Theorems · Theorem · field theory
Polynomial.ext
∀ {R : Type u} [inst : Semiring R] {p q : Polynomial R}, (∀ (n : ℕ), p.coeff n = q.coeff n) → p = q- Defined in
- Mathlib.Algebra.Polynomial.Basic
- Cited by
- 118 results in Mathlib
- Foundations
- Depth 61 from the axioms, rests on 875 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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.coeffstatement · cited by 1,045
- Polynomial.ext_iffproof · cited by 9
Cited by118
Results whose statement or proof uses this declaration.
- Polynomial.map_mapproof · cited by 75
- Polynomial.map_injectiveproof · cited by 27
- Polynomial.eq_C_of_degree_le_zeroproof · cited by 20
- Polynomial.C_mul'proof · cited by 12
- Polynomial.zero_scaleRootsproof · cited by 7
- Polynomial.content_eq_zero_iffproof · cited by 7
- Polynomial.map_expandproof · cited by 7
- Polynomial.divX_mul_X_addproof · cited by 6
- Polynomial.map_toSubringproof · cited by 6
- Polynomial.eq_X_add_C_of_degree_le_oneproof · cited by 5
- Polynomial.mirror_mirrorproof · cited by 5
- Polynomial.reflect_C_mul_X_powproof · cited by 5