---

Step * 2 1 of Lemma aa_bst_insert_sublemma_right


1. left_subtree : aa_ltree()@i
2. right_subtree : aa_ltree()@i
3. tp : aa_ltree()@i
4. val : @i
5. i : @i
6. aa_binary_search_tree(tp)@i
7. aa_binary_search_tree(aa_lt_node(val;left_subtree;right_subtree))@i
8. i > val@i
9. j:. (aa_bst_member_prop(j;tp)  (j = i)  aa_bst_member_prop(j;right_subtree))@i
10. j : @i
11. (j = i)  aa_bst_member_prop(j;aa_lt_node(val;left_subtree;right_subtree))@i
12. aa_bst_member_prop(j;tp)  ((j = i)  aa_bst_member_prop(j;right_subtree))
13. aa_bst_member_prop(j;tp)  (j = i)  aa_bst_member_prop(j;right_subtree)
14. j = i
 aa_bst_member_prop(j;aa_lt_node(val;left_subtree;tp))
BY
{ ... }



1.  left$_{subtree}$  :  aa\_ltree(\mBbbZ{})@i
2.  right$_{subtree}$  :  aa\_ltree(\mBbbZ{})@i
3.  tp  :  aa\_ltree(\mBbbZ{})@i
4.  val  :  \mBbbZ{}@i
5.  i  :  \mBbbZ{}@i
6.  aa\_binary\_search\_tree(tp)@i
7.  aa\_binary\_search\_tree(aa\_lt\_node(val;left$_{subtree}$;right$_{sub\000Ctree}$))@i
8.  i  >  val@i
9.  \mforall{}j:\mBbbZ{}.  (aa\_bst\_member\_prop(j;tp)  \mLeftarrow{}{}\mRightarrow{}  (j  =  i)  \mvee{}  aa\_bst\_member\_prop(j;right$_{subtree\mbackslash{}ff\000C7d$))@i
10.  j  :  \mBbbZ{}@i
11.  (j  =  i)  \mvee{}  aa\_bst\_member\_prop(j;aa\_lt\_node(val;left$_{subtree}$;right$\mbackslash{}ff\000C5f{subtree}$))@i
12.  aa\_bst\_member\_prop(j;tp)  {}\mRightarrow{}  ((j  =  i)  \mvee{}  aa\_bst\_member\_prop(j;right$_{subtree}\mbackslash{}ff2\000C4))
13.  aa\_bst\_member\_prop(j;tp)  \mLeftarrow{}{}  (j  =  i)  \mvee{}  aa\_bst\_member\_prop(j;right$_{subtree}$\000C)
14.  j  =  i
\mvdash{}  aa\_bst\_member\_prop(j;aa\_lt\_node(val;left$_{subtree}$;tp))


By

...\mcdot{}



Home Index