{ 
[T:Type]. [g:LabeledGraph(T)]. [x:
].
lg-remove(g;x) ~ g supposing lg-size(g) 
x }
{ Proof }
Definitions occuring in Statement :
lg-remove: lg-remove(g;n),
lg-size: lg-size(g),
labeled-graph: LabeledGraph(T),
nat: ,
uimplies: b supposing a,
uall: [x:A]. B[x],
le: A B,
universe: Type,
sqequal: s ~ t
Definitions :
member: t 
T,
all: x:A. B[x],
implies: P 
Q,
lg-remove: lg-remove(g;n),
nat: ,
le: A B,
top: Top,
not: 
A,
false: False,
subtype: S 
T,
map: map(f;as),
spreadn: spread3,
ifthenelse: if b then t else f fi ,
filter: filter(P;l),
bnot: 
b,
ycomb: Y,
reduce: reduce(f;k;as),
btrue: tt,
prop: 
,
bfalse: ff,
labeled-graph: LabeledGraph(T),
uall: [x:A]. B[x],
uimplies: b supposing a,
int_seg: {i..j
},
bool: 
,
lelt: i j < k,
unit: Unit,
iff: P 
Q,
and: P 
Q,
lg-size: lg-size(g),
it: 
Lemmas :
le_wf,
lg-size_wf,
nat_wf,
labeled-graph_wf,
int_seg_wf,
length_wf1,
nth_tl_is_nil,
top_wf,
append-nil,
firstn_wf,
firstn_all,
eq_int_wf,
bool_wf,
iff_weakening_uiff,
uiff_transitivity,
assert_wf,
eqtt_to_assert,
assert_of_eq_int,
not_wf,
bnot_wf,
eqff_to_assert,
assert_of_bnot,
not_functionality_wrt_uiff,
le_int_wf,
assert_of_le_int,
lt_int_wf,
assert_functionality_wrt_uiff,
bnot_of_le_int,
assert_of_lt_int
\mforall{}[T:Type]. \mforall{}[g:LabeledGraph(T)]. \mforall{}[x:\mBbbN{}]. lg-remove(g;x) \msim{} g supposing lg-size(g) \mleq{} x
Date html generated:
2011_08_16-PM-06_37_17
Last ObjectModification:
2011_06_20-AM-01_56_53
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