CorrespondenceSubgroupSaturationEvidence

Mathlib.Algebra.Group.Correspondence

Packages

Module

Theorem

750

Declarations

1016

信頼境界外の sidecar

Source text や表示 overlay は提示用メタデータです。信頼する証拠は署名済み証明書と checker の結果です。

Statement

forall (G : Sort succ u), forall (one : G), forall (mul : forall (a : G), forall (b : G), G), forall (inv : forall (a : G), G), forall (N : forall (x : G), Prop), forall (Hpred : forall (x : G), Prop), forall (group_args : @GroupLawArgs.{succ u} G one mul inv), forall (n_normal : @NormalSubgroupLawArgs.{succ u} G one mul inv N), forall (h_args : @SubgroupLawArgs.{succ u} G one mul inv Hpred), forall (n_le_h : forall (x : G), forall (hn : N x), Hpred x), Prop

Proof term

inductive CorrespondenceSubgroupSaturationEvidence.{u} : forall (G : Sort succ u), forall (one : G), forall (mul : forall (a : G), forall (b : G), G), forall (inv : forall (a : G), G), forall (N : forall (x : G), Prop), forall (Hpred : forall (x : G), Prop), forall (group_args : @GroupLawArgs.{succ u} G one mul inv), forall (n_normal : @NormalSubgroupLawArgs.{succ u} G one mul inv N), forall (h_args : @SubgroupLawArgs.{succ u} G one mul inv Hpred), forall (n_le_h : forall (x : G), forall (hn : N x), Hpred x), Prop where | mk : forall (G : Sort succ u), forall (one : G), forall (mul : forall (a : G), forall (b : G), G), forall (inv : forall (a : G), G), forall (N : forall (x : G), Prop), forall (Hpred : forall (x : G), Prop), forall (group_args : @GroupLawArgs.{succ u} G one mul inv), forall (n_normal : @NormalSubgroupLawArgs.{succ u} G one mul inv N), forall (h_args : @SubgroupLawArgs.{succ u} G one mul inv Hpred), forall (n_le_h : forall (x : G), forall (hn : N x), Hpred x), forall (subgroup_to_preimage_image : forall (x : G), forall (hx : Hpred x), @CorrespondencePreimagePred.{u} G one mul inv N group_args n_normal (@CorrespondenceImagePred.{u} G one mul inv N Hpred group_args n_normal) x), forall (subgroup_to_saturation : forall (x : G), forall (hx : Hpred x), @CorrespondenceSaturationPred.{u} G one mul inv N Hpred x), forall (saturation_to_subgroup : forall (x : G), forall (hx : @CorrespondenceSaturationPred.{u} G one mul inv N Hpred x), Hpred x), @CorrespondenceSubgroupSaturationEvidence.{u} G one mul inv N Hpred group_args n_normal h_args n_le_h