Theorems · Theorem · commutative algebra
AddSubmonoid.smul_le_smul
∀ {R : Type u_2} {A : Type u_3} [inst : AddMonoid R] [inst_1 : AddMonoid A] [inst_2 : DistribSMul R A]
{M M' : AddSubmonoid R} {N P : AddSubmonoid A}, M ≤ M' → N ≤ P → M • N ≤ M' • P- Defined in
- Mathlib.Algebra.Ring.Submonoid.Pointwise
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- DistribSMulstatement and proof · cited by 117
- AddSubmonoid.smulstatement · cited by 11
- AddSubmonoid.smul_leproof · cited by 8
- AddSubmonoid.smul_mem_smulproof · cited by 8
Cited by4
Results whose statement or proof uses this declaration.
- Submodule.smul_monoproof · cited by 5
- AddSubmonoid.smul_le_smul_rightproof · cited by 3
- AddSubmonoid.smul_le_smul_leftproof · cited by 1
- AddSubmonoid.mul_le_mulproof · cited by 0