Simple orders #
[UPSTREAM] In a simple order the only strict pair is ⊥ < ⊤: mathlib proves each half
(IsSimpleOrder.eq_bot_of_lt, IsSimpleOrder.eq_top_of_lt) and the special case Bool.lt_iff,
and the characterization holds for every simple order, so a two-element scale inherits it from its
IsSimpleOrder instance.
theorem
IsSimpleOrder.lt_iff_eq_bot_and_eq_top
{α : Type u_1}
[PartialOrder α]
[BoundedOrder α]
[IsSimpleOrder α]
{a b : α}
:
a < b ↔ a = ⊥ ∧ b = ⊤