Theorems · Theorem · commutative algebra
Ring.factorial_nsmul_multichoose_eq_ascPochhammer
∀ {R : Type u_1} [inst : AddCommMonoid R] [inst_1 : Pow R ℕ] [inst_2 : BinomialRing R] (r : R) (n : ℕ),
n.factorial • Ring.multichoose r n = (ascPochhammer ℕ n).smeval r- Defined in
- Mathlib.RingTheory.Binomial
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoidPowBinomialRing
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.
- AddCommMonoidstatement and proof · cited by 12,281
- Nat.factorialstatement · cited by 616
- ascPochhammerstatement · cited by 80
- Polynomial.smevalstatement · cited by 65
- BinomialRingstatement and proof · cited by 46
- Ring.multichoosestatement · cited by 25
- BinomialRing.factorial_nsmul_multichooseproof · cited by 1
Cited by12
Results whose statement or proof uses this declaration.
- Ring.descPochhammer_eq_factorial_smul_chooseproof · cited by 8
- Ring.multichoose_one_right'proof · cited by 2
- Ring.multichoose_succ_succproof · cited by 2
- Ring.multichoose_zero_right'proof · cited by 2
- Ring.map_multichooseproof · cited by 1
- Ring.ascPochhammer_succ_succproof · cited by 1
- Ring.multichoose_succ_neg_natCastproof · cited by 1
- Ring.multichoose_zero_succproof · cited by 1
- Ring.multichoose_neg_addproof · cited by 0
- Ring.multichoose_neg_of_ltproof · cited by 0
- Ring.multichoose_neg_selfproof · cited by 0
- Ring.multichoose_neg_succproof · cited by 0