Theorems · Theorem · field theory
Odd.zpow_nonpos
∀ {α : Type u_1} [inst : Field α] [inst_1 : LinearOrder α] [IsStrictOrderedRing α] {a : α} {n : ℤ},
Odd n → a ≤ 0 → a ^ n ≤ 0Alias of the reverse direction of Odd.zpow_nonpos_iff.
- Defined in
- Mathlib.Algebra.Order.Field.Power
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
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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
- Fieldstatement and proof · cited by 7,404
- IsStrictOrderedRingstatement and proof · cited by 2,490
- Oddstatement and proof · cited by 364
- Odd.zpow_nonpos_iffproof · cited by 2
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