Theorems · Theorem · field theory
Polynomial.zero_lt_eval_of_roots_lt_of_leadingCoeff_nonneg
∀ {P : Polynomial ℝ} {x : ℝ}, (∀ (y : ℝ), P.IsRoot y → y < x) → 0 ≤ P.leadingCoeff → 0 < Polynomial.eval x P- Defined in
- Mathlib.Analysis.Polynomial.Order
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites27
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement and proof · cited by 25,697
- Polynomialstatement and proof · cited by 5,681
- LT.lt.leproof · cited by 2,189
- le_reflproof · cited by 2,061
- Set.Iccproof · cited by 1,702
- Polynomial.Cproof · cited by 1,598
- Polynomial.coeffproof · cited by 1,045
- Polynomial.evalstatement and proof · cited by 796
- Polynomial.degreeproof · cited by 643
- Polynomial.leadingCoeffstatement and proof · cited by 498
- Continuous.continuousOnproof · cited by 311
Cited by3
Results whose statement or proof uses this declaration.
- Polynomial.zero_lt_negOnePow_mul_eval_of_lt_roots_of_leadingCoeff_nonnegproof · cited by 2
- Polynomial.eval_lt_zero_of_roots_lt_of_leadingCoeff_nonposproof · cited by 1
- Polynomial.zero_le_eval_of_roots_le_of_leadingCoeff_nonnegproof · cited by 1