(*#* #stop file *)

Require lift_props.
Require subst0_lift.
Require subst1_defs.

   Section subst1_lift. (****************************************************)

      Theorem subst1_lift_lt : (t1,t2,u:?; i:?) (subst1 i u t1 t2) ->
                               (d:?) (lt i d) -> (h:?)
                               (subst1 i (lift h (minus d (S i)) u) (lift h d t1) (lift h d t2)).
      Intros until 1; XElim H; Clear t2; XAuto.
      Qed.

      Theorem subst1_lift_ge : (t1,t2,u:?; i,h:?) (subst1 i u t1 t2) ->
                               (d:?) (le d i) ->
                               (subst1 (plus i h) u (lift h d t1) (lift h d t2)).
      Intros until 1; XElim H; Clear t2; XAuto.
      Qed.

   End subst1_lift.

      Hints Resolve subst1_lift_lt subst1_lift_ge : ltlc.