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kbuzzard/gist:a09dc87e290c0497db65c4c702b37c2f

Created April 20, 2018 17:44
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gistfile1.txt
goal before show (apply_instance fails)
⊢ @is_ring_hom.{u u} R
(@localization.away.{u}
(@localization.loc.{u} R _inst_1 (@powers.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f)
(@powers.is_submonoid.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f))
(@localization.comm_ring.{u} R _inst_1
(@powers.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f)
(@powers.is_submonoid.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f))
(@localization.of_comm_ring.{u} R _inst_1
(@powers.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f)
(@powers.is_submonoid.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f)
g))
(@comm_ring.to_ring.{u} R _inst_1)
(@comm_ring.to_ring.{u}
(@localization.away.{u}
(@localization.loc.{u} R _inst_1 (@powers.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f)
(@powers.is_submonoid.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f))
(@localization.comm_ring.{u} R _inst_1
(@powers.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f)
(@powers.is_submonoid.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f))
(@localization.of_comm_ring.{u} R _inst_1
(@powers.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f)
(@powers.is_submonoid.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f)
g))
(@localization.away.comm_ring.{u}
(@localization.loc.{u} R _inst_1 (@powers.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f)
(@powers.is_submonoid.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f))
(@localization.comm_ring.{u} R _inst_1
(@powers.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f)
(@powers.is_submonoid.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f))
(@localization.of_comm_ring.{u} R _inst_1
(@powers.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f)
(@powers.is_submonoid.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f)
g)))
(@function.comp.{u+1 u+1 u+1} R
(@localization.loc.{u} R _inst_1 (@powers.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f)
(@powers.is_submonoid.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f))
(@localization.away.{u}
(@localization.loc.{u} R _inst_1 (@powers.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f)
(@powers.is_submonoid.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f))
(@localization.comm_ring.{u} R _inst_1
(@powers.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f)
(@powers.is_submonoid.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f))
(@localization.of_comm_ring.{u} R _inst_1
(@powers.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f)
(@powers.is_submonoid.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f)
g))
(@localization.of_comm_ring.{u} (@localization.away.{u} R _inst_1 f)
(@localization.comm_ring.{u} R _inst_1
(@powers.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f)
(@powers.is_submonoid.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f))
(@powers.{u}
(@localization.loc.{u} R _inst_1
(@powers.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f)
(@powers.is_submonoid.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f))
(@ring.to_monoid.{u}
(@localization.loc.{u} R _inst_1
(@powers.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f)
(@powers.is_submonoid.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f))
(@comm_ring.to_ring.{u}
(@localization.loc.{u} R _inst_1
(@powers.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f)
(@powers.is_submonoid.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f))
(@localization.comm_ring.{u} R _inst_1
(@powers.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f)
(@powers.is_submonoid.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f))))
(@localization.of_comm_ring.{u} R _inst_1
(@powers.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f)
(@powers.is_submonoid.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f)
g))
(@localization.away._proof_1.{u}
(@localization.loc.{u} R _inst_1
(@powers.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f)
(@powers.is_submonoid.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f))
(@localization.comm_ring.{u} R _inst_1
(@powers.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f)
(@powers.is_submonoid.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f))
(@localization.of_comm_ring.{u} R _inst_1
(@powers.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f)
(@powers.is_submonoid.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f)
g)))
(@localization.of_comm_ring.{u} R _inst_1
(@powers.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f)
(@powers.is_submonoid.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f)))
