Theorems · Theorem · commutative algebra
MonomialOrder.degree_le_iff
∀ {σ : Type u_1} {m : MonomialOrder σ} {R : Type u_2} [inst : CommSemiring R] {f : MvPolynomial σ R} {d : σ →₀ ℕ},
m.toSyn (m.degree f) ≤ m.toSyn d ↔ ∀ c ∈ f.support, m.toSyn c ≤ m.toSyn d- Cited by
- 3 results in Mathlib
- Foundations
- Depth 71 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.
Cites14
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
- AddEquivstatement · cited by 1,087
- Finset.supproof · cited by 530
- MvPolynomial.coeffproof · cited by 315
- MvPolynomial.supportstatement and proof · cited by 220
- MonomialOrderstatement and proof · cited by 199
- MonomialOrder.degreestatement · cited by 132
- MonomialOrder.synstatement · cited by 85
Cited by3
Results whose statement or proof uses this declaration.
- MonomialOrder.degree_mul_leproof · cited by 10
- MonomialOrder.degree_add_leproof · cited by 5
- MonomialOrder.degree_eq_zero_iff_totalDegree_eq_zeroproof · cited by 1