Notation "'query' v" := (OC_Query  _ v) (at level 79) : comp_scope.

Theorem compMap_oc_spec : forall (C D : Set)(P2 : C -> D -> Prop)(A B : Set)(P1 : A -> B -> Prop)(eqdc : EqDec C)(eqdd : EqDec D)(E F S: Set)(eqds : EqDec S)(ls1 : list A)(ls2 : list B)(c1 : A -> Comp C)(c2 : B -> OracleComp E F D)o (s : S), list_pred P1 ls1 ls2 -> (forall a b z, P1 a b -> comp_spec (fun x y => P2 x (fst y)) (c1 a) (c2 b _ _ o z)) -> comp_spec (fun a b => list_pred P2 a (fst b)) (compMap _ c1 ls1)