Nuprl Lemma : aa_bst_insert_sublemma_left
left_subtree,right_subtree,tp:aa_ltree(
). val,i:.
((aa_binary_search_tree(tp)
aa_binary_search_tree(aa_lt_node(val;left_subtree;right_subtree))
(i < val)
(j:. (aa_bst_member_prop(j;tp) 
(j = i) 
aa_bst_member_prop(j;left_subtree))))
(j:
(aa_bst_member_prop(j;aa_lt_node(val;tp;right_subtree))
(j = i) aa_bst_member_prop(j;aa_lt_node(val;left_subtree;right_subtree)))))
Proof
Definitions occuring in Statement :
aa_binary_search_tree: aa_binary_search_tree(t),
aa_bst_member_prop: aa_bst_member_prop(i;t),
aa_lt_node: aa_lt_node(val;left_subtree;right_subtree),
aa_ltree: aa_ltree(T),
all: x:A. B[x],
iff: P Q,
implies: P Q,
or: P Q,
and: P Q,
less_than: a < b,
int: ,
equal: s = t
Definitions :
so_lambda: 
x.t[x],
prop: 
,
member: t 
T,
rev_implies: P Q,
or: P Q,
iff: P Q,
and: P Q,
implies: P Q,
all: x:A. B[x],
guard: {T},
not: 
A,
so_lambda: so_lambda(x,y,z,w,v.t[x; y; z; w; v]),
aa_bst_member_prop: aa_bst_member_prop(i;t),
so_apply: x[s],
uall: [x:A]. B[x],
uiff: uiff(P;Q),
uimplies: b supposing a,
unit: Unit,
bool: 
,
so_apply: x[s1;s2;s3;s4;s5],
false: False,
bfalse: ff,
btrue: tt,
it: 
Lemmas :
aa_ltree_wf,
iff_wf,
all_wf,
aa_binary_search_tree_wf,
equal_wf,
or_wf,
aa_lt_node_wf,
aa_bst_member_prop_wf,
assert_of_bnot,
eqff_to_assert,
iff_weakening_uiff,
not_wf,
bnot_wf,
iff_transitivity,
assert_of_eq_int,
eqtt_to_assert,
assert_wf,
uiff_transitivity,
bool_wf,
eq_int_wf,
subtype_rel_self,
false_wf,
aa_ltree_ind_wf
\mforall{}left$_{subtree}$,right$_{subtree}$,tp:aa\_ltree(\mBbbZ{}). \mforall{}val,i:\mBbbZ{}\000C.
((aa\_binary\_search\_tree(tp)
\mwedge{} aa\_binary\_search\_tree(aa\_lt\_node(val;left$_{subtree}$;right$_{su\000Cbtree}$))
\mwedge{} (i < val)
\mwedge{} (\mforall{}j:\mBbbZ{}. (aa\_bst\_member\_prop(j;tp) \mLeftarrow{}{}\mRightarrow{} (j = i) \mvee{} aa\_bst\_member\_prop(j;left$_{subtree\mbackslash{}f\000Cf7d$))))
{}\mRightarrow{} (\mforall{}j:\mBbbZ{}
(aa\_bst\_member\_prop(j;aa\_lt\_node(val;tp;right$_{subtree}$))
\mLeftarrow{}{}\mRightarrow{} (j = i) \mvee{} aa\_bst\_member\_prop(j;aa\_lt\_node(val;left$_{subtree}$;right\000C$_{subtree}$)))))
Date html generated:
2013_03_20-AM-09_54_19
Last ObjectModification:
2012_11_27-AM-10_32_59
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