Theorems · Theorem · commutative algebra
MonomialOrder.withBotDegree_mul_of_left_mem_nonZeroDivisors
∀ {σ : Type u_1} {m : MonomialOrder σ} {R : Type u_2} [inst : CommSemiring R] {f g : MvPolynomial σ R},
m.leadingCoeff f ∈ nonZeroDivisors R → m.withBotDegree (f * g) = m.withBotDegree f + m.withBotDegree g- Cited by
- 2 results in Mathlib
- Foundations
- Depth 93 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.
Cites19
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
- Submonoidstatement · cited by 3,086
- MvPolynomialstatement and proof · cited by 2,140
- MulZeroClass.mul_zeroproof · cited by 2,091
- MulZeroClass.zero_mulproof · cited by 1,625
- WithBotstatement · cited by 1,498
- nonZeroDivisorsstatement and proof · cited by 895
- WithBot.someproof · cited by 541
- MonomialOrderstatement and proof · cited by 199
- MonomialOrder.degreeproof · cited by 132
Cited by2
Results whose statement or proof uses this declaration.
- MonomialOrder.withBotDegree_mul_of_right_mem_nonZeroDivisorsproof · cited by 0
- MonomialOrder.withBotDegree_mulproof · cited by 0