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Declaration
group_rel_trans_reassoc
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), @Eq.{u} G (mul (mul (inv a) b) (mul (inv b) c)) (mul (inv a) c)Proof term
fun G => fun one => fun mul => fun inv => fun group_args => fun a => fun b => fun c => @eq_trans.{u} G (mul (mul (inv a) b) (mul (inv b) c)) (mul (mul (mul (inv a) b) (inv b)) c) (mul (inv a) c) (@eq_symm.{u} G (mul (mul (mul (inv a) b) (inv b)) c) (mul (mul (inv a) b) (mul (inv b) c)) (@group_mul_assoc.{u} G one mul inv group_args (mul (inv a) b) (inv b) c)) (@eq_trans.{u} G (mul (mul (mul (inv a) b) (inv b)) c) (mul (mul (inv a) (mul b (inv b))) c) (mul (inv a) c) (@eq_congr_arg.{u,u} G G (fun (z : G) => mul z c) (mul (mul (inv a) b) (inv b)) (mul (inv a) (mul b (inv b))) (@group_mul_assoc.{u} G one mul inv group_args (inv a) b (inv b))) (@eq_trans.{u} G (mul (mul (inv a) (mul b (inv b))) c) (mul (mul (inv a) one) c) (mul (inv a) c) (@eq_congr_arg.{u,u} G G (fun (z : G) => mul (mul (inv a) z) c) (mul b (inv b)) one (@group_mul_inv.{u} G one mul inv group_args b)) (@eq_congr_arg.{u,u} G G (fun (z : G) => mul z c) (mul (inv a) one) (inv a) (@group_mul_one.{u} G one mul inv group_args (inv a)))))