Theorems · Theorem · commutative algebra
MvPolynomial.vars_eq_empty_iff_eq_C
∀ {R : Type u} {σ : Type u_1} [inst : CommSemiring R] {p : MvPolynomial σ R},
p.vars = ∅ ↔ p = MvPolynomial.C (MvPolynomial.coeff 0 p)- Defined in
- Mathlib.Algebra.MvPolynomial.Variables
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
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Cites15
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
- RingHomstatement · cited by 10,189
- Finsuppstatement · cited by 5,255
- MvPolynomialstatement and proof · cited by 2,140
- MvPolynomial.Cstatement and proof · cited by 400
- Multiset.cardproof · cited by 375
- MvPolynomial.coeffstatement and proof · cited by 315
- MvPolynomial.varsstatement and proof · cited by 79
- MvPolynomial.degreesproof · cited by 51
- MvPolynomial.vars_defproof · cited by 11
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