Theorems · Theorem · number theory
Filter.nonneg_of_eventually_pow_nonneg
∀ {α : Type u_1} [inst : Ring α] [inst_1 : LinearOrder α] [IsStrictOrderedRing α] {a : α},
(∀ᶠ (n : ℕ) in Filter.atTop, 0 ≤ a ^ n) → 0 ≤ a- Defined in
- Mathlib.Order.Filter.AtTopBot.ModEq
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- Ringstatement and proof · cited by 7,463
- Filter.Eventuallystatement and proof · cited by 3,134
- IsStrictOrderedRingstatement and proof · cited by 2,490
- Filter.atTopstatement and proof · cited by 2,405
- Oddproof · cited by 364
- Filter.Frequently.and_eventuallyproof · cited by 49
- Filter.Frequently.existsproof · cited by 32
- Odd.pow_nonneg_iffproof · cited by 1
- Nat.frequently_oddproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- TFAE_exists_lt_isLittleO_powproof · cited by 4