ker_quot_inv_mul

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 (group_args : @GroupLawArgs.{succ u} G oneG mulG invG), 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), @Eq.{succ u} (@KerQuot.{u,v} G H f) (@KerQuotMul.{u,v} G oneG mulG invG H oneH mulH invH f hom_args (@KerQuotInv.{u,v} G oneG mulG invG H oneH mulH invH f hom_args q) q) (@KerQuotOne.{u,v} G oneG H f)

fun G => fun oneG => fun mulG => fun invG => fun H => fun oneH => fun mulH => fun invH => fun f => fun group_args => fun hom_args => @Quotient.indProp.{u} G (@KerSetoid.{u,v} G H f) (fun (q : @KerQuot.{u,v} G H f) => @Eq.{succ u} (@KerQuot.{u,v} G H f) (@KerQuotMul.{u,v} G oneG mulG invG H oneH mulH invH f hom_args (@KerQuotInv.{u,v} G oneG mulG invG H oneH mulH invH f hom_args q) q) (@KerQuotOne.{u,v} G oneG H f)) (fun (a : G) => @ker_quot_sound.{u,v} G H f (mulG (invG a) a) oneG (@eq_congr_arg.{succ u,succ v} G H f (mulG (invG a) a) oneG (@group_inv_mul.{succ u} G oneG mulG invG group_args a)))