Theorems · Theorem · commutative algebra
ascPochhammer_succ_comp_X_add_one
∀ (S : Type u) [inst : Semiring S] (n : ℕ),
(ascPochhammer S (n + 1)).comp (Polynomial.X + 1) =
ascPochhammer S (n + 1) + (n + 1) • (ascPochhammer S n).comp (Polynomial.X + 1)- Defined in
- Mathlib.RingTheory.Polynomial.Pochhammer
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
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Cites27
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
- Nat.cast_oneproof · cited by 2,501
- mul_commproof · cited by 2,262
- Polynomial.Xstatement and proof · cited by 1,639
- add_commproof · cited by 1,535
- Polynomial.mapproof · cited by 806
- add_assocproof · cited by 746
- Nat.cast_addproof · cited by 586
- nsmul_eq_mulproof · cited by 369
- add_mulproof · cited by 363
- Polynomial.compstatement and proof · cited by 193
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