normal_quot_inv_mul

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 (normal_args : @NormalSubgroupLawArgs.{succ u} G one mul inv N), forall (q : @NormalQuot.{u} G one mul inv N group_args normal_args), @Eq.{succ u} (@NormalQuot.{u} G one mul inv N group_args normal_args) (@NormalQuotMul.{u} G one mul inv N group_args normal_args (@NormalQuotInv.{u} G one mul inv N group_args normal_args q) q) (@NormalQuotOne.{u} G one mul inv N group_args normal_args)

fun G => fun one => fun mul => fun inv => fun N => fun group_args => fun normal_args => @Quotient.indProp.{u} G (@NormalSetoid.{u} G one mul inv N group_args normal_args) (fun (q : @NormalQuot.{u} G one mul inv N group_args normal_args) => @Eq.{succ u} (@NormalQuot.{u} G one mul inv N group_args normal_args) (@NormalQuotMul.{u} G one mul inv N group_args normal_args (@NormalQuotInv.{u} G one mul inv N group_args normal_args q) q) (@NormalQuotOne.{u} G one mul inv N group_args normal_args)) (fun (a : G) => @normal_quot_sound.{u} G one mul inv N group_args normal_args (mul (inv a) a) one (@normal_rel_of_eq.{succ u} G one mul inv group_args N normal_args (mul (inv a) a) one (@group_inv_mul.{succ u} G one mul inv group_args a)))