Theorems · Theorem · commutative algebra
MonomialOrder.withBotDegree_monomial
∀ {σ : Type u_1} {m : MonomialOrder σ} {R : Type u_2} [inst : CommSemiring R] (d : σ →₀ ℕ) (c : R)
[inst_1 : Decidable (c = 0)], m.withBotDegree ((MvPolynomial.monomial d) c) = if c = 0 then ⊥ else ↑d- Cited by
- 1 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringDecidable
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
- RingHom.idstatement · cited by 18,349
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- Finsuppstatement and proof · cited by 5,255
- Bot.botstatement and proof · cited by 4,720
- MvPolynomialstatement · cited by 2,140
- WithBotstatement · cited by 1,498
- WithBot.somestatement and proof · cited by 541
- MvPolynomial.monomialstatement and proof · cited by 253
- MonomialOrderstatement and proof · cited by 199
- MonomialOrder.degreeproof · cited by 132
Cited by1
Results whose statement or proof uses this declaration.
- MonomialOrder.withBotDegree_Cproof · cited by 0