Theorems · Theorem · commutative algebra
MonomialOrder.degree_leadingTerm
∀ {σ : Type u_1} {m : MonomialOrder σ} {R : Type u_2} [inst : CommSemiring R] (f : MvPolynomial σ R),
m.degree (m.leadingTerm f) = m.degree fThe degree of f equals to the degree of leadingTerm f
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 88 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.
Cites9
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
- MonomialOrderstatement and proof · cited by 199
- MonomialOrder.degreestatement and proof · cited by 132
- MonomialOrder.leadingCoeffproof · cited by 72
- MonomialOrder.degree_zeroproof · cited by 29
- MonomialOrder.leadingTermstatement · cited by 29
- MonomialOrder.degree_monomialproof · cited by 12
Cited by2
Results whose statement or proof uses this declaration.
- MonomialOrder.degree_sub_leadingTerm_leproof · cited by 1
- MonomialOrder.withBotDegree_leadingTermproof · cited by 0