Theorems · Theorem · field theory
Polynomial.degree_C_mul_X_pow_le
∀ {R : Type u} [inst : Semiring R] (n : ℕ) (a : R), (Polynomial.C a * Polynomial.X ^ n).degree ≤ ↑n- Defined in
- Mathlib.Algebra.Polynomial.Degree.Defs
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 103 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- RingHomstatement · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Polynomial.Xstatement · cited by 1,639
- Polynomial.Cstatement · cited by 1,598
- WithBotstatement · cited by 1,498
- Polynomial.degreestatement and proof · cited by 643
- Polynomial.C_mul_X_pow_eq_monomialproof · cited by 53
- Polynomial.degree_monomial_leproof · cited by 4
Cited by8
Results whose statement or proof uses this declaration.
- Polynomial.degree_X_pow_leproof · cited by 5
- Polynomial.degree_quadratic_leproof · cited by 4
- Polynomial.natDegree_C_mul_X_pow_leproof · cited by 4
- Polynomial.degree_sum_fin_ltproof · cited by 4
- Polynomial.degree_derivativeproof · cited by 3
- Polynomial.degree_cubic_leproof · cited by 3
- Polynomial.degree_C_mul_X_leproof · cited by 2
- IsPrimitiveRoot.sum_eq_zero_iff_forall_eqproof · cited by 1