Theorems · Theorem · field theory
Polynomial.ext_iff
∀ {R : Type u} [inst : Semiring R] {p q : Polynomial R}, p = q ↔ ∀ (n : ℕ), p.coeff n = q.coeff n- Defined in
- Mathlib.Algebra.Polynomial.Basic
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 60 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Polynomialstatement and proof · cited by 5,681
- Polynomial.coeffstatement · cited by 1,045
- AddMonoidAlgebraproof · cited by 649
- AddMonoidAlgebra.coeffproof · cited by 365
- DFunLike.ext_iffproof · cited by 102
- Polynomial.casesOnproof · cited by 15
- Polynomial.ofFinsupp.injEqproof · cited by 5
Cited by9
Results whose statement or proof uses this declaration.
- Polynomial.extproof · cited by 118
- Polynomial.derivative_eq_zeroproof · cited by 4
- Multiset.prod_X_add_C_coeffproof · cited by 3
- Polynomial.quotient_mk_comp_C_isIntegral_of_isJacobsonRingproof · cited by 2
- Polynomial.ker_mapRingHomproof · cited by 2
- Polynomial.ext_iff_natDegree_leproof · cited by 2
- Ideal.injective_quotient_le_comap_mapproof · cited by 1
- Polynomial.mul_X_pow_eq_zeroproof · cited by 1
- MvPolynomial.eq_zero_of_eval_zero_at_prod_finsetproof · cited by 1