Theorems · Theorem · order theory
nsmul_le_nsmul_left
∀ {M : Type u_3} [inst : AddMonoid M] [inst_1 : Preorder M] [AddLeftMono M] {a : M} {n m : ℕ},
0 ≤ a → n ≤ m → n • a ≤ m • a- Cited by
- 11 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddMonoidPreorderAddLeftMono
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement and proof · cited by 7,952
- AddMonoidstatement and proof · cited by 2,864
- AddLeftMonostatement and proof · cited by 687
- nsmul_left_monotoneproof · cited by 3
Cited by11
Results whose statement or proof uses this declaration.
- Filter.Tendsto.nsmul_atTopproof · cited by 4
- le_self_nsmulproof · cited by 3
- AddSubgroup.exists_isLeast_posproof · cited by 2
- BoxIntegral.HasIntegral.of_bRiemann_eq_false_of_forall_isLittleOproof · cited by 2
- Set.Icc.monotone_addNSMulproof · cited by 2
- Set.Icc.addNSMul_eq_rightproof · cited by 2
- Filter.Tendsto.atTop_nsmul_constproof · cited by 1
- AddCircle.isAddFundamentalDomain_of_ae_ballproof · cited by 1
- MeasureTheory.Measure.sum_restrict_leproof · cited by 0
- nsmul_le_nsmulproof · cited by 0
- nsmul_le_nsmul_left_of_nonposproof · cited by 0