Theorems · Theorem · commutative algebra
MvPolynomial.degreeOf_le_totalDegree
∀ {R : Type u} {σ : Type u_1} [inst : CommSemiring R] (f : MvPolynomial σ R) (i : σ),
MvPolynomial.degreeOf i f ≤ f.totalDegree- Defined in
- Mathlib.Algebra.MvPolynomial.Degrees
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 79 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.
Cites13
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
- Finsuppproof · cited by 5,255
- LE.le.transproof · cited by 3,151
- MvPolynomialstatement and proof · cited by 2,140
- eq_or_neproof · cited by 1,117
- MvPolynomial.supportproof · cited by 220
- Finsupp.mem_support_iffproof · cited by 89
- MvPolynomial.totalDegreestatement · cited by 76
- MvPolynomial.degreeOfstatement · cited by 53
- Finset.single_le_sumproof · cited by 34
- MvPolynomial.le_totalDegreeproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- MvPolynomial.restrictTotalDegree_le_restrictDegreeproof · cited by 0