Theorems · Theorem · group theory
AddSubmonoid.multiples_le
∀ {M : Type u_1} [inst : AddMonoid M] {n : M} {P : AddSubmonoid M}, AddSubmonoid.multiples n ≤ P ↔ n ∈ P- Cited by
- 4 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddMonoid
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.
- AddMonoidstatement and proof · cited by 2,864
- AddSubmonoidstatement and proof · cited by 1,178
- SetLike.mem_coeproof · cited by 302
- Set.singleton_subset_iffproof · cited by 206
- AddSubmonoid.multiplesstatement · cited by 40
- AddSubmonoid.closure_leproof · cited by 35
- AddSubmonoid.multiples_eq_closureproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- topologicalClosure_addSubgroupClosure_toAddSubmonoidproof · cited by 1
- AddSubgroup.closure_toAddSubmonoid_of_isOfFinAddOrderproof · cited by 1
- AddSubmonoid.multiples_zeroproof · cited by 0
- AddSubmonoid.addOrderOf_le_cardproof · cited by 0