Theorems · Theorem · commutative algebra
ascPochhammer_pos
∀ {S : Type u_1} [inst : Semiring S] [inst_1 : PartialOrder S] [IsStrictOrderedRing S] (n : ℕ) (s : S),
0 < s → 0 < Polynomial.eval s (ascPochhammer S n)- Defined in
- Mathlib.RingTheory.Polynomial.Pochhammer
- Cited by
- 3 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.
Cites19
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
- PartialOrderstatement and proof · cited by 6,410
- Polynomialproof · cited by 5,681
- IsStrictOrderedRingstatement and proof · cited by 2,490
- Polynomial.Xproof · cited by 1,639
- Polynomial.evalstatement and proof · cited by 796
- zero_lt_oneproof · cited by 598
- lt_of_lt_of_leproof · cited by 438
- mul_addproof · cited by 413
- mul_posproof · cited by 374
- Nat.cast_nonnegproof · cited by 109
- Polynomial.eval_oneproof · cited by 86
Cited by3
Results whose statement or proof uses this declaration.
- bernsteinPolynomial.iterate_derivative_at_1_ne_zeroproof · cited by 1
- descPochhammer_posproof · cited by 1
- bernsteinPolynomial.iterate_derivative_at_0_ne_zeroproof · cited by 0