Theorems · Theorem · field theory
Polynomial.degree_eq_natDegree
∀ {R : Type u} [inst : Semiring R] {p : Polynomial R}, p ≠ 0 → p.degree = ↑p.natDegree- Defined in
- Mathlib.Algebra.Polynomial.Degree.Defs
- Cited by
- 69 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Polynomialstatement and proof · cited by 5,681
- WithBotstatement and proof · cited by 1,498
- Polynomial.natDegreestatement and proof · cited by 1,105
- Polynomial.degreestatement and proof · cited by 643
- WithBot.unbotDproof · cited by 49
- Polynomial.degree_eq_botproof · cited by 34
Cited by69
Results whose statement or proof uses this declaration.
- Polynomial.leadingCoeff_eq_zeroproof · cited by 55
- Polynomial.coeff_eq_zero_of_natDegree_ltproof · cited by 55
- Polynomial.natDegree_mulproof · cited by 23
- Polynomial.natDegree_mul'proof · cited by 18
- Polynomial.natDegree_add_Cproof · cited by 18
- Polynomial.modByMonic_eq_zero_iff_dvdproof · cited by 15
- Polynomial.degree_lt_degreeproof · cited by 14
- Polynomial.le_natDegree_of_ne_zeroproof · cited by 14
- Polynomial.degree_mul'proof · cited by 13
- Polynomial.div_modByMonic_uniqueproof · cited by 12
- Polynomial.degree_map_eq_of_leadingCoeff_ne_zeroproof · cited by 9
- Polynomial.card_roots'proof · cited by 9