Theorems · Theorem · field theory
Polynomial.X_sub_C_ne_zero
∀ {R : Type u} [inst : Ring R] [Nontrivial R] (r : R), Polynomial.X - Polynomial.C r ≠ 0- Cited by
- 21 results in Mathlib
- Foundations
- Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingNontrivial
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHomstatement · cited by 10,189
- Ringstatement and proof · cited by 7,463
- Polynomialstatement · cited by 5,681
- Nontrivialstatement and proof · cited by 2,416
- Polynomial.Xstatement and proof · cited by 1,639
- Polynomial.Cstatement · cited by 1,598
- pow_oneproof · cited by 894
- zero_lt_oneproof · cited by 598
- Polynomial.X_pow_sub_C_ne_zeroproof · cited by 15
Cited by21
Results whose statement or proof uses this declaration.
- isAlgebraic_algebraMapproof · cited by 19
- Polynomial.prime_X_sub_Cproof · cited by 5
- Polynomial.roots_multiset_prod_X_sub_Cproof · cited by 3
- Polynomial.roots_prod_X_sub_Cproof · cited by 2
- Polynomial.roots_quadratic_eq_pair_iff_of_ne_zeroproof · cited by 2
- WeierstrassCurve.Affine.CoordinateRing.XClass_ne_zeroproof · cited by 2
- Polynomial.mahlerMeasure_X_sub_Cproof · cited by 2
- Lagrange.nodal_erase_eq_nodal_divproof · cited by 2
- Polynomial.natDegree_cyclotomic'proof · cited by 1
- Polynomial.eraseLead_mul_eq_mul_eraseLead_of_nextCoeff_zeroproof · cited by 1
- WeierstrassCurve.Affine.CoordinateRing.YClass_ne_zeroproof · cited by 1
- Polynomial.succ_signVariations_le_X_sub_C_mulproof · cited by 1