{ 
[T:Type]
g1,g2:LabeledGraph(T). a,b:
lg-size(g1) + lg-size(g2).
(lg-edge(lg-append(g1;g2);a;b)
((a < lg-size(g1)) 
(b < lg-size(g1)) lg-edge(g1;a;b))
((lg-size(g1) 
a)
(lg-size(g1) b)
lg-edge(g2;a - lg-size(g1);b - lg-size(g1)))) }
{ Proof }
Definitions occuring in Statement :
lg-edge: lg-edge(g;a;b),
lg-append: lg-append(g1;g2),
lg-size: lg-size(g),
labeled-graph: LabeledGraph(T),
int_seg: {i..j
},
uall: [x:A]. B[x],
le: A B,
all: x:A. B[x],
iff: P Q,
or: P Q,
and: P Q,
less_than: a < b,
subtract: n - m,
add: n + m,
natural_number: $n,
universe: Type
Definitions :
uall: [x:A]. B[x],
all: x:A. B[x],
lg-edge: lg-edge(g;a;b),
lg-append: lg-append(g1;g2),
lg-in-edges: lg-in-edges(g;x),
ifthenelse: if b then t else f fi ,
top: Top,
nat: ,
member: t 
T,
prop: 
,
implies: P Q,
btrue: tt,
bfalse: ff,
le: A B,
not: 
A,
false: False,
iff: P Q,
pi1: fst(t),
pi2: snd(t),
or: P Q,
and: P Q,
rev_implies: P Q,
cand: A c B,
guard: {T},
subtype: S 
T,
spreadn: spread3,
exists: 
x:A. B[x],
int_seg: {i..j},
lelt: i j < k,
l_member: (x l),
labeled-graph: LabeledGraph(T),
bool: 
,
unit: Unit,
uimplies: b supposing a,
decidable: Dec(P),
sq_type: SQType(T),
lg-size: lg-size(g),
it: 
Lemmas :
select-append,
map-is-top-list,
le_wf,
lt_int_wf,
bool_wf,
iff_weakening_uiff,
uiff_transitivity,
assert_wf,
eqtt_to_assert,
assert_of_lt_int,
le_int_wf,
bnot_wf,
eqff_to_assert,
assert_functionality_wrt_uiff,
bnot_of_lt_int,
assert_of_le_int,
select-map,
int_seg_wf,
lg-size_wf,
nat_wf,
labeled-graph_wf,
select_wf,
decidable__cand,
l_member_wf,
decidable__lt,
decidable__l_member,
decidable__equal_int,
pi1_wf_top,
subtype_base_sq,
int_subtype_base,
non_neg_length,
length_wf_nat,
top_wf,
map_wf,
iff_functionality_wrt_iff,
member_map,
l_member_subtype,
length_wf1
\mforall{}[T:Type]
\mforall{}g1,g2:LabeledGraph(T). \mforall{}a,b:\mBbbN{}lg-size(g1) + lg-size(g2).
(lg-edge(lg-append(g1;g2);a;b)
\mLeftarrow{}{}\mRightarrow{} ((a < lg-size(g1)) \mwedge{} (b < lg-size(g1)) \mwedge{} lg-edge(g1;a;b))
\mvee{} ((lg-size(g1) \mleq{} a) \mwedge{} (lg-size(g1) \mleq{} b) \mwedge{} lg-edge(g2;a - lg-size(g1);b - lg-size(g1))))
Date html generated:
2011_08_16-PM-06_40_10
Last ObjectModification:
2011_06_20-AM-01_59_06
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