CorrespondencePreimageSubgroupMk

forall (G : Sort succ u), forall (one : G), forall (mul : forall (a : G), forall (b : G), G), forall (inv : forall (a : G), G), forall (N : forall (x : G), Prop), forall (group_args : @GroupLawArgs.{succ u} G one mul inv), forall (n_normal : @NormalSubgroupLawArgs.{succ u} G one mul inv N), forall (K : forall (q : @NormalQuot.{u} G one mul inv N group_args n_normal), Prop), forall (P : Prop), Prop

fun G => fun one => fun mul => fun inv => fun N => fun group_args => fun n_normal => fun K => fun P => forall (one_mem : @CorrespondencePreimagePred.{u} G one mul inv N group_args n_normal K one), forall (mul_closed : forall (a : G), forall (b : G), forall (ha : @CorrespondencePreimagePred.{u} G one mul inv N group_args n_normal K a), forall (hb : @CorrespondencePreimagePred.{u} G one mul inv N group_args n_normal K b), @CorrespondencePreimagePred.{u} G one mul inv N group_args n_normal K (mul a b)), forall (inv_closed : forall (a : G), forall (ha : @CorrespondencePreimagePred.{u} G one mul inv N group_args n_normal K a), @CorrespondencePreimagePred.{u} G one mul inv N group_args n_normal K (inv a)), P