Definition prove_goal (exp : Expr.expr our_types) := false.Definition work_on_goal (exp : Expr.expr our_types) := exp.

(* Specifications: *)
Lemma work_on_goal_sound : forall exp exp2 f p p2, work_on_goal exp = exp2 -> Expr.exprD f nil nil exp prop_type_var = Some p -> (Expr.exprD f nil nil exp2 prop_type_var = Some p2 /\ (p2 -> p)).
Lemma prove_goal_sound : forall exp f p, prove_goal exp = true -> Expr.exprD f nil nil exp prop_type_var = Some p -> p.