Theorems · Theorem · commutative algebra
MonomialOrder.withBotDegree_le_withBotDegree_iff
∀ {σ : Type u_1} {m : MonomialOrder σ} {R : Type u_2} [inst : CommSemiring R] (f g : MvPolynomial σ R),
m.toWithBotSyn (m.withBotDegree f) ≤ m.toWithBotSyn (m.withBotDegree g) ↔
m.toSyn (m.degree f) ≤ m.toSyn (m.degree g) ∧ (g = 0 → f = 0)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
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Cites17
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
- Bot.botproof · cited by 4,720
- MvPolynomialstatement and proof · cited by 2,140
- map_zeroproof · cited by 1,614
- WithBotstatement · cited by 1,498
- AddEquivstatement · cited by 1,087
- WithBot.someproof · cited by 541
- MonomialOrderstatement and proof · cited by 199
- MonomialOrder.degreestatement and proof · cited by 132
- MonomialOrder.synstatement · cited by 85
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