Theorems · Theorem · field theory
Polynomial.degree_C_le
∀ {R : Type u} {a : R} [inst : Semiring R], (Polynomial.C a).degree ≤ 0- Defined in
- Mathlib.Algebra.Polynomial.Degree.Defs
- Cited by
- 21 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- RingHomstatement · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- le_reflproof · cited by 2,061
- Polynomial.Cstatement and proof · cited by 1,598
- WithBotstatement and proof · cited by 1,498
- Polynomial.degreestatement and proof · cited by 643
- bot_leproof · cited by 306
- Polynomial.C_0proof · cited by 40
- Polynomial.degree_Cproof · cited by 20
Cited by21
Results whose statement or proof uses this declaration.
- Polynomial.degree_le_zero_iffproof · cited by 5
- Polynomial.degree_linear_leproof · cited by 5
- Polynomial.monic_X_pow_add_Cproof · cited by 3
- Polynomial.card_nthRootsproof · cited by 3
- spectrum.map_polynomial_aeval_of_degree_posproof · cited by 2
- Polynomial.degree_X_add_Cproof · cited by 2
- Polynomial.degree_X_pow_add_Cproof · cited by 2
- Polynomial.degree_add_Cproof · cited by 2
- Polynomial.tendsto_abv_eval₂_atTopproof · cited by 2
- Polynomial.irreducible_C_mul_X_add_Cproof · cited by 2
- Polynomial.mem_roots_sub_Cproof · cited by 1
- Polynomial.degree_X_sub_C_leproof · cited by 1