Theorems · Theorem · field theory
Odd.zpow_nonpos_iff
∀ {α : Type u_1} [inst : Field α] [inst_1 : LinearOrder α] [IsStrictOrderedRing α] {a : α} {n : ℤ},
Odd n → (a ^ n ≤ 0 ↔ a ≤ 0)- Defined in
- Mathlib.Algebra.Order.Field.Power
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- le_iff_lt_or_eqproof · cited by 26
- Int.not_even_iff_oddproof · cited by 8
- Even.zeroproof · cited by 6
- zpow_eq_zero_iffproof · cited by 5
- Odd.zpow_neg_iffproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Odd.zpow_nonposproof · cited by 0
- Odd.zpow_pos_iffproof · cited by 0