Theorems · Theorem · commutative algebra
MonomialOrder.degree_sub_leadingTerm_le
∀ {σ : Type u_1} {m : MonomialOrder σ} {R : Type u_2} [inst : CommRing R] (f : MvPolynomial σ R),
m.toSyn (m.degree (f - m.leadingTerm f)) ≤ m.toSyn (m.degree f)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 89 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.
Cites14
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 · cited by 5,255
- MvPolynomialstatement and proof · cited by 2,140
- AddEquivstatement · cited by 1,087
- le_transproof · cited by 985
- 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
- max_selfproof · cited by 43
- MonomialOrder.leadingTermstatement · cited by 29
Cited by1
Results whose statement or proof uses this declaration.
- MonomialOrder.degree_sub_leadingTerm_lt_degreeproof · cited by 1