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Theorems · Theorem · order theory

nsmul_le_nsmul_right

∀ {M : Type u_3} [inst : AddMonoid M] [inst_1 : Preorder M] [AddLeftMono M] [AddRightMono M] {a b : M},
  a ≤ b → ∀ (i : ℕ), i • a ≤ i • b
Defined in
Mathlib.Algebra.Order.Monoid.Unbundled.Pow
Cited by
16 results in Mathlib
Foundations
Depth 11 from the axioms · uses propext
Assumes
AddMonoidPreorderAddLeftMonoAddRightMono
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Polynomial.natDegree_comp_le · cited by 2Polynomial.natDegree_comp…Module.Basis.opNNNorm_le · cited by 2Basis.opNNNorm_leMvPowerSeries.trunc'_expand · cited by 2MvPowerSeries.trunc'_expa…num_le_nat_mul_den · cited by 1num_le_nat_mul_denFinset.sum_schlomilch_le · cited by 1Finset.sum_schlomilch_leMvPolynomial.degrees_indicator · cited by 1MvPolynomial.degrees_indi…Function.locallyFinsuppWithin.nsmul_negPart · cited by 1locallyFinsuppWithin.nsmu…Function.locallyFinsuppWithin.nsmul_posPart · cited by 1locallyFinsuppWithin.nsmu…Set.inter_nsmul_subset · cited by 1Set.inter_nsmul_subsetFinset.inter_nsmul_subset · cited by 0Finset.inter_nsmul_subsetMonovary.nsmul_left · cited by 0Monovary.nsmul_leftMonovaryOn.nsmul_left · cited by 0MonovaryOn.nsmul_leftMeasureTheory.Measure.sum_restrict_le · cited by 0Measure.sum_restrict_lensmul_le_nsmul · cited by 0nsmul_le_nsmulAntivary.nsmul_left · cited by 0Antivary.nsmul_leftPreorder · cited by 7952PreorderAddMonoid · cited by 2864AddMonoidAddLeftMono · cited by 687AddLeftMonoAddRightMono · cited by 367AddRightMononsmul_le_nsmul_rightCITED BYCITES

Cites4

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Cited by16

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