Theorems · Theorem · order theory
zsmul_lt_zsmul_iff_left
∀ {α : Type u_1} [inst : AddCommGroup α] [inst_1 : PartialOrder α] [IsOrderedAddMonoid α] {m n : ℤ} {a : α},
0 < a → (m • a < n • a ↔ m < n)- Defined in
- Mathlib.Algebra.Order.Group.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 34 from the axioms · uses propext
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.
- AddCommGroupstatement and proof · cited by 12,871
- PartialOrderstatement and proof · cited by 6,410
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- StrictMono.lt_iff_ltproof · cited by 86
- zsmul_left_strictMonoproof · cited by 8
Cited by6
Results whose statement or proof uses this declaration.
- Set.pairwise_disjoint_Ioc_add_zsmulproof · cited by 3
- existsUnique_zsmul_near_of_posproof · cited by 3
- AddSubgroup.exists_isLeast_posproof · cited by 2
- Set.pairwise_disjoint_Ico_add_zsmulproof · cited by 2
- not_isAddCyclic_of_denselyOrderedproof · cited by 1
- denseRange_zsmul_iff_surjectiveproof · cited by 1