normal_rel_mul_compat

forall (G : Sort u), forall (one : G), forall (mul : forall (a : G), forall (b : G), G), forall (inv : forall (a : G), G), forall (group_args : @GroupLawArgs.{u} G one mul inv), forall (N : forall (x : G), Prop), forall (normal_args : @NormalSubgroupLawArgs.{u} G one mul inv N), forall (a : G), forall (a2 : G), forall (b : G), forall (b2 : G), forall (ha : @NormalRel.{u} G one mul inv N a a2), forall (hb : @NormalRel.{u} G one mul inv N b b2), @NormalRel.{u} G one mul inv N (mul a b) (mul a2 b2)

fun G => fun one => fun mul => fun inv => fun group_args => fun N => fun normal_args => fun a => fun a2 => fun b => fun b2 => fun ha => fun hb => @eq_subst.{u} G N (mul (mul (mul (inv b) (mul (inv a) a2)) b) (mul (inv b) b2)) (mul (inv (mul a b)) (mul a2 b2)) (@group_rel_mul_reassoc.{u} G one mul inv group_args a a2 b b2) (@subgroup_mul_closed.{u} G one mul inv N (@normal_subgroup_laws.{u} G one mul inv N normal_args) (mul (mul (inv b) (mul (inv a) a2)) b) (mul (inv b) b2) (@normal_inv_conj_closed.{u} G one mul inv group_args N normal_args b (mul (inv a) a2) ha) hb)