Nuprl Lemma : aa_bst_insert_trial4
t:aa_ltree(
). i:.
(aa_binary_search_tree(t)
(
tp:aa_ltree()
(aa_binary_search_tree(tp) 
(j:. (aa_bst_member_prop(j;tp) 
(j = i) 
aa_bst_member_prop(j;t))))))
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_ltree: aa_ltree(T),
all: x:A. B[x],
exists: x:A. B[x],
iff: P Q,
implies: P Q,
or: P Q,
and: P Q,
int: ,
equal: s = t
Definitions :
all: x:A. B[x],
implies: P Q,
member: t 
T,
and: P Q,
iff: P Q,
or: P Q,
prop: 
,
so_lambda: 
x.t[x],
rev_implies: P Q,
aa_binary_search_tree: aa_binary_search_tree(t),
exists: x:A. B[x],
aa_bst_member_prop: aa_bst_member_prop(i;t),
false: False,
le: A 
B,
aa_max_ltree: aa_max_ltree(t),
aa_min_ltree: aa_min_ltree(t),
not: 
A,
so_lambda: so_lambda(x,y,z,w,v.t[x; y; z; w; v]),
guard: {T},
gt: i > j,
uall: [x:A]. B[x],
so_apply: x[s],
so_apply: x[s1;s2;s3;s4;s5],
bool: 
,
unit: Unit,
uimplies: b supposing a,
uiff: uiff(P;Q),
it: 
,
btrue: tt,
bfalse: ff
Lemmas :
aa_binary_search_tree_wf,
aa_ltree_wf,
aa_ltree-induction,
exists_wf,
all_wf,
iff_wf,
aa_bst_member_prop_wf,
or_wf,
equal_wf,
aa_lt_leaf_wf,
aa_lt_node_wf,
false_wf,
aa_ltree_ind_wf,
eq_int_wf,
bool_wf,
uiff_transitivity,
assert_wf,
eqtt_to_assert,
assert_of_eq_int,
iff_transitivity,
bnot_wf,
not_wf,
iff_weakening_uiff,
eqff_to_assert,
assert_of_bnot,
subtype_rel_self,
lt_int_wf,
less_than_wf,
assert_of_lt_int,
le_int_wf,
le_wf,
assert_functionality_wrt_uiff,
bnot_of_lt_int,
assert_of_le_int,
aa_max_ltree_wf,
unit_wf2,
aa_max_ltree_spec2,
aa_bst_member_property2,
aa_bst_insert_sublemma_left,
aa_min_ltree_wf,
aa_min_ltree_spec2,
aa_bst_member_property2r,
aa_bst_insert_sublemma_right
\mforall{}t:aa\_ltree(\mBbbZ{}). \mforall{}i:\mBbbZ{}.
(aa\_binary\_search\_tree(t)
{}\mRightarrow{} (\mexists{}tp:aa\_ltree(\mBbbZ{})
(aa\_binary\_search\_tree(tp)
\mwedge{} (\mforall{}j:\mBbbZ{}. (aa\_bst\_member\_prop(j;tp) \mLeftarrow{}{}\mRightarrow{} (j = i) \mvee{} aa\_bst\_member\_prop(j;t))))))
Date html generated:
2013_03_20-AM-09_54_46
Last ObjectModification:
2012_11_27-AM-10_33_01
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