Theorems · Theorem · commutative algebra
Nat.cast_ascFactorial
∀ (S : Type u_1) [inst : Semiring S] (a b : ℕ), ↑(a.ascFactorial b) = Polynomial.eval (↑a) (ascPochhammer S b)
- Defined in
- Mathlib.RingTheory.Polynomial.Pochhammer
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 110 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.
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
- Polynomial.evalstatement and proof · cited by 796
- ascPochhammerstatement and proof · cited by 80
- Nat.ascFactorialstatement · cited by 41
- ascPochhammer_nat_eq_ascFactorialproof · cited by 6
- ascPochhammer_eval_castproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Nat.cast_factorialproof · cited by 0