Theorems · Theorem · commutative algebra
Nat.cast_factorial
∀ (S : Type u_1) [inst : Semiring S] (a : ℕ), ↑a.factorial = Polynomial.eval 1 (ascPochhammer S a)
- Defined in
- Mathlib.RingTheory.Polynomial.Pochhammer
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 111 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.
Cites7
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
- Nat.cast_oneproof · cited by 2,501
- Polynomial.evalstatement and proof · cited by 796
- Nat.factorialstatement · cited by 616
- ascPochhammerstatement and proof · cited by 80
- Nat.one_ascFactorialproof · cited by 4
- Nat.cast_ascFactorialproof · cited by 1
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