Theorems · Theorem · commutative algebra
descPochhammer_nonneg
∀ {S : Type u_1} [inst : Ring S] [inst_1 : PartialOrder S] [IsStrictOrderedRing S] {n : ℕ} {s : S},
↑n - 1 ≤ s → 0 ≤ Polynomial.eval s (descPochhammer S n)descPochhammer S n is nonnegative on [n-1, ∞).
- Defined in
- Mathlib.RingTheory.Polynomial.Pochhammer
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ringstatement and proof · cited by 7,463
- PartialOrderstatement and proof · cited by 6,410
- Nat.cast_oneproof · cited by 2,501
- IsStrictOrderedRingstatement and proof · cited by 2,490
- LT.lt.leproof · cited by 2,189
- Nat.cast_zeroproof · cited by 1,870
- Polynomial.evalstatement and proof · cited by 796
- neg_add_cancelproof · cited by 256
- eq_or_lt_of_leproof · cited by 92
- ascPochhammerproof · cited by 80
- descPochhammerstatement and proof · cited by 51
- sub_sub_cancel_leftproof · cited by 28
Cited by2
Results whose statement or proof uses this declaration.
- monotoneOn_descPochhammer_evalproof · cited by 0
- pow_le_descPochhammer_evalproof · cited by 0