Theorems · Theorem · commutative algebra
LocalizedModule.mk_mul_mk
∀ {R : Type u} [inst : CommSemiring R] {S : Submonoid R} {A : Type u_3} [inst_1 : Semiring A] [inst_2 : Algebra R A]
{a₁ a₂ : A} {s₁ s₂ : ↥S}, LocalizedModule.mk a₁ s₁ * LocalizedModule.mk a₂ s₂ = LocalizedModule.mk (a₁ * a₂) (s₁ * s₂)- Cited by
- 5 results in Mathlib
- Foundations
- Depth 32 from the axioms · uses propext, Quot.sound
- Assumes
- CommSemiringSemiringAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Submonoidstatement and proof · cited by 3,086
- mul_commproof · cited by 2,262
- LocalizedModulestatement and proof · cited by 154
- LocalizedModule.mkstatement and proof · cited by 73
- LocalizedModule.mk_mul_mk'proof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.StructureSheaf.const_mulproof · cited by 2
- LocalizedModule.smul'_mulproof · cited by 0
- LocalizedModule.mk_powproof · cited by 0
- LocalizedModule.mul_smul'proof · cited by 0
- LocalizedModule.prod_mkproof · cited by 0