Theorems · Theorem · commutative algebra
MonomialOrder.coeff_degree_ne_zero_iff
∀ {σ : Type u_1} {m : MonomialOrder σ} {R : Type u_2} [inst : CommSemiring R] {f : MvPolynomial σ R},
MvPolynomial.coeff (m.degree f) f ≠ 0 ↔ f ≠ 0- Cited by
- 3 results in Mathlib
- Foundations
- Depth 85 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.
Cites7
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
- MvPolynomialstatement and proof · cited by 2,140
- MvPolynomial.coeffstatement · cited by 315
- MonomialOrderstatement and proof · cited by 199
- MonomialOrder.degreestatement · cited by 132
- MonomialOrder.leadingCoeff_ne_zero_iffproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- MonomialOrder.degree_mem_supportproof · cited by 2
- MonomialOrder.degree_sub_LTerm_ltproof · cited by 1
- MonomialOrder.degree_mem_support_iffproof · cited by 0