--- /dev/null
+(*#* #stop file *)
+
+Require subst0_gen.
+Require subst1_defs.
+
+ Section subst1_gen_lift. (************************************************)
+
+ Theorem subst1_gen_lift_lt : (u,t1,x:?; i,h,d:?) (subst1 i (lift h d u) (lift h (S (plus i d)) t1) x) ->
+ (EX t2 | x = (lift h (S (plus i d)) t2) & (subst1 i u t1 t2)).
+ Intros; XElim H; Clear x; Intros;
+ Try Subst0Gen; XEAuto.
+ Qed.
+
+ Theorem subst1_gen_lift_eq : (t,u,x:?; h,d,i:?)
+ (le d i) -> (lt i (plus d h)) ->
+ (subst1 i u (lift h d t) x) ->
+ x = (lift h d t).
+ Intros; XElim H1; Clear x; Intros;
+ Try Subst0Gen; XAuto.
+ Qed.
+
+ Theorem subst1_gen_lift_ge : (u,t1,x:?; i,h,d:?) (subst1 i u (lift h d t1) x) ->
+ (le (plus d h) i) ->
+ (EX t2 | x = (lift h d t2) & (subst1 (minus i h) u t1 t2)).
+ Intros; XElim H; Clear x; Intros;
+ Try Subst0Gen; XEAuto.
+ Qed.
+
+ End subst1_gen_lift.
+
+ Tactic Definition Subst1Gen :=
+ Match Context With
+ | [ H: (subst1 ?0 (lift ?1 ?2 ?3) (lift ?1 (S (plus ?0 ?2)) ?4) ?5) |- ? ] ->
+ LApply (subst1_gen_lift_lt ?3 ?4 ?5 ?0 ?1 ?2); [ Clear H; Intros H | XAuto ];
+ XElim H; Intros
+ | [ H: (subst1 ?0 ?1 (lift (1) ?0 ?2) ?3) |- ? ] ->
+ LApply (subst1_gen_lift_eq ?2 ?1 ?3 (1) ?0 ?0); [ Intros H_x | XAuto ];
+ LApply H_x; [ Clear H_x; Intros H_x | Rewrite plus_sym; XAuto ];
+ LApply H_x; [ Clear H H_x; Intros | XAuto ]
+ | [ H0: (subst1 ?0 ?1 (lift (1) ?4 ?2) ?3); H1: (lt ?4 ?0) |- ? ] ->
+ LApply (subst1_gen_lift_ge ?1 ?2 ?3 ?0 (1) ?4); [ Clear H0; Intros H0 | XAuto ];
+ LApply H0; [ Clear H0; Intros H0 | Rewrite plus_sym; XAuto ];
+ XElim H0; Intros
+ | _ -> Subst1GenBase.