Theorems · Theorem · commutative algebra
ascPochhammer_succ_left
∀ (S : Type u) [inst : Semiring S] (n : ℕ), ascPochhammer S (n + 1) = Polynomial.X * (ascPochhammer S n).comp (Polynomial.X + 1)
- Defined in
- Mathlib.RingTheory.Polynomial.Pochhammer
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Polynomialstatement and proof · cited by 5,681
- Polynomial.Xstatement and proof · cited by 1,639
- Polynomial.compstatement and proof · cited by 193
- ascPochhammerstatement and proof · cited by 80
Cited by11
Results whose statement or proof uses this declaration.
- ascPochhammer_succ_rightproof · cited by 11
- ascPochhammer_mapproof · cited by 5
- descPochhammer_eval_eq_ascPochhammerproof · cited by 4
- ascPochhammer_eval_zeroproof · cited by 3
- Polynomial.descPochhammer_smeval_eq_ascPochhammerproof · cited by 2
- monic_ascPochhammerproof · cited by 2
- bernsteinPolynomial.iterate_derivative_at_0proof · cited by 2
- Ring.multichoose_zero_succproof · cited by 1
- descPochhammer_eq_ascPochhammerproof · cited by 1
- Ring.ascPochhammer_succ_succproof · cited by 1
- ascPochhammer_succ_comp_X_add_oneproof · cited by 0