Theorems · Theorem · commutative algebra
Nat.cast_choose_eq_descPochhammer_div
∀ (K : Type u_1) [inst : DivisionRing K] [CharZero K] (a b : ℕ), ↑(a.choose b) = Polynomial.eval (↑a) (descPochhammer K b) / ↑b.factorial
- Defined in
- Mathlib.RingTheory.Polynomial.Pochhammer
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DivisionRingCharZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_commproof · cited by 2,262
- DivisionRingstatement and proof · cited by 1,062
- CharZerostatement and proof · cited by 932
- Polynomial.evalstatement and proof · cited by 796
- Nat.factorialstatement and proof · cited by 616
- Nat.choosestatement and proof · cited by 494
- Nat.cast_mulproof · cited by 309
- Nat.cast_ne_zeroproof · cited by 113
- Nat.descFactorialproof · cited by 68
- Nat.factorial_ne_zeroproof · cited by 56
- descPochhammerstatement and proof · cited by 51
- eq_div_iff_mul_eqproof · cited by 19
Cited by1
Results whose statement or proof uses this declaration.
- descPochhammer_eval_div_factorial_le_sum_chooseproof · cited by 0