Theorems · Theorem · commutative algebra
MvPolynomial.aeval_ite_mem_eq_self
∀ {R : Type u} {σ : Type u_1} [inst : CommSemiring R] (q : MvPolynomial σ R) {s : Set σ},
↑q.vars ⊆ s →
∀ [inst_1 : (i : σ) → Decidable (i ∈ s)], (MvPolynomial.aeval fun i => if i ∈ s then MvPolynomial.X i else 0) q = q- Defined in
- Mathlib.Algebra.MvPolynomial.Variables
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringDecidable
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Finsetstatement · cited by 13,712
- CommSemiringstatement and proof · cited by 10,911
- SetLike.coestatement and proof · cited by 8,199
- Finsuppstatement and proof · cited by 5,255
- Finset.sumproof · cited by 5,195
- Algebra.algebraMapproof · cited by 4,706
- AlgHomstatement · cited by 3,236
- Finset.sum_congrproof · cited by 2,323
- MvPolynomialstatement and proof · cited by 2,140
- Finsupp.supportproof · cited by 828
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.compactSpace_of_universallyClosedproof · cited by 1