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Declaration
subgroup_inv_closed
Mathlib.Algebra.Group.Subgroup
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 (S : forall (x : G), Prop), forall (subgroup_args : @SubgroupLawArgs.{u} G one mul inv S), forall (a : G), forall (ha : S a), S (inv a)Proof term
fun G => fun one => fun mul => fun inv => fun S => fun subgroup_args => fun a => fun ha => subgroup_args (S (inv a)) (fun (one_mem : S one) => fun (mul_closed : forall (a : G), forall (b : G), forall (ha : S a), forall (hb : S b), S (mul a b)) => fun (inv_closed : forall (a : G), forall (ha : S a), S (inv a)) => inv_closed a ha)