Theorems · Theorem · commutative algebra
descPochhammer_eval_eq_descFactorial
∀ (R : Type u) [inst : Ring R] (n k : ℕ), Polynomial.eval (↑n) (descPochhammer R k) = ↑(n.descFactorial k)
- Defined in
- Mathlib.RingTheory.Polynomial.Pochhammer
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Ring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ringstatement and proof · cited by 7,463
- Polynomialproof · cited by 5,681
- Nat.cast_oneproof · cited by 2,501
- MulZeroClass.mul_zeroproof · cited by 2,091
- Nat.cast_zeroproof · cited by 1,870
- Polynomial.Xproof · cited by 1,639
- Polynomial.evalstatement and proof · cited by 796
- Nat.cast_mulproof · cited by 309
- mul_subproof · cited by 201
- sub_mulproof · cited by 170
- Polynomial.eval_subproof · cited by 124
- Polynomial.eval_oneproof · cited by 86
Cited by3
Results whose statement or proof uses this declaration.
- Nat.cast_choose_eq_descPochhammer_divproof · cited by 1
- descPochhammer_int_eq_ascFactorialproof · cited by 0
- descPochhammer_eval_div_factorial_le_sum_chooseproof · cited by 0