KerQuotInv

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 (q : @KerQuot.{u,v} G H f), @KerQuot.{u,v} G H f

fun G => fun oneG => fun mulG => fun invG => fun H => fun oneH => fun mulH => fun invH => fun f => fun hom_args => @Quotient.lift.{u,u} G (@KerQuot.{u,v} G H f) (@KerSetoid.{u,v} G H f) (fun (a : G) => @KerQuotMk.{u,v} G H f (invG a)) (fun (a : G) => fun (b : G) => fun (h : @Setoid.r.{u} G (@KerSetoid.{u,v} G H f) a b) => @ker_quot_sound.{u,v} G H f (invG a) (invG b) (@eq_trans.{succ v} H (f (invG a)) (invH (f a)) (f (invG b)) (@hom_inv.{succ u,succ v} G oneG mulG invG H oneH mulH invH f hom_args a) (@eq_trans.{succ v} H (invH (f a)) (invH (f b)) (f (invG b)) (@eq_congr_arg.{succ v,succ v} H H invH (f a) (f b) h) (@eq_symm.{succ v} H (f (invG b)) (invH (f b)) (@hom_inv.{succ u,succ v} G oneG mulG invG H oneH mulH invH f hom_args b)))))