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Theorems · Theorem · field theory

Even.zpow_pos

∀ {α : Type u_1} [inst : Field α] [inst_1 : LinearOrder α] [IsStrictOrderedRing α] {a : α} {n : ℤ},
  Even n → a ≠ 0 → 0 < a ^ n
Defined in
Mathlib.Algebra.Order.Field.Power
Cited by
2 results in Mathlib
Foundations
Depth 52 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldLinearOrderIsStrictOrderedRing
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Odd.zpow_neg_iff · cited by 3Odd.zpow_neg_iffzpow_two_pos_of_ne_zero · cited by 0zpow_two_pos_of_ne_zeroLinearOrder · cited by 8572LinearOrderField · cited by 7404FieldIsStrictOrderedRing · cited by 2490IsStrictOrderedRingEven · cited by 444EvenLE.le.lt_of_ne' · cited by 41le.lt_of_ne'zpow_ne_zero · cited by 30zpow_ne_zeroEven.zpow_nonneg · cited by 3Even.zpow_nonnegEven.zpow_posCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.