kernel_inv_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 (ha : @KernelPred.{u,v} G H oneH f a), @KernelPred.{u,v} G H oneH f (invG a)

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 ha => @eq_trans.{v} H (f (invG a)) (invH (f a)) oneH (@hom_inv.{u,v} G oneG mulG invG H oneH mulH invH f hom_args a) (@eq_trans.{v} H (invH (f a)) (invH oneH) oneH (@eq_congr_arg.{v,v} H H invH (f a) oneH ha) (@eq_trans.{v} H (invH oneH) (mulH (invH oneH) oneH) oneH (@eq_symm.{v} H (mulH (invH oneH) oneH) (invH oneH) (@group_mul_one.{v} H oneH mulH invH groupH_args (invH oneH))) (@group_inv_mul.{v} H oneH mulH invH groupH_args oneH)))