Theorems · Theorem · commutative algebra
AddSubmonoid.smul_subset_smul
∀ {R : Type u_2} {A : Type u_3} [inst : AddMonoid R] [inst_1 : AddMonoid A] [inst_2 : DistribSMul R A]
{M : AddSubmonoid R} {N : AddSubmonoid A}, ↑M • ↑N ⊆ ↑(M • N)- Defined in
- Mathlib.Algebra.Ring.Submonoid.Pointwise
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- SetLike.coestatement and proof · cited by 8,199
- AddMonoidstatement and proof · cited by 2,864
- AddSubmonoidstatement and proof · cited by 1,178
- DistribSMulstatement and proof · cited by 117
- Set.smulstatement · cited by 110
- AddSubmonoid.smulstatement · cited by 11
- AddSubmonoid.smul_mem_smulproof · cited by 8
- Set.smul_subset_iffproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- Submodule.smul_subset_smulproof · cited by 1
- AddSubmonoid.mul_subset_mulproof · cited by 0