Theorems · Theorem · commutative algebra
Nat.cast_descFactorial
∀ (S : Type u_1) [inst : Semiring S] (a b : ℕ), ↑(a.descFactorial b) = Polynomial.eval (↑(a - (b - 1))) (ascPochhammer S b)
- Defined in
- Mathlib.RingTheory.Polynomial.Pochhammer
- Cited by
- 1 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.
Cites16
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
- add_zeroproof · cited by 2,707
- Nat.cast_oneproof · cited by 2,501
- zero_addproof · cited by 2,366
- le_reflproof · cited by 2,061
- Polynomial.evalstatement · cited by 796
- le_totalproof · cited by 294
- tsub_zeroproof · cited by 123
- tsub_add_cancel_of_leproof · cited by 112
- zero_tsubproof · cited by 100
- ascPochhammerstatement · cited by 80
- Nat.descFactorialstatement and proof · cited by 68
Cited by1
Results whose statement or proof uses this declaration.
- Nat.cast_choose_eq_ascPochhammer_divproof · cited by 0