Theorems · Theorem · field theory
Polynomial.degree_divByMonic_le
∀ {R : Type u} [inst : Ring R] (p q : Polynomial R), (p /ₘ q).degree ≤ p.degree- Defined in
- Mathlib.Algebra.Polynomial.Div
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 122 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.
Cites19
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
- 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
- Polynomial.Monicproof · cited by 461
- bot_leproof · cited by 306
- not_ltproof · cited by 306
- Polynomial.divByMonicstatement and proof · cited by 77
- WithBot.coe_le_coeproof · cited by 76
- Polynomial.degree_eq_natDegreeproof · cited by 69
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.degree_div_leproof · cited by 0