Theorems · Theorem · commutative algebra
ascPochhammer_succ_right
∀ (S : Type u) [inst : Semiring S] (n : ℕ), ascPochhammer S (n + 1) = ascPochhammer S n * (Polynomial.X + ↑n)
- Defined in
- Mathlib.RingTheory.Polynomial.Pochhammer
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 107 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.
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
- RingHomproof · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Algebra.algebraMapproof · cited by 4,706
- one_mulproof · cited by 2,841
- add_zeroproof · cited by 2,707
- zero_addproof · cited by 2,366
- mul_assocproof · cited by 1,667
- Polynomial.Xstatement and proof · cited by 1,639
- add_commproof · cited by 1,535
- Polynomial.mapproof · cited by 806
- add_assocproof · cited by 746
Cited by11
Results whose statement or proof uses this declaration.
- Polynomial.ascPochhammer_smeval_castproof · cited by 3
- ascPochhammer_posproof · cited by 3
- ascPochhammer_succ_evalproof · cited by 3
- ascPochhammer_natDegreeproof · cited by 2
- Ring.smeval_ascPochhammer_succ_negproof · cited by 2
- Polynomial.ascPochhammer_smeval_neg_eq_descPochhammerproof · cited by 1
- Complex.regularizedHGFunCoeff_add_oneproof · cited by 1
- Ring.ascPochhammer_succ_succproof · cited by 1
- Complex.Gamma_add_nat_div_Gamma_eqproof · cited by 1
- ascPochhammer_mulproof · cited by 0
- ascPochhammer_succ_comp_X_add_oneproof · cited by 0