Theorems · Theorem · field theory
Polynomial.degree_add_div
∀ {R : Type u} [inst : Field R] {p q : Polynomial R}, q ≠ 0 → q.degree ≤ p.degree → q.degree + (p / q).degree = p.degree- Defined in
- Mathlib.Algebra.Polynomial.FieldDivision
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 124 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- not_lt_of_geproof · cited by 52
- Polynomial.degree_mulproof · cited by 25
- Polynomial.degree_add_eq_left_of_degree_ltproof · cited by 14
- EuclideanDomain.div_add_modproof · cited by 10
- EuclideanDomain.mod_ltproof · cited by 8
- Polynomial.degree_le_mul_leftproof · cited by 2
- Polynomial.div_eq_zero_iffproof · cited by 1
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