Theorems · Theorem · commutative algebra

Ring.ascPochhammer_succ_succ

∀ {R : Type u_2} [inst : NonAssocSemiring R] [inst_1 : Pow R ℕ] [NatPowAssoc R] [inst_3 : BinomialRing R] (r : R)
  (k : ℕ),
  (ascPochhammer ℕ (k + 1)).smeval (r + 1) =
    (k + 1).factorial • Ring.multichoose (r + 1) k + (ascPochhammer ℕ (k + 1)).smeval r

Defined in

Mathlib.RingTheory.Binomial

Cited by

1 results in Mathlib

Foundations

Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NonAssocSemiringPowNatPowAssocBinomialRing