Theorems · Theorem · commutative algebra
MvPolynomial.disjoint_support_monomial
∀ {R : Type u} {σ : Type u_1} [inst : CommSemiring R] {a : σ →₀ ℕ} {p : MvPolynomial σ R} {s : R},
a ∉ p.support → s ≠ 0 → Disjoint ((MvPolynomial.monomial a) s).support p.support- Defined in
- Mathlib.Algebra.MvPolynomial.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHom.idstatement · cited by 18,349
- Finsetstatement · cited by 13,712
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- Finsuppstatement and proof · cited by 5,255
- Disjointstatement and proof · cited by 2,201
- MvPolynomialstatement and proof · cited by 2,140
- MvPolynomial.monomialstatement · cited by 253
- MvPolynomial.supportstatement and proof · cited by 220
- MvPolynomial.notMem_support_iffproof · cited by 12
- MvPolynomial.support_monomialproof · cited by 10
Cited by2
Results whose statement or proof uses this declaration.
- MvPolynomial.mem_range_map_iff_coeffs_subsetproof · cited by 5
- MvPolynomial.coeffs_mapproof · cited by 1