Theorems · Theorem · field theory
Polynomial.degree_add_divByMonic
∀ {R : Type u} [inst : Ring R] {p q : Polynomial R},
q.Monic → q.degree ≤ p.degree → q.degree + (p /ₘ q).degree = p.degree- Defined in
- Mathlib.Algebra.Polynomial.Div
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 121 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.
Cites26
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
- one_mulproof · cited by 2,841
- Nontrivialproof · cited by 2,416
- WithBotstatement and proof · cited by 1,498
- Polynomial.natDegreeproof · cited by 1,105
- Polynomial.degreestatement and proof · cited by 643
- Nat.cast_addproof · cited by 586
- Polynomial.leadingCoeffproof · cited by 498
- Polynomial.Monicstatement and proof · cited by 461
- not_ltproof · cited by 306
Cited by4
Results whose statement or proof uses this declaration.
- Polynomial.natDegree_divByMonicproof · cited by 5
- Polynomial.leadingCoeff_divByMonic_of_monicproof · cited by 2
- Polynomial.degree_divByMonic_ltproof · cited by 1
- Polynomial.degree_divByMonic_leproof · cited by 1