Theorems · Theorem · field theory
Polynomial.degree_X_pow_add_C
∀ {R : Type u} [Nontrivial R] [inst : Semiring R] {n : ℕ},
0 < n → ∀ (a : R), (Polynomial.X ^ n + Polynomial.C a).degree = ↑n- Cited by
- 2 results in Mathlib
- Foundations
- Depth 104 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.
Cites14
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 · cited by 5,681
- Nontrivialstatement and proof · cited by 2,416
- Polynomial.Xstatement and proof · cited by 1,639
- Polynomial.Cstatement and proof · cited by 1,598
- WithBotstatement and proof · cited by 1,498
- LE.le.trans_ltproof · cited by 795
- Polynomial.degreestatement and proof · cited by 643
- Nat.cast_posproof · cited by 113
- Polynomial.degree_C_leproof · cited by 21
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.degree_X_pow_sub_Cproof · cited by 14
- Polynomial.X_pow_add_C_ne_zeroproof · cited by 2