Theorems · Theorem · order theory
Order.one_le_iff_ne_zero
∀ {α : Type u_1} {x : α} [inst : PartialOrder α] [inst_1 : AddMonoidWithOne α] [NeZero 1] [SuccAddOrder α]
[IsBotZeroClass α], 1 ≤ x ↔ x ≠ 0- Defined in
- Mathlib.Algebra.Order.SuccPred
- Cited by
- 32 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- AddMonoidWithOnestatement and proof · cited by 313
- pos_iff_ne_zeroproof · cited by 180
- SuccAddOrderstatement and proof · cited by 108
- IsBotZeroClassstatement and proof · cited by 71
- Order.one_le_iff_posproof · cited by 27
Cited by32
Results whose statement or proof uses this declaration.
- Order.lt_one_iffproof · cited by 14
- Ordinal.zero_opowproof · cited by 13
- Ordinal.opow_log_le_selfproof · cited by 11
- Ordinal.opow_addproof · cited by 9
- Ordinal.opow_mulproof · cited by 4
- ENat.self_le_mul_rightproof · cited by 4
- ENat.epow_right_monoproof · cited by 3
- Set.one_le_encard_iff_nonemptyproof · cited by 3
- Ordinal.le_of_dvdproof · cited by 3
- Set.encard_le_one_iff_eqproof · cited by 2
- ONote.NF.of_dvd_omega0proof · cited by 2
- MvPowerSeries.order_ne_zero_iff_constCoeff_eq_zeroproof · cited by 2