{ 
[T:Type]. [g:LabeledGraph(T)]. [k:
lg-size(g)]. [x:lg-size(g) - 1].
(lg-label(lg-remove(g;k);x) ~ if x <z k
then lg-label(g;x)
else lg-label(g;x + 1)
fi ) }
{ Proof }
Definitions occuring in Statement :
lg-label: lg-label(g;x),
lg-remove: lg-remove(g;n),
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,
add: n + m,
natural_number: $n,
universe: Type,
sqequal: s ~ t
Definitions :
lg-label: lg-label(g;x),
lg-remove: lg-remove(g;n),
member: t 
T,
nat: ,
top: Top,
int_seg: {i..j},
lelt: i 
j < k,
and: P 
Q,
le: A B,
not: 
A,
implies: P 
Q,
false: False,
all: x:A. B[x],
lg-size: lg-size(g),
rev_implies: P 
Q,
iff: P Q,
prop: 
,
int_iseg: {i...j},
so_lambda: 
x.t[x],
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff,
pi1: fst(t),
spreadn: spread3,
labeled-graph: LabeledGraph(T),
uall: [x:A]. B[x],
sq_type: SQType(T),
uimplies: b supposing a,
so_apply: x[s],
guard: {T},
bool: 
,
unit: Unit,
it: 
Lemmas :
lg-size_wf,
int_seg_wf,
nat_wf,
labeled-graph_wf,
select-map,
append_wf,
top_wf,
firstn_wf,
nth_tl_wf,
le_wf,
length_wf1,
select-append,
length-map-sq,
lg-size-remove,
length_firstn,
subtype_base_sq,
set_subtype_base,
int_subtype_base,
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-firstn,
select_wf,
int_seg_properties,
select-nth_tl
\mforall{}[T:Type]. \mforall{}[g:LabeledGraph(T)]. \mforall{}[k:\mBbbN{}lg-size(g)]. \mforall{}[x:\mBbbN{}lg-size(g) - 1].
(lg-label(lg-remove(g;k);x) \msim{} if x <z k then lg-label(g;x) else lg-label(g;x + 1) fi )
Date html generated:
2011_08_16-PM-06_45_15
Last ObjectModification:
2011_06_18-AM-10_57_14
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