English
A lattice that is a simple order is distributive.
Русский
Ладная система, являющаяся простым порядком, распр.
LaTeX
$$$\mathrm{IsSimpleOrder.distribLattice}(\alpha)$$$
Lean4
/-- A lattice that is a `BoundedOrder` is a distributive lattice.
This is not an instance to prevent loops -/
protected def distribLattice : DistribLattice α :=
{ (inferInstance : Lattice α) with le_sup_inf := fun x y z => by rcases eq_bot_or_eq_top x with (rfl | rfl) <;> simp }
-- see Note [lower instance priority]