Theorems · Theorem · order theory
zpow_right_strictMono
∀ {α : Type u_1} [inst : CommGroup α] [inst_1 : PartialOrder α] [IsOrderedMonoid α] {a : α},
1 < a → StrictMono fun n => a ^ n- Defined in
- Mathlib.Algebra.Order.Group.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 33 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- StrictMonostatement · cited by 706
- IsOrderedMonoidstatement and proof · cited by 577
- zpow_add_oneproof · cited by 18
- strictMono_int_of_lt_succproof · cited by 6
- lt_mul_of_one_lt_right'proof · cited by 6
Cited by5
Results whose statement or proof uses this declaration.
- zpow_lt_zpow_iff_rightproof · cited by 6
- zpow_le_zpow_iff_rightproof · cited by 2
- zpow_lt_zpow_rightproof · cited by 1
- zpow_right_injproof · cited by 1
- Subgroup.mem_closure_singleton_iff_existsUnique_zpowproof · cited by 0