Theorems · Theorem · field theory
Polynomial.C_dvd_iff_dvd_coeff
∀ {R : Type u} [inst : Semiring R] (r : R) (φ : Polynomial R), Polynomial.C r ∣ φ ↔ ∀ (i : ℕ), r ∣ φ.coeff i- Defined in
- Mathlib.Algebra.Polynomial.Coeff
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 102 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.
- DFunLike.coestatement and proof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- RingHomstatement · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Finset.sumproof · cited by 5,195
- Finset.sum_congrproof · cited by 2,323
- MulZeroClass.mul_zeroproof · cited by 2,091
- Polynomial.Cstatement and proof · cited by 1,598
- Polynomial.coeffstatement and proof · cited by 1,045
- Polynomial.monomialproof · cited by 256
- Polynomial.supportproof · cited by 237
- Polynomial.extproof · cited by 118
Cited by3
Results whose statement or proof uses this declaration.
- Polynomial.dvd_content_iff_C_dvdproof · cited by 3
- Submodule.IsPrincipal.contentIdeal_generator_dvdproof · cited by 2
- Polynomial.Monic.C_dvd_iff_isUnitproof · cited by 1