Theorems · Theorem · commutative algebra
ascPochhammer_eval_cast
∀ (S : Type u) [inst : Semiring S] (n k : ℕ), ↑(Polynomial.eval k (ascPochhammer ℕ n)) = Polynomial.eval (↑k) (ascPochhammer S n)
- Defined in
- Mathlib.RingTheory.Polynomial.Pochhammer
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 108 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Polynomialproof · cited by 5,681
- Algebra.algebraMapproof · cited by 4,706
- Polynomial.evalstatement and proof · cited by 796
- Polynomial.eval₂proof · cited by 267
- eq_natCastproof · cited by 104
- ascPochhammerstatement and proof · cited by 80
- Polynomial.eval_mapproof · cited by 37
- Nat.cast_idproof · cited by 12
- ascPochhammer_mapproof · cited by 5
- Polynomial.eval₂_at_natCastproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- bernsteinPolynomial.iterate_derivative_at_0proof · cited by 2
- bernsteinPolynomial.iterate_derivative_at_1_ne_zeroproof · cited by 1
- Nat.cast_ascFactorialproof · cited by 1
- Nat.cast_descFactorialproof · cited by 1