Theorems · Theorem · field theory
Polynomial.degree_comp_neg_X
∀ {R : Type u} [inst : Ring R] {p : Polynomial R}, (p.comp (-Polynomial.X)).degree = p.degree- Defined in
- Mathlib.Algebra.Polynomial.Degree.Lemmas
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Ring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ringstatement and proof · cited by 7,463
- Polynomialstatement and proof · cited by 5,681
- Bot.botproof · cited by 4,720
- mul_oneproof · cited by 3,885
- Nontrivialproof · cited by 2,416
- Polynomial.Xstatement and proof · cited by 1,639
- WithBotstatement and proof · cited by 1,498
- eq_or_neproof · cited by 1,117
- Polynomial.natDegreeproof · cited by 1,105
- Polynomial.degreestatement and proof · cited by 643
- Polynomial.leadingCoeffproof · cited by 498
- Polynomial.compstatement and proof · cited by 193
Cited by7
Results whose statement or proof uses this declaration.
- Polynomial.abs_tendsto_atBotproof · cited by 2
- minpoly.negproof · cited by 2
- Polynomial.div_tendsto_atBot_zero_of_degree_ltproof · cited by 1
- Polynomial.isBigO_atBot_of_degree_leproof · cited by 0
- Polynomial.abs_div_tendsto_atBot_atTop_of_degree_gtproof · cited by 0
- Polynomial.div_tendsto_atBot_zero_iff_degree_ltproof · cited by 0
- Polynomial.isLittleO_atBot_of_degree_ltproof · cited by 0