Theorems · Theorem · group theory
AddSubgroup.index_dvd_of_le
∀ {G : Type u_1} [inst : AddGroup G] {H K : AddSubgroup G}, H ≤ K → K.index ∣ H.index- Defined in
- Mathlib.GroupTheory.Index
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- AddSubgroup.indexstatement · cited by 104
- AddSubgroup.relIndexproof · cited by 67
- dvd_of_mul_left_eqproof · cited by 14
- AddSubgroup.relIndex_mul_indexproof · cited by 12
Cited by3
Results whose statement or proof uses this declaration.
- AddSubgroup.finiteIndex_of_leproof · cited by 1
- AddSubgroup.index_antitoneproof · cited by 1
- AddSubgroup.index_map_dvdproof · cited by 1