Theorems · Theorem · field theory
Polynomial.natDegree_add_le_iff_left
∀ {R : Type u} [inst : Semiring R] {n : ℕ} (p q : Polynomial R),
q.natDegree ≤ n → ((p + q).natDegree ≤ n ↔ p.natDegree ≤ n)- Defined in
- Mathlib.Algebra.Polynomial.Degree.Lemmas
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 87 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.
Cites8
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.natDegreestatement and proof · cited by 1,105
- Polynomial.coeffproof · cited by 1,045
- Polynomial.coeff_addproof · cited by 77
- Polynomial.natDegree_le_iff_coeff_eq_zeroproof · cited by 4
- Polynomial.natDegree_add_le_of_degree_leproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.natDegree_sub_le_iff_leftproof · cited by 2
- Polynomial.natDegree_add_le_iff_rightproof · cited by 0