Theorems · Theorem · commutative algebra
MvPolynomial.mem_supported
∀ {σ : Type u_1} {R : Type u} [inst : CommSemiring R] {p : MvPolynomial σ R} {s : Set σ},
p ∈ MvPolynomial.supported R s ↔ ↑p.vars ⊆ s- Defined in
- Mathlib.Algebra.MvPolynomial.Supported
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 98 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.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · 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 · cited by 5,255
- MvPolynomialstatement and proof · cited by 2,140
- Subalgebrastatement and proof · cited by 1,353
- Subtype.val_injectiveproof · cited by 232
- Finset.coe_imageproof · cited by 222
- Subtype.range_coe_subtypeproof · cited by 170
- MvPolynomial.renameproof · cited by 168
Cited by4
Results whose statement or proof uses this declaration.
- MvPolynomial.mem_supported_varsproof · cited by 2
- MvPolynomial.exists_restrict_to_varsproof · cited by 1
- algebraicIndependent_of_finiteproof · cited by 1
- MvPolynomial.supported_eq_vars_subsetproof · cited by 0