FirstIsoImageGroupFacts

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

fun G => fun oneG => fun mulG => fun invG => fun H => fun oneH => fun mulH => fun invH => fun f => fun hom_args => forall (P : Prop), forall (mk : forall (one_member : @ImagePred.{succ u,succ v} G H f oneH), forall (mul_closed : forall (x : H), forall (y : H), forall (hx : @ImagePred.{succ u,succ v} G H f x), forall (hy : @ImagePred.{succ u,succ v} G H f y), @ImagePred.{succ u,succ v} G H f (mulH x y)), forall (inv_closed : forall (y : H), forall (hy : @ImagePred.{succ u,succ v} G H f y), @ImagePred.{succ u,succ v} G H f (invH y)), P), P