Theorems · Theorem · field theory
Polynomial.degree_erase_le
∀ {R : Type u} [inst : Semiring R] (p : Polynomial R) (n : ℕ), (Polynomial.erase n p).degree ≤ p.degree- Defined in
- Mathlib.Algebra.Polynomial.Degree.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 71 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.
Cites9
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
- Polynomialstatement and proof · cited by 5,681
- WithBotstatement · cited by 1,498
- Polynomial.degreestatement · cited by 643
- Polynomial.supportproof · cited by 237
- Finset.erase_subsetproof · cited by 31
- Finset.sup_monoproof · cited by 25
- Polynomial.erasestatement · cited by 16
- Polynomial.support_eraseproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.degree_erase_ltproof · cited by 3
- Polynomial.eraseLead_degree_leproof · cited by 1