Theorems · Theorem · commutative algebra
pow_le_descPochhammer_eval
∀ {S : Type u_1} [inst : Ring S] [inst_1 : PartialOrder S] [IsStrictOrderedRing S] {n : ℕ} {s : S},
↑n - 1 ≤ s → (s - ↑n + 1) ^ n ≤ Polynomial.eval s (descPochhammer S n)descPochhammer S n is at least (s-n+1)^n on [n-1, ∞).
- Defined in
- Mathlib.RingTheory.Polynomial.Pochhammer
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites25
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
- LE.le.transproof · cited by 3,151
- IsStrictOrderedRingstatement and proof · cited by 2,490
- le_rflproof · cited by 1,558
- pow_zeroproof · cited by 1,094
- sub_zeroproof · cited by 938
- Polynomial.evalstatement and proof · cited by 796
- pow_succproof · cited by 374
- CharP.cast_eq_zeroproof · cited by 357
- zero_le_oneproof · cited by 316
- add_sub_cancel_rightproof · cited by 187
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