Theorems · Theorem · field theory
Polynomial.eval_le_zero_of_roots_le_of_leadingCoeff_nonpos
∀ {P : Polynomial ℝ} {x : ℝ}, (∀ (y : ℝ), P.IsRoot y → y ≤ x) → P.leadingCoeff ≤ 0 → Polynomial.eval x P ≤ 0- Defined in
- Mathlib.Analysis.Polynomial.Order
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Polynomialstatement and proof · cited by 5,681
- Polynomial.evalstatement and proof · cited by 796
- neg_zeroproof · cited by 542
- Polynomial.leadingCoeffstatement and proof · cited by 498
- Polynomial.IsRootstatement and proof · cited by 152
- neg_nonnegproof · cited by 60
- neg_eq_iff_eq_negproof · cited by 60
- Polynomial.eval_negproof · cited by 30
- Polynomial.leadingCoeff_negproof · cited by 10
- Polynomial.zero_le_eval_of_roots_le_of_leadingCoeff_nonnegproof · cited by 1
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