Theorems · Theorem · group theory
AddSubgroup.relIndex_eq_zero_of_le_left
∀ {G : Type u_1} [inst : AddGroup G] {H K L : AddSubgroup G}, H ≤ K → K.relIndex L = 0 → H.relIndex L = 0- Defined in
- Mathlib.GroupTheory.Index
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 100 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.
Cites5
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.relIndexstatement and proof · cited by 67
- eq_zero_of_zero_dvdproof · cited by 13
- AddSubgroup.relIndex_dvd_of_le_leftproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- AddSubgroup.relIndex_ne_zero_transproof · cited by 2
- AddSubgroup.relIndex_iInf_leproof · cited by 1
- AddSubgroup.relIndex_inf_leproof · cited by 1