ascPochhammer_nat_eq_natCast_ascFactorial

English

For semiring S and natural numbers n,k, the cast of ascPochhammer S k evaluated at n equals n ascFactorial k cast.

Русский

Для полугруппы S и натуральных n,k: приведение ascPochhammer S k к n равно n ascFactorial k с приводом.

LaTeX

$$$\\mathrm{NatCast}\\Big((ascPochhammer\\ S\\ k).\\mathrm{eval}\\ n\\Big) = \\mathrm{NatCast}\\Big((ascPochhammer\\ S\\ k).\\mathrm{eval}\\ n\\Big)$$$

Lean4

theorem ascPochhammer_nat_eq_natCast_ascFactorial (S : Type*) [Semiring S] (n k : ℕ) :
    (ascPochhammer S k).eval (n : S) = n.ascFactorial k :=
  by
  norm_cast
  rw [ascPochhammer_nat_eq_ascFactorial]

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