Theorems · Theorem · commutative algebra
MonomialOrder.degree_mul_lt_iff_left_lt_of_ne_zero
∀ {σ : Type u_1} {m : MonomialOrder σ} {R : Type u_2} [inst : CommSemiring R] [NoZeroDivisors R]
{p p' q : MvPolynomial σ R},
p ≠ 0 →
q ≠ 0 → (m.toSyn (m.degree (p * q)) < m.toSyn (m.degree (p' * q)) ↔ m.toSyn (m.degree p) < m.toSyn (m.degree p'))- Cited by
- 0 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringNoZeroDivisors
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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
- CommSemiringstatement and proof · cited by 10,911
- Finsuppstatement · cited by 5,255
- MvPolynomialstatement and proof · cited by 2,140
- map_zeroproof · cited by 1,614
- AddEquivstatement · cited by 1,087
- map_addproof · cited by 964
- NoZeroDivisorsstatement and proof · cited by 545
- MonomialOrderstatement and proof · cited by 199
- MonomialOrder.degreestatement and proof · cited by 132
- MonomialOrder.synstatement · cited by 85
- MonomialOrder.toSynstatement and proof · cited by 82
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