Theorems · Theorem · field theory
Polynomial.C_ne_zero
∀ {R : Type u} {a : R} [inst : Semiring R], Polynomial.C a ≠ 0 ↔ a ≠ 0- Defined in
- Mathlib.Algebra.Polynomial.Basic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 103 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- RingHomstatement · cited by 10,189
- Polynomialstatement · cited by 5,681
- Polynomial.Cstatement · cited by 1,598
- Iff.notproof · cited by 489
- Polynomial.C_eq_zeroproof · cited by 16
Cited by10
Results whose statement or proof uses this declaration.
- minpoly.eq_X_sub_C_of_algebraMap_injproof · cited by 4
- Polynomial.coeffList_eraseLeadproof · cited by 4
- WeierstrassCurve.Affine.CoordinateRing.XClass_ne_zeroproof · cited by 2
- Polynomial.coeffList_Cproof · cited by 1
- Polynomial.isRoot_of_isRoot_of_dvd_derivative_mulproof · cited by 1
- WeierstrassCurve.Affine.CoordinateRing.XYIdeal_mul_XYIdealproof · cited by 1
- root_X_pow_sub_C_ne_zero'proof · cited by 1
- WeierstrassCurve.Affine.CoordinateRing.XYIdeal_neg_mulproof · cited by 1
- Polynomial.derivative_pow_eq_zeroproof · cited by 0
- fermatLastTheoremWith'_polynomialproof · cited by 0