Theorems · Theorem · ring theory
SetLike.pow_mem_graded
∀ {ι : Type u_1} {R : Type u_2} {S : Type u_3} [inst : SetLike S R] [inst_1 : Monoid R] [inst_2 : AddMonoid ι]
{A : ι → S} [SetLike.GradedMonoid A] (n : ℕ) {r : R} {i : ι}, r ∈ A i → r ^ n ∈ A (n • i)- Defined in
- Mathlib.Algebra.GradedMonoid
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Monoidstatement and proof · cited by 3,887
- AddMonoidstatement and proof · cited by 2,864
- SetLikestatement and proof · cited by 1,084
- SetLike.GradedMonoidstatement and proof · cited by 48
Cited by16
Results whose statement or proof uses this declaration.
- SetLike.prod_pow_mem_gradedproof · cited by 4
- HomogeneousLocalization.Away.mk_surjectiveproof · cited by 2
- AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.mem_carrier_iff_of_memstatement and proof · cited by 2
- HomogeneousLocalization.Away.isLocalization_mulproof · cited by 2
- HomogeneousLocalization.Away.span_mk_prod_pow_eq_topproof · cited by 1
- AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.carrier.add_memproof · cited by 1
- AlgebraicGeometry.Proj.valuativeCriterion_existence_auxproof · cited by 1
- AlgebraicGeometry.ProjIsoSpecTopComponent.fromSpec_toSpecproof · cited by 1
- HomogeneousLocalization.range_awayMapAux_subsetproof · cited by 1
- AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.num_mem_carrier_iffproof · cited by 1
- AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec.image_basicOpen_eq_basicOpenstatement and proof · cited by 0