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Declaration
group_left_cancel
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), forall (c : G), forall (h : @Eq.{u} G (mul a b) (mul a c)), @Eq.{u} G b cProof term
fun G => fun one => fun mul => fun inv => fun group_args => fun a => fun b => fun c => fun h => @eq_trans.{u} G b (mul one b) c (@eq_symm.{u} G (mul one b) b (@group_one_mul.{u} G one mul inv group_args b)) (@eq_trans.{u} G (mul one b) (mul (mul (inv a) a) b) c (@eq_congr_arg.{u,u} G G (fun (z : G) => mul z b) one (mul (inv a) a) (@eq_symm.{u} G (mul (inv a) a) one (@group_inv_mul.{u} G one mul inv group_args a))) (@eq_trans.{u} G (mul (mul (inv a) a) b) (mul (inv a) (mul a b)) c (@group_mul_assoc.{u} G one mul inv group_args (inv a) a b) (@eq_trans.{u} G (mul (inv a) (mul a b)) (mul (inv a) (mul a c)) c (@eq_congr_arg.{u,u} G G (fun (z : G) => mul (inv a) z) (mul a b) (mul a c) h) (@eq_trans.{u} G (mul (inv a) (mul a c)) (mul (mul (inv a) a) c) c (@eq_symm.{u} G (mul (mul (inv a) a) c) (mul (inv a) (mul a c)) (@group_mul_assoc.{u} G one mul inv group_args (inv a) a c)) (@eq_trans.{u} G (mul (mul (inv a) a) c) (mul one c) c (@eq_congr_arg.{u,u} G G (fun (z : G) => mul z c) (mul (inv a) a) one (@group_inv_mul.{u} G one mul inv group_args a)) (@group_one_mul.{u} G one mul inv group_args c))))))