Module Type BOOLEAN_ALGEBRA.
Parameters (t:Type) (Ord : t -> t -> Prop)
(top bot : t) (lub glb : t -> t -> t) (comp : t -> t).
Declare Scope ba.
Delimit Scope ba with ba. Open Scope ba.
Notation "x <= y" := (Ord x y) (at level 70, no associativity) : ba.

Axiom glb_lower1 : forall x y, (glb x y) <= x.
Axiom glb_lower2 : forall x y, (glb x y) <= y.
Axiom glb_greatest : forall x y z, z <= x -> z <= y -> z <= (glb x y).