Theorems · Theorem · field theory
Polynomial.degree_erase_lt
∀ {R : Type u} [inst : Semiring R] {p : Polynomial R}, p ≠ 0 → (Polynomial.erase p.natDegree p).degree < p.degree- Defined in
- Mathlib.Algebra.Polynomial.Degree.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Finsetproof · cited by 13,712
- Polynomialstatement and proof · cited by 5,681
- WithBotstatement and proof · cited by 1,498
- Polynomial.natDegreestatement and proof · cited by 1,105
- Polynomial.degreestatement and proof · cited by 643
- Finset.eraseproof · cited by 455
- Polynomial.supportproof · cited by 237
- lt_of_le_of_neproof · cited by 230
- Polynomial.degree_eq_natDegreeproof · cited by 69
- Finset.notMem_eraseproof · cited by 59
- Finset.maxproof · cited by 50
Cited by3
Results whose statement or proof uses this declaration.
- Polynomial.degree_sub_lt_leftproof · cited by 9
- Polynomial.associated_content_mulproof · cited by 6
- Polynomial.degree_eraseLead_ltproof · cited by 0