Theorems · Theorem · field theory
Odd.zpow_neg_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
- 3 results in Mathlib
- Foundations
- Depth 53 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- LT.lt.neproof · cited by 872
- Oddstatement and proof · cited by 364
- even_two_mulproof · cited by 102
- lt_imp_lt_of_le_imp_leproof · cited by 18
- mul_neg_of_pos_of_negproof · cited by 13
- zpow_add_one₀proof · cited by 9
- zpow_nonnegproof · cited by 7
- Even.zpow_posproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Odd.zpow_nonpos_iffproof · cited by 2
- Odd.zpow_negproof · cited by 0
- Odd.zpow_nonneg_iffproof · cited by 0