Theorems · Theorem · commutative algebra

MonomialOrder.degree_reduce_lt

∀ {σ : Type u_1} {m : MonomialOrder σ} {R : Type u_2} [inst : CommRing R] {f b : MvPolynomial σ R}
  (hb : IsUnit (m.leadingCoeff b)),
  m.degree b ≤ m.degree f → m.degree f ≠ 0 → m.toSyn (m.degree (m.reduce hb f)) < m.toSyn (m.degree f)

Defined in: Mathlib.RingTheory.MvPolynomial.Groebner
Cited by: 1 results in Mathlib
Foundations: Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites33

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
one_mulproof · cited by 2,841
mul_commproof · cited by 2,262
MvPolynomialstatement and proof · cited by 2,140
Units.valproof · cited by 1,966
mul_assocproof · cited by 1,667
IsUnitstatement and proof · cited by 1,602
AddEquivstatement · cited by 1,087
le_transproof · cited by 985
Finsupp.extproof · cited by 399

Cited by1

Results whose statement or proof uses this declaration.

MonomialOrder.divproof · cited by 2