{ 
[T:Type]. [P:T 
].
g1,g2:LabeledGraph(T).
(x
lg-append(g1;g2).P[x] 
xg1.P[x] 
xg2.P[x]) }
{ Proof }
Definitions occuring in Statement :
lg-all: xG.P[x],
lg-append: lg-append(g1;g2),
labeled-graph: LabeledGraph(T),
uall: [x:A]. B[x],
prop: ,
so_apply: x[s],
all: x:A. B[x],
iff: P Q,
and: P Q,
function: x:A B[x],
universe: Type
Definitions :
uall: [x:A]. B[x],
prop: ,
all: x:A. B[x],
lg-all: xG.P[x],
lg-append: lg-append(g1;g2),
lg-size: lg-size(g),
top: Top,
member: t T,
implies: P Q,
iff: P Q,
so_apply: x[s],
and: P Q,
rev_implies: P Q,
int_seg: {i..j
},
lelt: i 
j < k,
ifthenelse: if b then t else f fi ,
le: A B,
btrue: tt,
bfalse: ff,
not: 
A,
false: False,
labeled-graph: LabeledGraph(T),
nat: 
,
bool: 
,
unit: Unit,
uimplies: b supposing a,
sq_type: SQType(T),
guard: {T},
it: 
Lemmas :
lg-size_wf,
length-append,
map_wf,
int_seg_wf,
nat_wf,
top_wf,
length-map-sq,
labeled-graph_wf,
lg-label_wf,
lg-append_wf,
lg-label-append,
lt_int_wf,
bool_wf,
iff_weakening_uiff,
uiff_transitivity,
assert_wf,
eqtt_to_assert,
assert_of_lt_int,
le_wf,
le_int_wf,
bnot_wf,
eqff_to_assert,
assert_functionality_wrt_uiff,
bnot_of_lt_int,
assert_of_le_int,
lg-label_wf_dag,
subtype_base_sq,
int_subtype_base,
nat_properties,
int_seg_properties
\mforall{}[T:Type]. \mforall{}[P:T {}\mrightarrow{} \mBbbP{}].
\mforall{}g1,g2:LabeledGraph(T). (\mforall{}x\mmember{}lg-append(g1;g2).P[x] \mLeftarrow{}{}\mRightarrow{} \mforall{}x\mmember{}g1.P[x] \mwedge{} \mforall{}x\mmember{}g2.P[x])
Date html generated:
2011_08_16-PM-06_46_00
Last ObjectModification:
2011_06_18-AM-10_58_14
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