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Theorems · Theorem · commutative algebra

AddSubmonoid.smul_le_smul_right

∀ {R : Type u_2} {A : Type u_3} [inst : AddMonoid R] [inst_1 : AddMonoid A] [inst_2 : DistribSMul R A]
  {M : AddSubmonoid R} {N P : AddSubmonoid A}, N ≤ P → M • N ≤ M • P
Defined in
Mathlib.Algebra.Ring.Submonoid.Pointwise
Cited by
3 results in Mathlib
Foundations
Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddMonoidAddMonoidDistribSMul
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Around this declaration

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

AddSubmonoid.smul_iSup · cited by 2AddSubmonoid.smul_iSupAddSubmonoid.addSubmonoid_smul_sup · cited by 2AddSubmonoid.addSubmonoid…AddSubmonoid.mul_le_mul_right · cited by 0AddSubmonoid.mul_le_mul_r…AddMonoid · cited by 2864AddMonoidle_rfl · cited by 1558le_rflAddSubmonoid · cited by 1178AddSubmonoidDistribSMul · cited by 117DistribSMulAddSubmonoid.smul · cited by 11AddSubmonoid.smulAddSubmonoid.smul_le_smul · cited by 4AddSubmonoid.smul_le_smulAddSubmonoid.smul_le_smul_rig…CITED BYCITES

Cites6

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Cited by3

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