Linear locally finite orders are densely ordered iff they are trivial #
Main results #
LocallyFiniteOrder.denselyOrdered_iff_subsingleton
: A linear locally finite order is densely ordered if and only if it is a subsingleton.
theorem
LocallyFiniteOrder.denselyOrdered_iff_subsingleton
{X : Type u_1}
[LinearOrder X]
[LocallyFiniteOrder X]
:
theorem
denselyOrdered_set_iff_subsingleton
{X : Type u_1}
[LinearOrder X]
[LocallyFiniteOrder X]
{s : Set X}
:
theorem
WithBot.denselyOrdered_set_iff_subsingleton
{X : Type u_1}
[LinearOrder X]
[LocallyFiniteOrder X]
{s : Set (WithBot X)}
:
theorem
WithTop.denselyOrdered_set_iff_subsingleton
{X : Type u_1}
[LinearOrder X]
[LocallyFiniteOrder X]
{s : Set (WithTop X)}
: