Theorems · Theorem · order theory
zpow_left_strictMono
∀ (α : Type u_1) [inst : CommGroup α] [inst_1 : PartialOrder α] [IsOrderedMonoid α] {n : ℤ},
0 < n → StrictMono fun x => x ^ n- Defined in
- Mathlib.Algebra.Order.Group.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
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
- div_zpowproof · cited by 4
- one_lt_div'proof · cited by 3
- one_lt_zpowproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- zpow_lt_zpow_leftproof · cited by 0
- zpow_lt_zpow_iff_leftproof · cited by 0
- zpow_le_zpow_iff_leftproof · cited by 0