Theorems · Theorem · commutative algebra
AddSubmonoid.addSubmonoid_smul_sup
∀ {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}, M • (N ⊔ P) = M • N ⊔ M • P- Defined in
- Mathlib.Algebra.Ring.Submonoid.Pointwise
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLike.coeproof · cited by 8,199
- AddMonoidstatement and proof · cited by 2,864
- le_antisymmproof · cited by 2,068
- AddSubmonoidstatement and proof · cited by 1,178
- smul_zeroproof · cited by 665
- le_sup_leftproof · cited by 265
- smul_addproof · cited by 263
- le_sup_rightproof · cited by 242
- AddMemClass.add_memproof · cited by 229
- AddSubmonoid.closureproof · cited by 224
- sup_leproof · cited by 159
- DistribSMulstatement and proof · cited by 117
Cited by2
Results whose statement or proof uses this declaration.
- Submodule.smul_supproof · cited by 3
- AddSubmonoid.mul_supproof · cited by 0