#n #p1 elim p1 //
qed.
+(*
+lemma admissible_node_cons:
+ ∀x1,x2,p1,p2.
+ admissible (node x1 x2) (rev_append bool p1 [true]@p2)=true →
+ admissible x2 p1=true.
+ #x1 #x2 #p1 elim p1 normalize // #dir #tl #IH #p2 cases x2 normalize
+ [ #n *)
+
theorem update_correct2:
∀A,v,p1,p2,k,t.
- admissible t (reverse … p2 @ p1) = true →
+ admissible t (p2 @ reverse … p1) = true →
update A v k p1 〈t,p2〉 = update … v k [] 〈t,reverse … p1 @ p2〉.
#A #v #p1 elim p1 normalize //
#dir #ptl #IH #p2 #k #t cases dir normalize nodelta cases t normalize nodelta
[1,3: #n >admissible_leaf_cons #abs destruct
-|*: #x1 #x2 change with (reverse ? (?::ptl)) in match (rev_append ???); >reverse_cons
- >associative_append #H normalize >IH //
-
- normalize change with (reverse ? (true::ptl)) in match (rev_append bool ptl [true]);
-[>(reverse_cons … true ptl) | >(reverse_cons … false ptl)]
-[ >(associative_append ??[?])
-
-
+|*: #x1 #x2 #H >IH // >rev_append_cons >(?:admissible ? p2 = true) try %
+ <rev_append_cons in H; change with (reverse ??) in match (rev_append ???);
+
+(* OLD
theorem update_correct:
∀v,p1,p2,t.
let 〈t',res〉 ≝ setleaf_fun v t (reverse … p1 @ p2) in
#path #IH #x elim x normalize
[ #v cases res normalize lapply (IH (leaf v)) -IH elim path
normalize // * normalize
- [2: #path' #IH #IH2 @IH
\ No newline at end of file
+ [2: #path' #IH #IH2 @IH
+*)
\ No newline at end of file