Theorems · Theorem · order theory
zpow_le_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
- 2 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.le_iff_leproof · cited by 104
- zpow_right_strictMonoproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- existsUnique_zpow_near_of_one_ltproof · cited by 3
- Subgroup.isLeast_of_closure_iff_eq_mabsproof · cited by 0