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Declaration
group_mul_assoc
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 a b) c) (mul a (mul b c))Proof term
fun G => fun one => fun mul => fun inv => fun group_args => fun a => fun b => fun c => group_args (@Eq.{u} G (mul (mul a b) c) (mul a (mul b c))) (fun (mul_assoc_arg : forall (a : G), forall (b : G), forall (c : G), @Eq.{u} G (mul (mul a b) c) (mul a (mul b c))) => fun (one_mul_arg : forall (a : G), @Eq.{u} G (mul one a) a) => fun (mul_one_arg : forall (a : G), @Eq.{u} G (mul a one) a) => fun (inv_mul_arg : forall (a : G), @Eq.{u} G (mul (inv a) a) one) => fun (mul_inv_arg : forall (a : G), @Eq.{u} G (mul a (inv a)) one) => mul_assoc_arg a b c)