Theorems · Theorem · commutative algebra
MvPolynomial.vars_def
∀ {R : Type u} {σ : Type u_1} [inst : CommSemiring R] [inst_1 : DecidableEq σ] (p : MvPolynomial σ R),
p.vars = p.degrees.toFinset- Defined in
- Mathlib.Algebra.MvPolynomial.Variables
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 76 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- CommSemiringstatement and proof · cited by 10,911
- Multisetproof · cited by 2,627
- MvPolynomialstatement and proof · cited by 2,140
- Multiset.toFinsetstatement and proof · cited by 230
- Classical.decEqproof · cited by 134
- MvPolynomial.varsstatement · cited by 79
- MvPolynomial.degreesstatement and proof · cited by 51
Cited by11
Results whose statement or proof uses this declaration.
- MvPolynomial.mem_vars_iff_mem_supportproof · cited by 9
- MvPolynomial.vars_mulproof · cited by 6
- MvPolynomial.vars_monomialproof · cited by 4
- MvPolynomial.vars_Cproof · cited by 4
- MvPolynomial.vars_add_subsetproof · cited by 3
- MvPolynomial.vars_renameproof · cited by 3
- MvPolynomial.vars_0proof · cited by 2
- MvPolynomial.vars_add_of_disjointproof · cited by 2
- MvPolynomial.vars_mapproof · cited by 1
- MvPolynomial.vars_eq_empty_iff_eq_Cproof · cited by 0
- MvPolynomial.mem_vars_iff_degreeOf_ne_zeroproof · cited by 0