FirstIsoImageGroupEvidence

Mathlib.Algebra.Group.FirstIsomorphism.Image

Packages

Module

Theorems

750

Declarations

1016

Untrusted sidecar

Source text and display overlays are presentation metadata. The signed certificate and checker result are the trusted evidence.

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 FirstIsoImageGroupEvidence.{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 (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)), @FirstIsoImageGroupEvidence.{u,v} G oneG mulG invG H oneH mulH invH f hom_args