Theorems · Theorem · commutative algebra
MonomialOrder.degree_sub_LTerm_lt
∀ {σ : Type u_1} {m : MonomialOrder σ} {R : Type u_2} [inst : CommRing R] {f : MvPolynomial σ R},
m.degree f ≠ 0 → m.toSyn (m.degree (m.subLTerm f)) < m.toSyn (m.degree f)- Defined in
- Mathlib.RingTheory.MvPolynomial.Groebner
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
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.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Finsuppstatement and proof · cited by 5,255
- MvPolynomialstatement and proof · cited by 2,140
- AddEquivstatement · cited by 1,087
- sub_selfproof · cited by 996
- MvPolynomial.coeffproof · cited by 315
- MvPolynomial.monomialproof · cited by 253
- MonomialOrderstatement and proof · cited by 199
- MonomialOrder.degreestatement and proof · cited by 132
- MonomialOrder.synstatement · cited by 85
- MonomialOrder.toSynstatement and proof · cited by 82
Cited by1
Results whose statement or proof uses this declaration.
- MonomialOrder.divproof · cited by 2