Theorems · Theorem · order theory
zpow_lt_zpow_iff_left
∀ {α : Type u_1} [inst : CommGroup α] [inst_1 : LinearOrder α] [IsOrderedMonoid α] {n : ℤ} {a b : α},
0 < n → (a ^ n < b ^ n ↔ a < b)- Defined in
- Mathlib.Algebra.Order.Group.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 31 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
- CommGroupstatement and proof · cited by 990
- IsOrderedMonoidstatement and proof · cited by 577
- StrictMono.lt_iff_ltproof · cited by 86
- zpow_left_strictMonoproof · cited by 3
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