Theorems · Theorem · field theory
Polynomial.eval_C
∀ {R : Type u} {a : R} [inst : Semiring R] {x : R}, Polynomial.eval x (Polynomial.C a) = a- Defined in
- Mathlib.Algebra.Polynomial.Eval.Defs
- Cited by
- 145 results in Mathlib
- Foundations
- Depth 103 from the axioms, rests on 1,814 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHom.idproof · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- RingHomstatement · cited by 10,189
- Polynomialstatement · cited by 5,681
- Polynomial.Cstatement · cited by 1,598
- Polynomial.evalstatement · cited by 796
- Polynomial.eval₂_Cproof · cited by 50
Cited by145
Results whose statement or proof uses this declaration.
- Polynomial.eval_compproof · cited by 29
- Polynomial.eval_natCastproof · cited by 24
- Polynomial.Splits.exists_eval_eq_zeroproof · cited by 14
- Polynomial.mem_nthRootsproof · cited by 9
- Polynomial.modByMonic_X_sub_C_eq_C_evalproof · cited by 7
- taylorWithinEval_succproof · cited by 6
- IsAlgClosed.of_exists_rootproof · cited by 5
- Matrix.det_eq_sign_charpoly_coeffproof · cited by 5
- WeierstrassCurve.Affine.evalEval_polynomialXproof · cited by 5
- WeierstrassCurve.Affine.evalEval_polynomialYproof · cited by 5
- Polynomial.mul_divByMonic_eq_iff_isRootproof · cited by 5
- Lagrange.eval_interpolate_at_nodeproof · cited by 5