Theorems · Theorem · field theory
Polynomial.degree_sub_lt_left
∀ {R : Type u} [inst : Ring R] {p q : Polynomial R},
p.degree = q.degree → p ≠ 0 → p.leadingCoeff = q.leadingCoeff → (p - q).degree < p.degree- Defined in
- Mathlib.Algebra.Polynomial.Degree.Defs
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 99 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.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Ringstatement and proof · cited by 7,463
- Polynomialstatement and proof · cited by 5,681
- WithBotstatement and proof · cited by 1,498
- Polynomial.natDegreeproof · cited by 1,105
- sub_eq_add_negproof · cited by 1,023
- Polynomial.degreestatement and proof · cited by 643
- Polynomial.leadingCoeffstatement and proof · cited by 498
- Polynomial.monomialproof · cited by 256
- WithBot.unbotDproof · cited by 49
- Polynomial.degree_eq_botproof · cited by 34
- max_lt_iffproof · cited by 22
Cited by9
Results whose statement or proof uses this declaration.
- minpoly.uniqueproof · cited by 7
- Polynomial.Sequence.span_degreeLTproof · cited by 3
- Polynomial.div_wf_lemmaproof · cited by 3
- IsIntegrallyClosed.minpoly.uniqueproof · cited by 2
- PowerSeries.IsWeierstrassFactorization.isWeierstrassDivisionproof · cited by 1
- Polynomial.eq_of_degree_le_of_eval_index_eqproof · cited by 1
- Polynomial.degree_sub_ltproof · cited by 0
- Polynomial.degree_sub_lt_rightproof · cited by 0
- Polynomial.eq_of_degree_le_of_eval_finset_eqproof · cited by 0