Theorems · Theorem · order theory
Order.lt_one_iff
∀ {α : Type u_1} {x : α} [inst : LinearOrder α] [inst_1 : AddMonoidWithOne α] [SuccAddOrder α] [IsBotZeroClass α]
[NeZero 1], x < 1 ↔ x = 0- Defined in
- Mathlib.Algebra.Order.SuccPred
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 17 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.
- LinearOrderstatement and proof · cited by 8,572
- Iff.notproof · cited by 489
- AddMonoidWithOnestatement and proof · cited by 313
- SuccAddOrderstatement and proof · cited by 108
- IsBotZeroClassstatement and proof · cited by 71
- Order.one_le_iff_ne_zeroproof · cited by 32
Cited by14
Results whose statement or proof uses this declaration.
- Order.le_one_iffproof · cited by 10
- ENat.epow_right_monoproof · cited by 3
- Ordinal.left_le_opowproof · cited by 2
- Ideal.eq_span_singleton_of_height_eq_oneproof · cited by 2
- Ideal.mem_minimalPrimes_span_of_mem_minimalPrimes_span_insertproof · cited by 1
- Ordinal.lt_one_iff_zeroproof · cited by 1
- ENat.mul_epowproof · cited by 0
- ENat.epow_left_monoproof · cited by 0
- ENat.epow_mulproof · cited by 0
- ENat.lt_one_iff_eq_zeroproof · cited by 0
- ENat.sInf_eq_zeroproof · cited by 0
- ENat.card_funproof · cited by 0