Theorems · Theorem · field theory
Polynomial.ext_iff_natDegree_le
∀ {R : Type u} [inst : Semiring R] {p q : Polynomial R} {n : ℕ},
p.natDegree ≤ n → q.natDegree ≤ n → (p = q ↔ ∀ i ≤ n, p.coeff i = q.coeff i)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 90 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
- Polynomial.natDegreestatement and proof · cited by 1,105
- Polynomial.coeffstatement and proof · cited by 1,045
- LE.le.trans_ltproof · cited by 795
- le_or_gtproof · cited by 269
- Polynomial.coeff_eq_zero_of_natDegree_ltproof · cited by 55
- Polynomial.ext_iffproof · cited by 9
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.bUnion_roots_finiteproof · cited by 3
- Polynomial.ext_iff_degree_leproof · cited by 0