Theorems · Theorem · field theory
Polynomial.comp_C_mul_X_eq_zero_iff
∀ {R : Type u} [inst : Semiring R] {p : Polynomial R} {r : R},
r ∈ nonZeroDivisors R → (p.comp (Polynomial.C r * Polynomial.X) = 0 ↔ p = 0)- Defined in
- Mathlib.Algebra.Polynomial.Eval.Degree
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 107 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.
Cites14
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 and proof · cited by 5,681
- Submonoidstatement · cited by 3,086
- Polynomial.Xstatement · cited by 1,639
- Polynomial.Cstatement · cited by 1,598
- Polynomial.coeffproof · cited by 1,045
- nonZeroDivisorsstatement and proof · cited by 895
- Polynomial.compstatement · cited by 193
- pow_memproof · cited by 46
- Polynomial.coeff_zeroproof · cited by 12
Cited by2
Results whose statement or proof uses this declaration.
- Ideal.IsFractionRing.normalproof · cited by 3
- IsAlgebraic.of_smulproof · cited by 1