Theorems · Theorem · order theory
Order.one_le_iff_pos
∀ {α : Type u_1} {x : α} [inst : PartialOrder α] [inst_1 : AddMonoidWithOne α] [ZeroLEOneClass α] [NeZero 1]
[SuccAddOrder α], 1 ≤ x ↔ 0 < x- Defined in
- Mathlib.Algebra.Order.SuccPred
- Cited by
- 27 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- zero_addproof · cited by 2,366
- AddMonoidWithOnestatement and proof · cited by 313
- ZeroLEOneClassstatement and proof · cited by 304
- Order.succ_eq_add_oneproof · cited by 115
- SuccAddOrderstatement and proof · cited by 108
- Order.succ_le_iff_of_not_isMaxproof · cited by 15
- Order.not_isMax_zeroproof · cited by 2
Cited by27
Results whose statement or proof uses this declaration.
- Order.one_le_iff_ne_zeroproof · cited by 32
- Ordinal.opow_le_opow_rightproof · cited by 5
- SimpleGraph.edist_eq_one_iff_adjproof · cited by 5
- SimpleGraph.eccent_topproof · cited by 4
- Module.End.HasUnifEigenvalue.ltproof · cited by 4
- Ordinal.isPrincipal_mul_iff_mul_left_eqproof · cited by 3
- ENat.epow_posproof · cited by 2
- PowerSeries.one_le_order_iff_constCoeff_eq_zeroproof · cited by 2
- Ordinal.left_le_opowproof · cited by 2
- MvPowerSeries.one_le_order_iff_constCoeff_eq_zeroproof · cited by 2
- SimpleGraph.eccent_le_one_iffproof · cited by 1
- ONote.repr_opow_aux₂proof · cited by 1