Theorems · Theorem · field theory
Polynomial.degree_add_C
∀ {R : Type u} {a : R} [inst : Semiring R] {p : Polynomial R}, 0 < p.degree → (p + Polynomial.C a).degree = p.degree- Cited by
- 2 results in Mathlib
- Foundations
- Depth 104 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
- Polynomial.Cstatement and proof · cited by 1,598
- add_commproof · cited by 1,535
- WithBotstatement · cited by 1,498
- Polynomial.degreestatement and proof · cited by 643
- lt_of_le_of_ltproof · cited by 432
- Polynomial.degree_C_leproof · cited by 21
- Polynomial.degree_add_eq_right_of_degree_ltproof · cited by 9
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.card_roots_sub_Cproof · cited by 1
- Polynomial.degree_sub_Cproof · cited by 1