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Declaration
group_mul_inv_rev
Mathlib.Algebra.Group.Basic
Packages
2
Module
63
Theorem
750
Declarations
1016
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Statement
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 (a : G), forall (b : G), @Eq.{u} G (mul (inv b) (inv a)) (inv (mul a b))Proof term
fun G => fun one => fun mul => fun inv => fun group_args => fun a => fun b => @group_left_cancel.{u} G one mul inv group_args (mul a b) (mul (inv b) (inv a)) (inv (mul a b)) (@eq_trans.{u} G (mul (mul a b) (mul (inv b) (inv a))) one (mul (mul a b) (inv (mul a b))) (@eq_trans.{u} G (mul (mul a b) (mul (inv b) (inv a))) (mul (mul (mul a b) (inv b)) (inv a)) one (@eq_symm.{u} G (mul (mul (mul a b) (inv b)) (inv a)) (mul (mul a b) (mul (inv b) (inv a))) (@group_mul_assoc.{u} G one mul inv group_args (mul a b) (inv b) (inv a))) (@eq_trans.{u} G (mul (mul (mul a b) (inv b)) (inv a)) (mul (mul a (mul b (inv b))) (inv a)) one (@eq_congr_arg.{u,u} G G (fun (z : G) => mul z (inv a)) (mul (mul a b) (inv b)) (mul a (mul b (inv b))) (@group_mul_assoc.{u} G one mul inv group_args a b (inv b))) (@eq_trans.{u} G (mul (mul a (mul b (inv b))) (inv a)) (mul (mul a one) (inv a)) one (@eq_congr_arg.{u,u} G G (fun (z : G) => mul (mul a z) (inv a)) (mul b (inv b)) one (@group_mul_inv.{u} G one mul inv group_args b)) (@eq_trans.{u} G (mul (mul a one) (inv a)) (mul a (inv a)) one (@eq_congr_arg.{u,u} G G (fun (z : G) => mul z (inv a)) (mul a one) a (@group_mul_one.{u} G one mul inv group_args a)) (@group_mul_inv.{u} G one mul inv group_args a))))) (@eq_symm.{u} G (mul (mul a b) (inv (mul a b))) one (@group_mul_inv.{u} G one mul inv group_args (mul a b))))