{ 
[T:Type]. [G:LabeledGraph(T)]. [P:T 
].
(lg-search(G;x.P[x]) 
lg-size(G)?) }
{ Proof }
Definitions occuring in Statement :
lg-search: lg-search(G;x.P[x]),
lg-size: lg-size(g),
labeled-graph: LabeledGraph(T),
bool: ,
int_seg: {i..j
},
uall: [x:A]. B[x],
so_apply: x[s],
unit: Unit,
member: t T,
function: x:A B[x],
union: left + right,
natural_number: $n,
universe: Type
Definitions :
uall: [x:A]. B[x],
member: t T,
lg-search: lg-search(G;x.P[x]),
all: x:A. B[x],
implies: P 
Q,
int_seg: {i..j},
let: let,
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff,
prop: 
,
and: P 
Q,
le: A 
B,
not: 
A,
lelt: i j < k,
squash: 
T,
true: True,
false: False,
so_apply: x[s],
bool: ,
nat: ,
unit: Unit,
iff: P 
Q,
it: 
Lemmas :
bool_wf,
labeled-graph_wf,
lg-size_wf,
nat_wf,
search_wf,
int_seg_wf,
eq_int_wf,
iff_weakening_uiff,
uiff_transitivity,
assert_wf,
eqtt_to_assert,
assert_of_eq_int,
it_wf,
nat_properties,
not_wf,
bnot_wf,
eqff_to_assert,
assert_of_bnot,
not_functionality_wrt_uiff,
le_wf,
unit_wf,
lg-label_wf
\mforall{}[T:Type]. \mforall{}[G:LabeledGraph(T)]. \mforall{}[P:T {}\mrightarrow{} \mBbbB{}]. (lg-search(G;x.P[x]) \mmember{} \mBbbN{}lg-size(G)?)
Date html generated:
2011_08_16-PM-06_46_29
Last ObjectModification:
2011_06_18-AM-10_58_44
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