*****************************************************************************************
goal after show (apply_instance now succeeds):
⊢ @is_ring_hom.{u u} R
(@localization.loc.{u} (@localization.away.{u} R _inst_1 f) (@localization.away.comm_ring.{u} R _inst_1 f)
(@powers.{u} (@localization.away.{u} R _inst_1 f)
(@ring.to_monoid.{u} (@localization.away.{u} R _inst_1 f)
(@comm_ring.to_ring.{u} (@localization.away.{u} R _inst_1 f)
(@localization.away.comm_ring.{u} R _inst_1 f)))
(@localization.of_comm_ring.{u} R _inst_1
(@powers.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f)
(@localization.away._proof_1.{u} R _inst_1 f)
g))
(@powers.is_submonoid.{u} (@localization.away.{u} R _inst_1 f)
(@ring.to_monoid.{u} (@localization.away.{u} R _inst_1 f)
(@comm_ring.to_ring.{u} (@localization.away.{u} R _inst_1 f)
(@localization.away.comm_ring.{u} R _inst_1 f)))
(@localization.of_comm_ring.{u} R _inst_1
(@powers.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f)
(@localization.away._proof_1.{u} R _inst_1 f)
g)))
(@comm_ring.to_ring.{u} R _inst_1)
(@comm_ring.to_ring.{u}
(@localization.loc.{u} (@localization.away.{u} R _inst_1 f) (@localization.away.comm_ring.{u} R _inst_1 f)
(@powers.{u} (@localization.away.{u} R _inst_1 f)
(@ring.to_monoid.{u} (@localization.away.{u} R _inst_1 f)
(@comm_ring.to_ring.{u} (@localization.away.{u} R _inst_1 f)
(@localization.away.comm_ring.{u} R _inst_1 f)))
(@localization.of_comm_ring.{u} R _inst_1
(@powers.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f)
(@localization.away._proof_1.{u} R _inst_1 f)
g))
(@powers.is_submonoid.{u} (@localization.away.{u} R _inst_1 f)
(@ring.to_monoid.{u} (@localization.away.{u} R _inst_1 f)
(@comm_ring.to_ring.{u} (@localization.away.{u} R _inst_1 f)
(@localization.away.comm_ring.{u} R _inst_1 f)))
(@localization.of_comm_ring.{u} R _inst_1
(@powers.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f)
(@localization.away._proof_1.{u} R _inst_1 f)
g)))
(@localization.comm_ring.{u} (@localization.away.{u} R _inst_1 f) (@localization.away.comm_ring.{u} R _inst_1 f)
(@powers.{u} (@localization.away.{u} R _inst_1 f)
(@ring.to_monoid.{u} (@localization.away.{u} R _inst_1 f)
(@comm_ring.to_ring.{u} (@localization.away.{u} R _inst_1 f)
(@localization.away.comm_ring.{u} R _inst_1 f)))
(@localization.of_comm_ring.{u} R _inst_1
(@powers.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f)
(@localization.away._proof_1.{u} R _inst_1 f)
g))
(@powers.is_submonoid.{u} (@localization.away.{u} R _inst_1 f)
(@ring.to_monoid.{u} (@localization.away.{u} R _inst_1 f)
(@comm_ring.to_ring.{u} (@localization.away.{u} R _inst_1 f)
(@localization.away.comm_ring.{u} R _inst_1 f)))
(@localization.of_comm_ring.{u} R _inst_1
(@powers.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f)
(@localization.away._proof_1.{u} R _inst_1 f)
g))))
(@function.comp.{u+1 u+1 u+1} R (@localization.away.{u} R _inst_1 f)
(@localization.loc.{u} (@localization.away.{u} R _inst_1 f) (@localization.away.comm_ring.{u} R _inst_1 f)
(@powers.{u} (@localization.away.{u} R _inst_1 f)
(@ring.to_monoid.{u} (@localization.away.{u} R _inst_1 f)
(@comm_ring.to_ring.{u} (@localization.away.{u} R _inst_1 f)
(@localization.away.comm_ring.{u} R _inst_1 f)))
(@localization.of_comm_ring.{u} R _inst_1
(@powers.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f)
(@localization.away._proof_1.{u} R _inst_1 f)
g))
(@powers.is_submonoid.{u} (@localization.away.{u} R _inst_1 f)
(@ring.to_monoid.{u} (@localization.away.{u} R _inst_1 f)
(@comm_ring.to_ring.{u} (@localization.away.{u} R _inst_1 f)
(@localization.away.comm_ring.{u} R _inst_1 f)))
(@localization.of_comm_ring.{u} R _inst_1
(@powers.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f)
(@localization.away._proof_1.{u} R _inst_1 f)
g)))
(@localization.of_comm_ring.{u} (@localization.away.{u} R _inst_1 f)
(@localization.away.comm_ring.{u} R _inst_1 f)
(@powers.{u} (@localization.away.{u} R _inst_1 f)
(@ring.to_monoid.{u} (@localization.away.{u} R _inst_1 f)
(@comm_ring.to_ring.{u} (@localization.away.{u} R _inst_1 f)
(@localization.away.comm_ring.{u} R _inst_1 f)))
(@localization.of_comm_ring.{u} R _inst_1
(@powers.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f)
(@localization.away._proof_1.{u} R _inst_1 f)
g))
(@powers.is_submonoid.{u} (@localization.away.{u} R _inst_1 f)
(@ring.to_monoid.{u} (@localization.away.{u} R _inst_1 f)
(@comm_ring.to_ring.{u} (@localization.away.{u} R _inst_1 f)
(@localization.away.comm_ring.{u} R _inst_1 f)))
(@localization.of_comm_ring.{u} R _inst_1
(@powers.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f)
(@localization.away._proof_1.{u} R _inst_1 f)
g)))
(@localization.of_comm_ring.{u} R _inst_1
(@powers.{u} R (@ring.to_monoid.{u} R (@comm_ring.to_ring.{u} R _inst_1)) f)
(@localization.away._proof_1.{u} R _inst_1 f)))
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