Theorems · Theorem · order theory
Order.le_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 ∨ x = 1- Defined in
- Mathlib.Algebra.Order.SuccPred
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 18 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
- AddMonoidWithOnestatement and proof · cited by 313
- SuccAddOrderstatement and proof · cited by 108
- IsBotZeroClassstatement and proof · cited by 71
- le_iff_lt_or_eqproof · cited by 26
- Order.lt_one_iffproof · cited by 14
Cited by10
Results whose statement or proof uses this declaration.
- Ordinal.log_of_left_le_oneproof · cited by 13
- Ordinal.opow_log_le_selfproof · cited by 11
- Ordinal.log_eq_zeroproof · cited by 3
- Ordinal.isPrincipal_add_iff_add_left_eq_selfproof · cited by 3
- Ordinal.CNF.of_le_oneproof · cited by 2
- Ordinal.isPrincipal_add_of_le_oneproof · cited by 2
- Ordinal.one_lt_opowproof · cited by 1
- Order.le_two_iffproof · cited by 1
- Ordinal.le_one_iffproof · cited by 0
- ENat.le_one_iff_eq_zero_or_eq_oneproof · cited by 0