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Theorems · Theorem · group theory

Subgroup.isCyclic_of_le

∀ {G : Type u_2} [inst : Group G] {H H' : Subgroup G}, H ≤ H' → ∀ [IsCyclic ↥H'], IsCyclic ↥H
Defined in
Mathlib.GroupTheory.SpecificGroups.Cyclic.Basic
Cited by
3 results in Mathlib
Foundations
Depth 50 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
GroupIsCyclic
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Around this declaration

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

HasEnoughRootsOfUnity.of_dvd · cited by 5HasEnoughRootsOfUnity.of_…IsPGroup.isCyclic_of_isZGroup · cited by 1IsPGroup.isCyclic_of_isZG…Subgroup.le_zpowers_iff · cited by 0Subgroup.le_zpowers_iffGroup · cited by 6238GroupSubgroup · cited by 3593SubgroupIsCyclic · cited by 122IsCyclicSubgroup.inclusion · cited by 21Subgroup.inclusionSubgroup.inclusion_injective · cited by 4Subgroup.inclusion_inject…isCyclic_of_injective · cited by 2isCyclic_of_injectiveSubgroup.isCyclic_of_leCITED BYCITES

Cites6

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Cited by3

Results whose statement or proof uses this declaration.