Theorems · Theorem · field theory
Polynomial.natDegree_X_add_C
∀ {R : Type u} [Nontrivial R] [inst : Semiring R] (x : R), (Polynomial.X + Polynomial.C x).natDegree = 1- Cited by
- 9 results in Mathlib
- Foundations
- Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NontrivialSemiring
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 · cited by 5,681
- Nontrivialstatement and proof · cited by 2,416
- Polynomial.Xstatement · cited by 1,639
- Polynomial.Cstatement · cited by 1,598
- Polynomial.natDegreestatement · cited by 1,105
- Polynomial.natDegree_eq_of_degree_eq_someproof · cited by 42
- Polynomial.degree_X_add_Cproof · cited by 2
Cited by9
Results whose statement or proof uses this declaration.
- minpoly.add_algebraMapproof · cited by 4
- Polynomial.Monic.comp_X_add_Cproof · cited by 3
- ascPochhammer_natDegreeproof · cited by 2
- monic_ascPochhammerproof · cited by 2
- summable_pow_mul_geometric_of_norm_lt_oneproof · cited by 1
- cyclotomic_comp_X_add_one_isEisensteinAtproof · cited by 1
- cyclotomic_prime_pow_comp_X_add_one_isEisensteinAtproof · cited by 1
- Polynomial.natDegree_pow_X_add_Cproof · cited by 1
- Polynomial.not_isUnit_X_add_Cproof · cited by 0