Theorems · Theorem · order theory
Order.lt_two_iff
∀ {α : Type u_1} {x : α} [inst : LinearOrder α] [inst_1 : AddMonoidWithOne α] [SuccAddOrder α] [NoMaxOrder α],
x < 2 ↔ x ≤ 1- Defined in
- Mathlib.Algebra.Order.SuccPred
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 20 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
- NoMaxOrderstatement and proof · cited by 340
- AddMonoidWithOnestatement and proof · cited by 313
- SuccAddOrderstatement and proof · cited by 108
- one_add_one_eq_twoproof · cited by 65
- Order.lt_add_one_iffproof · cited by 13
Cited by5
Results whose statement or proof uses this declaration.
- Ordinal.isPrincipal_add_of_isPrincipal_mulproof · cited by 3
- Ordinal.isPrincipal_mul_twoproof · cited by 2
- Order.le_two_iffproof · cited by 1
- AddAction.IsPreprimitive.of_card_ltproof · cited by 0
- AddAction.IsBlock.subsingleton_of_card_ltproof · cited by 0