Theorems · Theorem · group theory
AddSubgroup.relIndex_ne_zero_trans
∀ {G : Type u_1} [inst : AddGroup G] {H K L : AddSubgroup G}, H.relIndex K ≠ 0 → K.relIndex L ≠ 0 → H.relIndex L ≠ 0- Defined in
- Mathlib.GroupTheory.Index
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 101 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.
Cites8
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
- inf_le_leftproof · cited by 286
- mul_ne_zeroproof · cited by 178
- AddSubgroup.relIndexstatement and proof · cited by 67
- AddSubgroup.relIndex_eq_zero_of_le_rightproof · cited by 5
- AddSubgroup.relIndex_eq_zero_of_le_leftproof · cited by 3
- AddSubgroup.relIndex_inf_mul_relIndexproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- AddSubgroup.relIndex_inf_ne_zeroproof · cited by 1
- AddSubgroup.Commensurable.transproof · cited by 1