Theorems · Theorem · commutative algebra
MonomialOrder.le_degree
∀ {σ : Type u_1} {m : MonomialOrder σ} {R : Type u_2} [inst : CommSemiring R] {f : MvPolynomial σ R} {d : σ →₀ ℕ},
d ∈ f.support → m.toSyn d ≤ m.toSyn (m.degree f)- Cited by
- 11 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.
Cites16
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
- OrderBotproof · cited by 1,055
- SemilatticeSupproof · cited by 785
- Finset.supproof · cited by 530
- MvPolynomial.supportstatement and proof · cited by 220
- MonomialOrderstatement and proof · cited by 199
- MonomialOrder.degreestatement · cited by 132
Cited by11
Results whose statement or proof uses this declaration.
- MonomialOrder.degree_add_of_ltproof · cited by 6
- MonomialOrder.coeff_eq_zero_of_ltproof · cited by 6
- MonomialOrder.degree_mul_of_mul_leadingCoeff_ne_zeroproof · cited by 5
- MonomialOrder.degree_add_leproof · cited by 5
- MonomialOrder.degree_pow_of_pow_leadingCoeff_ne_zeroproof · cited by 2
- MonomialOrder.degree_prod_of_mem_nonZeroDivisorsproof · cited by 1
- MonomialOrder.degree_prod_of_regularproof · cited by 1
- MonomialOrder.degree_smul_of_mem_nonZeroDivisorsproof · cited by 1
- MvPolynomial.degree_degLexDegreeproof · cited by 1
- MonomialOrder.degree_prodproof · cited by 0
- MonomialOrder.le_withBotDegreeproof · cited by 0