Theorems · Theorem · field theory
Polynomial.degree_eq_bot
∀ {R : Type u} [inst : Semiring R] {p : Polynomial R}, p.degree = ⊥ ↔ p = 0- Defined in
- Mathlib.Algebra.Polynomial.Degree.Defs
- Cited by
- 34 results in Mathlib
- Foundations
- Depth 87 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
- Bot.botstatement and proof · cited by 4,720
- WithBotstatement · cited by 1,498
- Polynomial.degreestatement and proof · cited by 643
- Polynomial.support_eq_emptyproof · cited by 5
- Finset.max_eq_botproof · cited by 2
Cited by34
Results whose statement or proof uses this declaration.
- Polynomial.degree_eq_natDegreeproof · cited by 69
- Polynomial.natDegree_Cproof · cited by 59
- Polynomial.degree_lt_degreeproof · cited by 14
- Polynomial.ne_zero_of_degree_gtproof · cited by 13
- Polynomial.degree_ne_botproof · cited by 11
- IsAlgebraic.extendScalarsproof · cited by 10
- Polynomial.degree_sub_lt_leftproof · cited by 9
- Polynomial.natDegree_lt_iff_degree_ltproof · cited by 7
- Polynomial.associated_content_mulproof · cited by 6
- Irreducible.separableproof · cited by 6
- Polynomial.zero_le_degree_iffproof · cited by 4
- Polynomial.degree_derivative_ltproof · cited by 4