Theorems · Theorem · order theory
zpow_lt_zpow_iff_right
∀ {α : Type u_1} [inst : CommGroup α] [inst_1 : PartialOrder α] [IsOrderedMonoid α] {m n : ℤ} {a : α},
1 < a → (a ^ m < a ^ n ↔ m < n)- Defined in
- Mathlib.Algebra.Order.Group.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 34 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- PartialOrderstatement and proof · cited by 6,410
- CommGroupstatement and proof · cited by 990
- IsOrderedMonoidstatement and proof · cited by 577
- StrictMono.lt_iff_ltproof · cited by 86
- zpow_right_strictMonoproof · cited by 5
Cited by6
Results whose statement or proof uses this declaration.
- existsUnique_zpow_near_of_one_ltproof · cited by 3
- Set.pairwise_disjoint_Ioc_mul_zpowproof · cited by 2
- Subgroup.exists_isLeast_one_ltproof · cited by 2
- not_isCyclic_of_denselyOrderedproof · cited by 1
- denseRange_zpow_iff_surjectiveproof · cited by 1
- Set.pairwise_disjoint_Ico_mul_zpowproof · cited by 1