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Theorems · Theorem · group theory

IsPGroup.to_le

∀ {p : ℕ} {G : Type u_1} [inst : Group G] {H K : Subgroup G}, IsPGroup p ↥K → H ≤ K → IsPGroup p ↥H
Defined in
Mathlib.GroupTheory.PGroup
Cited by
5 results in Mathlib
Foundations
Depth 27 from the axioms · uses propext, Quot.sound
Assumes
Group
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Sylow.iSup_of_normal · cited by 1Sylow.iSup_of_normalIsPGroup.to_inf_left · cited by 1IsPGroup.to_inf_leftSylow.finite_of_finiteIndex · cited by 1Sylow.finite_of_finiteInd…IsPGroup.to_inf_right · cited by 0IsPGroup.to_inf_rightMonoidHom.ker_transferSylow_disjoint · cited by 0MonoidHom.ker_transferSyl…DFunLike.coe · cited by 62936DFunLike.coeGroup · cited by 6238GroupSubgroup · cited by 3593SubgroupIsPGroup · cited by 96IsPGroupSubgroup.inclusion · cited by 21Subgroup.inclusionIsPGroup.of_injective · cited by 2IsPGroup.of_injectiveIsPGroup.to_leCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by5

Results whose statement or proof uses this declaration.