Theorems · Theorem · commutative algebra
MonomialOrder.withBotDegree_mul
∀ {σ : Type u_1} {m : MonomialOrder σ} {R : Type u_2} [inst : CommSemiring R] (f g : MvPolynomial σ R)
[NoZeroDivisors R], m.withBotDegree (f * g) = m.withBotDegree f + m.withBotDegree g- Cited by
- 0 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringNoZeroDivisors
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- Finsuppstatement · cited by 5,255
- Bot.botproof · cited by 4,720
- Nontrivialproof · cited by 2,416
- MvPolynomialstatement and proof · cited by 2,140
- MulZeroClass.zero_mulproof · cited by 1,625
- WithBotstatement · cited by 1,498
- NoZeroDivisorsstatement and proof · cited by 545
- MonomialOrderstatement and proof · cited by 199
- mem_nonZeroDivisors_iff_ne_zeroproof · cited by 38
- Subsingleton.eq_zeroproof · cited by 32
- MonomialOrder.withBotDegreestatement and proof · cited by 26
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