Theorems · Theorem · field theory
Polynomial.eval_natCast
∀ {R : Type u} [inst : Semiring R] {x : R} {n : ℕ}, Polynomial.eval x ↑n = ↑n- Defined in
- Mathlib.Algebra.Polynomial.Eval.Defs
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 104 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.
Cites4
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 · cited by 5,681
- Polynomial.evalstatement and proof · cited by 796
- Polynomial.eval_Cproof · cited by 145
Cited by24
Results whose statement or proof uses this declaration.
- Polynomial.eval_ofNatproof · cited by 18
- hasDerivAt_bernoulliFunproof · cited by 5
- bernstein_applyproof · cited by 4
- Polynomial.Chebyshev.one_sub_X_sq_mul_iterate_derivative_T_evalproof · cited by 2
- descPochhammer_eval_eq_prod_rangeproof · cited by 2
- Polynomial.Chebyshev.one_sub_X_sq_mul_iterate_derivative_U_evalproof · cited by 2
- bernsteinPolynomial.eval_at_0proof · cited by 2
- bernsteinPolynomial.iterate_derivative_at_0proof · cited by 2
- bernsteinPolynomial.iterate_derivative_at_0_eq_zero_of_ltproof · cited by 2
- summable_pow_mul_geometric_of_norm_lt_oneproof · cited by 1
- Polynomial.preHilbertPoly_eq_choose_sub_addproof · cited by 1
- isCoveringMapOn_npowproof · cited by 1