(*#* #stop file *)

Require subst1_defs.
Require pr2_subst1.
Require pr3_defs.

   Section pr3_subst1_props. (***********************************************)

      Theorem pr3_subst1: (c,e:?; v:?; i:?) (drop i (0) c (CTail e (Bind Abbr) v)) ->
                          (t1,t2:?) (pr3 c t1 t2) ->
                          (w1:?) (subst1 i v t1 w1) ->
                          (EX w2 | (pr3 c w1 w2) & (subst1 i v t2 w2)).
     Intros until 2; XElim H0; Clear t1 t2; Intros.
(* case 1: pr3_refl *)
     XEAuto.
(* case 2: pr3_single *)
     Pr2Subst1.
     LApply (H2 x); [ Clear H2; Intros H2 | XAuto ].
     XElim H2; XEAuto.
     Qed.

   End pr3_subst1_props.

      Tactic Definition Pr3Subst1 :=
         Match Context With
            | [ H0: (drop ?1 (0) ?2 (CTail ?3 (Bind Abbr) ?4));
                H1: (pr3 ?2 ?5 ?6); H3: (subst1 ?1 ?4 ?5 ?7) |- ? ] ->
               LApply (pr3_subst1 ?2 ?3 ?4 ?1); [ Intros H_x | XAuto ];
               LApply (H_x ?5 ?6); [ Clear H_x H1; Intros H1 | XAuto ];
               LApply (H1 ?7); [ Clear H1; Intros H1 | XAuto ];
               XElim H1; Intros
            | _ -> Pr2Subst1.