Nuprl Lemma : lg-label-append
[T:Type]. [g1,g2:LabeledGraph(T)]. [x:
lg-size(lg-append(g1;g2))].
(lg-label(lg-append(g1;g2);x) ~ if x <z lg-size(g1) then lg-label(g1;x) else lg-label(g2;x - lg-size(g1)) fi )
Proof not projected
Definitions occuring in Statement :
lg-label: lg-label(g;x),
lg-append: lg-append(g1;g2),
lg-size: lg-size(g),
labeled-graph: LabeledGraph(T),
lt_int: i <z j,
ifthenelse: if b then t else f fi ,
int_seg: {i..j
},
uall: [x:A]. B[x],
subtract: n - m,
natural_number: $n,
universe: Type,
sqequal: s ~ t
Definitions :
member: t 
T,
lg-label: lg-label(g;x),
lg-append: lg-append(g1;g2),
bfalse: ff,
btrue: tt,
prop: 
,
implies: P 
Q,
all: x:A. B[x],
ifthenelse: if b then t else f fi ,
top: Top,
nat: ,
lg-size: lg-size(g),
spreadn: spread3,
pi1: fst(t),
uall: [x:A]. B[x],
labeled-graph: LabeledGraph(T),
uimplies: b supposing a,
iff: P 
Q,
unit: Unit,
bool: 
,
and: P 
Q,
lelt: i 
j < k,
int_seg: {i..j},
it: 
,
guard: {T}
Lemmas :
labeled-graph_wf,
nat_wf,
lg-append_wf,
int_seg_wf,
lg-size_wf,
assert_of_le_int,
bnot_of_lt_int,
assert_functionality_wrt_uiff,
eqff_to_assert,
bnot_wf,
le_int_wf,
assert_of_lt_int,
eqtt_to_assert,
assert_wf,
uiff_transitivity,
iff_weakening_uiff,
bool_wf,
lt_int_wf,
le_wf,
top_wf,
map_wf,
select-append,
length-map-sq,
length-append,
select-map,
select_wf
\mforall{}[T:Type]. \mforall{}[g1,g2:LabeledGraph(T)]. \mforall{}[x:\mBbbN{}lg-size(lg-append(g1;g2))].
(lg-label(lg-append(g1;g2);x) \msim{} if x <z lg-size(g1)
then lg-label(g1;x)
else lg-label(g2;x - lg-size(g1))
fi )
Date html generated:
2012_01_23-PM-12_39_11
Last ObjectModification:
2012_01_06-AM-10_23_23
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