first_isomorphism_to_image

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 (P : Prop), forall (mk : forall (image_group : @FirstIsoImageGroupFacts.{u,v} G oneG mulG invG H oneH mulH invH f hom_args), forall (mul_compat : forall (q1 : @KerQuot.{u,v} G H f), forall (q2 : @KerQuot.{u,v} G H f), @Eq.{succ v} H (@KerQuotToH.{u,v} G H f (@KerQuotMul.{u,v} G oneG mulG invG H oneH mulH invH f hom_args q1 q2)) (mulH (@KerQuotToH.{u,v} G H f q1) (@KerQuotToH.{u,v} G H f q2))), forall (injective : forall (q1 : @KerQuot.{u,v} G H f), forall (q2 : @KerQuot.{u,v} G H f), forall (h : @Eq.{succ v} H (@KerQuotToH.{u,v} G H f q1) (@KerQuotToH.{u,v} G H f q2)), @Eq.{succ u} (@KerQuot.{u,v} G H f) q1 q2), forall (hits_image : forall (q : @KerQuot.{u,v} G H f), @ImagePred.{succ u,succ v} G H f (@KerQuotToH.{u,v} G H f q)), forall (surj_image : forall (y : H), forall (hy : @ImagePred.{succ u,succ v} G H f y), forall (Q : Prop), forall (mk_surj : forall (q : @KerQuot.{u,v} G H f), forall (h : @Eq.{succ v} H (@KerQuotToH.{u,v} G H f q) y), Q), Q), P), P

fun G => fun oneG => fun mulG => fun invG => fun H => fun oneH => fun mulH => fun invH => fun f => fun group_args => fun hom_args => fun (P : Prop) => fun mk => mk (@first_iso_image_group_facts.{u,v} G oneG mulG invG H oneH mulH invH f hom_args) (@first_iso_phi_mul.{u,v} G oneG mulG invG H oneH mulH invH f hom_args) (@first_iso_phi_injective.{u,v} G H f) (@first_iso_phi_hits_image.{u,v} G H f) (@first_iso_phi_surj_image.{u,v} G H f)