7 Section subst1_lift. (****************************************************)
9 Theorem subst1_lift_lt : (t1,t2,u:?; i:?) (subst1 i u t1 t2) ->
10 (d:?) (lt i d) -> (h:?)
11 (subst1 i (lift h (minus d (S i)) u) (lift h d t1) (lift h d t2)).
12 Intros until 1; XElim H; Clear t2; XAuto.
15 Theorem subst1_lift_ge : (t1,t2,u:?; i,h:?) (subst1 i u t1 t2) ->
17 (subst1 (plus i h) u (lift h d t1) (lift h d t2)).
18 Intros until 1; XElim H; Clear t2; XAuto.
23 Hints Resolve subst1_lift_lt subst1_lift_ge : ltlc.