Theorems · Theorem · ring theory
SetLike.mul_mem_graded
∀ {ι : Type u_1} {R : Type u_2} {S : Type u_3} [inst : SetLike S R] [inst_1 : Mul R] [inst_2 : Add ι] {A : ι → S}
[SetLike.GradedMul A] ⦃i j : ι⦄ {gi gj : R}, gi ∈ A i → gj ∈ A j → gi * gj ∈ A (i + j)- Defined in
- Mathlib.Algebra.GradedMonoid
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLikestatement and proof · cited by 1,084
- SetLike.GradedMulstatement and proof · cited by 4
- SetLike.GradedMul.mul_memproof · cited by 4
Cited by22
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Proj.SpecMap_awayMap_awayιstatement and proof · cited by 5
- AlgebraicGeometry.Proj.pullbackAwayιIso_hom_awayιstatement · cited by 3
- CliffordAlgebra.even_inductionstatement and proof · cited by 3
- AlgebraicGeometry.Proj.pullbackAwayιIso_hom_SpecMap_awayMap_leftproof · cited by 2
- AlgebraicGeometry.Proj.pullbackAwayιIso_hom_SpecMap_awayMap_rightproof · cited by 2
- CliffordAlgebra.evenOdd_inductionstatement and proof · cited by 2
- HomogeneousLocalization.awayMap_mkstatement and proof · cited by 2
- HomogeneousLocalization.Away.isLocalization_mulproof · cited by 2
- AlgebraicGeometry.Proj.valuativeCriterion_existence_auxproof · cited by 1
- CliffordAlgebra.odd_inductionstatement and proof · cited by 1
- HomogeneousLocalization.range_awayMapAux_subsetproof · cited by 1
- SetLike.prod_mem_gradedproof · cited by 1