89, 1], [[88, 17], [88, 16], []], [89, 18]]]], [[90, 59], [[90, 8], [[89, 22], [[89, 21], [89, 20], []], [89, 88]], [[90, 44], [[90, 43], [90, 13], []], [90, 58]]], [[91, 46], [[91, 15], [[91, 12], [90, 88], []], [91, 41]], [[91, 64], [91, 61], [91, 88]]]]], [[94, 88], [[93, 47], [[92, 67], [[92, 45], [[92, 39], [92, 16], []], [92, 66]], [[93, 14], [[93, 11], [92, 88], []], [93, 42]]], [[94, 17], [[93, 88], [[93, 63], [93, 62], []], [94, 10]], [[94, 60], [[94, 40], [94, 38], []], [94, 65]]]], [[96, 32], [[95, 35], [[95, 30], [[95, 28], [95, 1], []], [95, 33]], [[96, 29], [[96, 1], [95, 36], []], [96, 31]]], [[97, 51], [[97, 1], [[96, 37], [96, 34], []], [97, 49]], [[97, 54], [97, 53], [97, 55]]]]]], [[103, 67], [[101, 1], [[99, 61], [[98, 56], [[98, 50], [[98, 48], [98, 1], []], [98, 52]], [[99, 1], [[98, 95], [98, 57], []], [99, 59]]], [[100, 58], [[99, 66], [[99, 65], [99, 62], []], [100, 1]], 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125]], [[207, 141], [207, 133], [207, 165]]]]]]]]]]]

time.sh

#!/bin/bash
echo Cleaning files
/bin/rm *.agdai *.vo *.vok *.cmi *.cmo
time ocamlc -c example.ml
time lean example.lean
time agda example.agda
time coqc example.v
time lean exampleDependentNoTactic.lean
time lean exampleDependentTactic.lean
time agda exampleDependent.agda
time coqc exampleDependent.v