Back to NPA
Declaration
hom_mul
Mathlib.Algebra.Group.Basic
Packages
2
Module
63
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 u), forall (oneG : G), forall (mulG : forall (a : G), forall (b : G), G), forall (invG : forall (a : G), G), forall (H : Sort 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.{u,v} G oneG mulG invG H oneH mulH invH f), forall (a : G), forall (b : G), @Eq.{v} H (f (mulG a b)) (mulH (f a) (f b))Proof term
fun G => fun oneG => fun mulG => fun invG => fun H => fun oneH => fun mulH => fun invH => fun f => fun hom_args => fun a => fun b => hom_args (@Eq.{v} H (f (mulG a b)) (mulH (f a) (f b))) (fun (hom_mul_arg : forall (a : G), forall (b : G), @Eq.{v} H (f (mulG a b)) (mulH (f a) (f b))) => fun (hom_one_arg : @Eq.{v} H (f oneG) oneH) => fun (hom_inv_arg : forall (a : G), @Eq.{v} H (f (invG a)) (invH (f a))) => hom_mul_arg a b)