{ 
[f:Top]. [g:LabeledGraph(Top)]. [x:
lg-size(g)].
(lg-label(lg-map(f;g);x) ~ f lg-label(g;x)) }
{ Proof }
Definitions occuring in Statement :
lg-map: lg-map(f;g),
lg-label: lg-label(g;x),
lg-size: lg-size(g),
labeled-graph: LabeledGraph(T),
int_seg: {i..j
},
uall: [x:A]. B[x],
top: Top,
apply: f a,
natural_number: $n,
sqequal: s ~ t
Definitions :
uall: [x:A]. B[x],
member: t 
T,
lg-label: lg-label(g;x),
lg-map: lg-map(f;g),
all: x:A. B[x],
implies: P 
Q,
prop: 
,
top: Top,
int_seg: {i..j},
length: ||as||,
pi1: fst(t),
map: map(f;as),
spreadn: spread3,
ycomb: Y,
lelt: i 
j < k,
and: P 
Q,
le: A B,
not: 
A,
false: False,
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff,
labeled-graph: LabeledGraph(T),
nat: ,
bool: 
,
unit: Unit,
iff: P 
Q,
uimplies: b supposing a,
lg-size: lg-size(g),
it: 
,
guard: {T}
Lemmas :
lg-size_wf,
int_seg_wf,
top_wf,
nat_wf,
labeled-graph_wf,
length_wf1,
le_int_wf,
bool_wf,
iff_weakening_uiff,
le_wf,
uiff_transitivity,
assert_wf,
eqtt_to_assert,
assert_of_le_int,
lt_int_wf,
bnot_wf,
eqff_to_assert,
assert_functionality_wrt_uiff,
bnot_of_le_int,
assert_of_lt_int,
select-cons
\mforall{}[f:Top]. \mforall{}[g:LabeledGraph(Top)]. \mforall{}[x:\mBbbN{}lg-size(g)]. (lg-label(lg-map(f;g);x) \msim{} f lg-label(g;x))
Date html generated:
2011_08_16-PM-06_44_56
Last ObjectModification:
2011_06_18-AM-10_56_54
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