kernel_mul_closed

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 (groupH_args : @GroupLawArgs.{v} H oneH mulH invH), forall (hom_args : @GroupHomLawArgs.{u,v} G oneG mulG invG H oneH mulH invH f), forall (a : G), forall (b : G), forall (ha : @KernelPred.{u,v} G H oneH f a), forall (hb : @KernelPred.{u,v} G H oneH f b), @KernelPred.{u,v} G H oneH f (mulG a b)

fun G => fun oneG => fun mulG => fun invG => fun H => fun oneH => fun mulH => fun invH => fun f => fun groupH_args => fun hom_args => fun a => fun b => fun ha => fun hb => @eq_trans.{v} H (f (mulG a b)) (mulH (f a) (f b)) oneH (@hom_mul.{u,v} G oneG mulG invG H oneH mulH invH f hom_args a b) (@eq_trans.{v} H (mulH (f a) (f b)) (mulH oneH oneH) oneH (@eq_congr2.{v,v,v} H H H mulH (f a) oneH (f b) oneH ha hb) (@group_one_mul.{v} H oneH mulH invH groupH_args oneH))