FirstIsoQuotientGroupEvidence

Mathlib.Algebra.Group.FirstIsomorphism.Image

Packages

Module

Theorem

750

Declarations

1016

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Statement

forall (G : Sort succ u), forall (oneG : G), forall (mulG : forall (a : G), forall (b : G), G), forall (invG : forall (a : G), G), forall (H : Sort succ v), forall (oneH : H), forall (mulH : forall (a : H), forall (b : H), H), forall (invH : forall (a : H), H), forall (f : forall (x : G), H), forall (hom_args : @GroupHomLawArgs.{succ u,succ v} G oneG mulG invG H oneH mulH invH f), Prop

Proof term

inductive FirstIsoQuotientGroupEvidence.{u,v} : forall (G : Sort succ u), forall (oneG : G), forall (mulG : forall (a : G), forall (b : G), G), forall (invG : forall (a : G), G), forall (H : Sort succ v), forall (oneH : H), forall (mulH : forall (a : H), forall (b : H), H), forall (invH : forall (a : H), H), forall (f : forall (x : G), H), forall (hom_args : @GroupHomLawArgs.{succ u,succ v} G oneG mulG invG H oneH mulH invH f), Prop where | mk : forall (G : Sort succ u), forall (oneG : G), forall (mulG : forall (a : G), forall (b : G), G), forall (invG : forall (a : G), G), forall (H : Sort succ v), forall (oneH : H), forall (mulH : forall (a : H), forall (b : H), H), forall (invH : forall (a : H), H), forall (f : forall (x : G), H), forall (hom_args : @GroupHomLawArgs.{succ u,succ v} G oneG mulG invG H oneH mulH invH f), forall (assoc : @FirstIsoQuotientAssocEvidence.{u,v} G oneG mulG invG H oneH mulH invH f hom_args), forall (one_mul : @FirstIsoQuotientOneMulEvidence.{u,v} G oneG mulG invG H oneH mulH invH f hom_args), forall (mul_one : @FirstIsoQuotientMulOneEvidence.{u,v} G oneG mulG invG H oneH mulH invH f hom_args), forall (inv_mul : @FirstIsoQuotientInvMulEvidence.{u,v} G oneG mulG invG H oneH mulH invH f hom_args), forall (mul_inv : @FirstIsoQuotientMulInvEvidence.{u,v} G oneG mulG invG H oneH mulH invH f hom_args), @FirstIsoQuotientGroupEvidence.{u,v} G oneG mulG invG H oneH mulH invH f hom_args