(** * Lattice for dataflow analysis *)
Module VA <: SEMILATTICE.
Inductive t' := Bot | State (ae: aenv) (am: amem).
Definition t := t'.
Definition eq (x y: t) :=
match x, y with
| Bot, Bot => True
| State ae1 am1, State ae2 am2 =>
AE.eq ae1 ae2 /\ forall bc m, mmatch bc m am1 <-> mmatch bc m am2
| _, _ => False
end.

Lemma beq_correct: forall x y, beq x y = true -> eq x y.
Definition ge (x y: t) : Prop :=
match x, y with
| _, Bot => True
| Bot, _ => False
| State ae1 am1, State ae2 am2 => AE.ge ae1 ae2 /\ forall bc m, mmatch bc m am2 -> mmatch bc m am1
end.