NPAへ戻る
Declaration
group_conj_slide
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 (k : G), forall (n : G), @Eq.{u} G (mul k (mul (mul (inv k) n) k)) (mul n k)Proof term
fun G => fun one => fun mul => fun inv => fun group_args => fun k => fun n => @eq_trans.{u} G (mul k (mul (mul (inv k) n) k)) (mul (mul k (mul (inv k) n)) k) (mul n k) (@eq_symm.{u} G (mul (mul k (mul (inv k) n)) k) (mul k (mul (mul (inv k) n) k)) (@group_mul_assoc.{u} G one mul inv group_args k (mul (inv k) n) k)) (@eq_trans.{u} G (mul (mul k (mul (inv k) n)) k) (mul (mul (mul k (inv k)) n) k) (mul n k) (@eq_congr_arg.{u,u} G G (fun (z : G) => mul z k) (mul k (mul (inv k) n)) (mul (mul k (inv k)) n) (@eq_symm.{u} G (mul (mul k (inv k)) n) (mul k (mul (inv k) n)) (@group_mul_assoc.{u} G one mul inv group_args k (inv k) n))) (@eq_trans.{u} G (mul (mul (mul k (inv k)) n) k) (mul (mul one n) k) (mul n k) (@eq_congr_arg.{u,u} G G (fun (z : G) => mul (mul z n) k) (mul k (inv k)) one (@group_mul_inv.{u} G one mul inv group_args k)) (@eq_congr_arg.{u,u} G G (fun (z : G) => mul z k) (mul one n) n (@group_one_mul.{u} G one mul inv group_args n))))