Theorems · Theorem · commutative algebra
MonomialOrder.leadingCoeff_ne_zero_iff
∀ {σ : Type u_1} {m : MonomialOrder σ} {R : Type u_2} [inst : CommSemiring R] {f : MvPolynomial σ R},
m.leadingCoeff f ≠ 0 ↔ f ≠ 0- Cited by
- 5 results in Mathlib
- Foundations
- Depth 84 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.
- DFunLike.coeproof · cited by 62,936
- CommSemiringstatement and proof · cited by 10,911
- SetLike.coeproof · cited by 8,199
- Set.imageproof · cited by 5,609
- Finsuppstatement and proof · cited by 5,255
- MvPolynomialstatement and proof · cited by 2,140
- AddEquiv.symmproof · cited by 530
- Finset.supproof · cited by 530
- MvPolynomial.supportproof · cited by 220
- MonomialOrderstatement and proof · cited by 199
- MonomialOrder.synproof · cited by 85
- MonomialOrder.toSynproof · cited by 82
Cited by5
Results whose statement or proof uses this declaration.
- MonomialOrder.degree_add_of_ltproof · cited by 6
- MonomialOrder.coeff_degree_ne_zero_iffproof · cited by 3
- MonomialOrder.degree_powproof · cited by 1
- MonomialOrder.degree_smul_of_mem_nonZeroDivisorsproof · cited by 1
- MonomialOrder.withBotDegree_mulproof · cited by 0