Theorems · Theorem · commutative algebra
MonomialOrder.leadingCoeff_zero
∀ {σ : Type u_1} {m : MonomialOrder σ} {R : Type u_2} [inst : CommSemiring R], m.leadingCoeff 0 = 0- Cited by
- 14 results in Mathlib
- Foundations
- Depth 82 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.
Cites11
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
- Finsuppstatement · cited by 5,255
- MvPolynomialstatement · cited by 2,140
- map_zeroproof · cited by 1,614
- AddEquiv.symmproof · cited by 530
- MvPolynomial.coeffproof · cited by 315
- MonomialOrderstatement and proof · cited by 199
- MonomialOrder.toSynproof · cited by 82
- MonomialOrder.leadingCoeffstatement · cited by 72
- Finset.sup_emptyproof · cited by 72
Cited by14
Results whose statement or proof uses this declaration.
- MonomialOrder.sPolynomial_left_zeroproof · cited by 5
- MonomialOrder.leadingCoeff_ne_zero_iffproof · cited by 5
- MonomialOrder.sPolynomial_monomial_mulproof · cited by 3
- MonomialOrder.leadingCoeff_mulproof · cited by 2
- MonomialOrder.sPolynomial_decompositionproof · cited by 1
- MonomialOrder.leadingCoeff_mul_of_left_mem_nonZeroDivisorsproof · cited by 1
- MonomialOrder.leadingTerm_eq_leadingTerm_iffproof · cited by 0
- MonomialOrder.leadingTerm_leadingTermproof · cited by 0
- MonomialOrder.leadingTerm_monomialproof · cited by 0
- MonomialOrder.sPolynomial_leadingTerm_mul'proof · cited by 0
- MonomialOrder.Monic.ne_zeroproof · cited by 0
- MonomialOrder.leadingCoeff_mul_of_isRegular_leftproof · cited by 0