Theorems · Theorem · field theory
Polynomial.natDegree_comp_le
∀ {R : Type u} [inst : Semiring R] {p q : Polynomial R}, (p.comp q).natDegree ≤ p.natDegree * q.natDegree- Defined in
- Mathlib.Algebra.Polynomial.Degree.Lemmas
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 107 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.
Cites32
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Polynomialstatement and proof · cited by 5,681
- zero_addproof · cited by 2,366
- le_reflproof · cited by 2,061
- Nat.cast_zeroproof · cited by 1,870
- Polynomial.Cproof · cited by 1,598
- WithBotproof · cited by 1,498
- Polynomial.natDegreestatement and proof · cited by 1,105
- Polynomial.coeffproof · cited by 1,045
- add_le_addproof · cited by 666
- Polynomial.degreeproof · cited by 643
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.natDegree_comp_eq_of_mul_ne_zeroproof · cited by 4
- Polynomial.IsMonicOfDegree.compproof · cited by 1