Theorems · Theorem · field theory
Polynomial.negOnePow_mul_eval_lt_zero_of_lt_roots_of_leadingCoeff_nonpos
∀ {P : Polynomial ℝ} {x : ℝ},
(∀ (y : ℝ), P.IsRoot y → x < y) → P.leadingCoeff ≤ 0 → ↑↑(↑P.natDegree).negOnePow * Polynomial.eval x P < 0- Defined in
- Mathlib.Analysis.Polynomial.Order
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites18
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
- Units.valstatement and proof · cited by 1,966
- Polynomial.natDegreestatement and proof · cited by 1,105
- Polynomial.evalstatement and proof · cited by 796
- mul_negproof · cited by 590
- neg_zeroproof · cited by 542
- Polynomial.leadingCoeffstatement and proof · cited by 498
- Int.negOnePowstatement and proof · cited by 156
- Polynomial.IsRootstatement and proof · cited by 152
- neg_posproof · cited by 74
- neg_eq_iff_eq_negproof · cited by 60
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