Theorems · Theorem · field theory
Polynomial.X_ne_zero
∀ {R : Type u} [inst : Semiring R] [Nontrivial R], Polynomial.X ≠ 0- Defined in
- Mathlib.Algebra.Polynomial.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringNontrivial
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Nontrivialstatement and proof · cited by 2,416
- Polynomial.Xstatement · cited by 1,639
- Polynomial.coeffproof · cited by 1,045
- Polynomial.coeff_X_oneproof · cited by 12
Cited by7
Results whose statement or proof uses this declaration.
- isAlgebraic_zeroproof · cited by 3
- Polynomial.not_isFieldproof · cited by 3
- Polynomial.valuation_X_eq_neg_oneproof · cited by 2
- root_X_pow_sub_C_ne_zeroproof · cited by 2
- PowerSeries.intValuation_eq_of_coeproof · cited by 2
- RatFunc.X_ne_zeroproof · cited by 1
- PowerSeries.intValuation_Xproof · cited by 1