Theorems · Theorem · group theory
AddSubgroup.zmultiples_le
∀ {G : Type u_1} [inst : AddGroup G] {g : G} {H : AddSubgroup G}, AddSubgroup.zmultiples g ≤ H ↔ g ∈ H- Cited by
- 7 results in Mathlib
- Foundations
- Depth 73 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.
Cites7
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.zmultiplesstatement · cited by 493
- SetLike.mem_coeproof · cited by 302
- Set.singleton_subset_iffproof · cited by 206
- AddSubgroup.closure_leproof · cited by 30
- AddSubgroup.zmultiples_eq_closureproof · cited by 9
Cited by7
Results whose statement or proof uses this declaration.
- AddSubgroup.zmultiples_negproof · cited by 6
- AddSubgroup.zmultiples_eq_botproof · cited by 5
- AddMonoid.le_minOrder_iff_forall_addSubgroupproof · cited by 2
- MeasureTheory.vadd_ae_eq_self_of_mem_zmultiplesproof · cited by 1
- AddSubgroup.zmultiples_le_of_memproof · cited by 1
- ergodic_vadd_of_denseRange_zsmulproof · cited by 1
- Subgroup.isRegularAtInfty_iffproof · cited by 0