Theorems · Theorem · real analysis
Polynomial.finite_abs_eval_le_of_degree_lt
∀ {P Q : Polynomial ℤ}, Q.degree < P.degree → {x | |Polynomial.eval x P| ≤ |Polynomial.eval x Q|}.FiniteIf deg Q < deg P, there are only finitely many integers x where |P(x)| ≤ |Q(x)|.
- Defined in
- Mathlib.Analysis.Polynomial.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Filterproof · cited by 8,121
- Set.ofPredstatement and proof · cited by 6,101
- Polynomialstatement and proof · cited by 5,681
- Norm.normproof · cited by 5,413
- Filter.Eventuallyproof · cited by 3,134
- absstatement · cited by 1,814
- Set.Finitestatement and proof · cited by 1,814
- WithBotstatement · cited by 1,498
- Polynomial.evalstatement and proof · cited by 796
- Polynomial.degreestatement and proof · cited by 643
- Filter.Eventually.of_forallproof · cited by 526
- Asymptotics.IsLittleOproof · cited by 375
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.dvd_of_infinite_eval_dvd_evalproof · cited by 0