Theorems · Theorem · commutative algebra
MvPolynomial.support_expand_subset
∀ {σ : Type u_1} {R : Type u_3} [inst : CommSemiring R] {p : ℕ} (φ : MvPolynomial σ R) [inst_1 : DecidableEq σ],
((MvPolynomial.expand p) φ).support ⊆ Finset.image (fun x => p • x) φ.support- Defined in
- Mathlib.Algebra.MvPolynomial.Expand
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringDecidableEq
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.
- DFunLike.coestatement and proof · cited by 62,936
- Finsetstatement and proof · cited by 13,712
- CommSemiringstatement and proof · cited by 10,911
- Finsuppstatement and proof · cited by 5,255
- Finset.sumproof · cited by 5,195
- AlgHomstatement · cited by 3,236
- LE.le.transproof · cited by 3,151
- Finset.sum_congrproof · cited by 2,323
- MvPolynomialstatement and proof · cited by 2,140
- Finset.imagestatement and proof · cited by 910
- map_sumproof · cited by 455
- MvPolynomial.coeffproof · cited by 315
Cited by2
Results whose statement or proof uses this declaration.
- MvPolynomial.coeff_expand_of_not_dvdproof · cited by 2
- MvPolynomial.support_expandproof · cited by 1