Theorems · Theorem · commutative algebra
ascPochhammer_natDegree
∀ (S : Type u) [inst : Semiring S] (n : ℕ) [NoZeroDivisors S] [Nontrivial S], (ascPochhammer S n).natDegree = n
- Defined in
- Mathlib.RingTheory.Polynomial.Pochhammer
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Polynomialproof · cited by 5,681
- Nontrivialstatement and proof · cited by 2,416
- Polynomial.Xproof · cited by 1,639
- Polynomial.natDegreestatement and proof · cited by 1,105
- NoZeroDivisorsstatement and proof · cited by 545
- ascPochhammerstatement and proof · cited by 80
- Polynomial.natDegree_oneproof · cited by 43
- Polynomial.natDegree_mulproof · cited by 23
- Polynomial.ne_zero_of_natDegree_gtproof · cited by 13
- ascPochhammer_succ_rightproof · cited by 11
- Polynomial.natDegree_X_add_Cproof · cited by 9
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.natDegree_preHilbertPolyproof · cited by 3
- summable_pow_mul_geometric_of_norm_lt_oneproof · cited by 1