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Declaration
group_product_inv_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 (h : G), forall (n : G), @Eq.{u} G (mul (inv h) (mul (mul h (inv n)) (inv h))) (inv (mul h n))Proof term
fun G => fun one => fun mul => fun inv => fun group_args => fun h => fun n => @eq_trans.{u} G (mul (inv h) (mul (mul h (inv n)) (inv h))) (mul (mul (inv h) (mul h (inv n))) (inv h)) (inv (mul h n)) (@eq_symm.{u} G (mul (mul (inv h) (mul h (inv n))) (inv h)) (mul (inv h) (mul (mul h (inv n)) (inv h))) (@group_mul_assoc.{u} G one mul inv group_args (inv h) (mul h (inv n)) (inv h))) (@eq_trans.{u} G (mul (mul (inv h) (mul h (inv n))) (inv h)) (mul (mul (mul (inv h) h) (inv n)) (inv h)) (inv (mul h n)) (@eq_congr_arg.{u,u} G G (fun (z : G) => mul z (inv h)) (mul (inv h) (mul h (inv n))) (mul (mul (inv h) h) (inv n)) (@eq_symm.{u} G (mul (mul (inv h) h) (inv n)) (mul (inv h) (mul h (inv n))) (@group_mul_assoc.{u} G one mul inv group_args (inv h) h (inv n)))) (@eq_trans.{u} G (mul (mul (mul (inv h) h) (inv n)) (inv h)) (mul (mul one (inv n)) (inv h)) (inv (mul h n)) (@eq_congr_arg.{u,u} G G (fun (z : G) => mul (mul z (inv n)) (inv h)) (mul (inv h) h) one (@group_inv_mul.{u} G one mul inv group_args h)) (@eq_trans.{u} G (mul (mul one (inv n)) (inv h)) (mul (inv n) (inv h)) (inv (mul h n)) (@eq_congr_arg.{u,u} G G (fun (z : G) => mul z (inv h)) (mul one (inv n)) (inv n) (@group_one_mul.{u} G one mul inv group_args (inv n))) (@group_mul_inv_rev.{u} G one mul inv group_args h n))))