Theorems · Theorem · commutative algebra
MvPolynomial.le_degreeOf_of_mem_support
∀ {R : Type u} {σ : Type u_1} [inst : CommSemiring R] {p : MvPolynomial σ R} (i : σ) {s : σ →₀ ℕ},
s ∈ p.support → s i ≤ MvPolynomial.degreeOf i p- Defined in
- Mathlib.Algebra.MvPolynomial.Degrees
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 78 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.
Cites11
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 · cited by 13,712
- CommSemiringstatement and proof · cited by 10,911
- Finsuppstatement and proof · cited by 5,255
- MvPolynomialstatement and proof · cited by 2,140
- le_reflproof · cited by 2,061
- MvPolynomial.supportstatement and proof · cited by 220
- eq_or_lt_of_leproof · cited by 92
- MvPolynomial.degreeOfstatement and proof · cited by 53
- MvPolynomial.degreeOf_eq_supproof · cited by 15
- Finset.le_sup_iffproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- MvPolynomial.degreeOf_add_eq_of_degreeOf_ltproof · cited by 1
- MvPolynomial.notMem_support_of_degreeOf_ltproof · cited by 0