Theorems · Theorem · field theory
Polynomial.monic_X_pow_add
∀ {R : Type u} [inst : Semiring R] {p : Polynomial R} {n : ℕ}, p.degree < ↑n → (Polynomial.X ^ n + p).Monic- Defined in
- Mathlib.Algebra.Polynomial.Monic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 106 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.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Polynomialstatement and proof · cited by 5,681
- add_zeroproof · cited by 2,707
- Polynomial.Xstatement and proof · cited by 1,639
- WithBotstatement · cited by 1,498
- le_of_ltproof · cited by 1,175
- Polynomial.coeffproof · cited by 1,045
- le_transproof · cited by 985
- Polynomial.degreestatement and proof · cited by 643
- Polynomial.Monicstatement · cited by 461
- Polynomial.coeff_addproof · cited by 77
- max_leproof · cited by 71
Cited by3
Results whose statement or proof uses this declaration.
- Polynomial.lifts_and_degree_eq_and_monicproof · cited by 3
- Polynomial.monic_X_pow_add_Cproof · cited by 3
- Polynomial.monic_X_pow_subproof · cited by 0