{ 
[T:Type]. [g:LabeledGraph(T)]. [i:
lg-size(g)].
uiff(
lg-is-source(g;i);[j:lg-size(g)]. (
lg-edge(g;j;i))) }
{ Proof }
Definitions occuring in Statement :
lg-is-source: lg-is-source(g;i),
lg-edge: lg-edge(g;a;b),
lg-size: lg-size(g),
labeled-graph: LabeledGraph(T),
assert: b,
int_seg: {i..j
},
uiff: uiff(P;Q),
uall: [x:A]. B[x],
not: A,
natural_number: $n,
universe: Type
Definitions :
uall: [x:A]. B[x],
uiff: uiff(P;Q),
assert: b,
lg-is-source: lg-is-source(g;i),
not: A,
lg-edge: lg-edge(g;a;b),
ifthenelse: if b then t else f fi ,
bfalse: ff,
member: t 
T,
all: x:A. B[x],
implies: P 
Q,
btrue: tt,
prop: 
,
and: P 
Q,
uimplies: b supposing a,
false: False,
subtype: S 
T,
top: Top,
so_lambda: 
x.t[x],
null: null(as),
true: True,
or: P 
Q,
int_seg: {i..j},
bool: 
,
lelt: i 
j < k,
unit: Unit,
iff: P 
Q,
so_apply: x[s],
le: A B,
nat: ,
rev_implies: P Q,
it: 
Lemmas :
lt_int_wf,
bool_wf,
iff_weakening_uiff,
uiff_transitivity,
assert_wf,
eqtt_to_assert,
assert_of_lt_int,
lg-in-edges_wf,
l_member_wf,
null_wf3,
top_wf,
assert_witness,
uall_wf,
not_wf,
le_wf,
le_int_wf,
bnot_wf,
eqff_to_assert,
assert_functionality_wrt_uiff,
bnot_of_lt_int,
assert_of_le_int,
false_wf,
int_seg_wf,
lg-size_wf,
nat_wf,
ifthenelse_wf,
bfalse_wf,
labeled-graph_wf,
not_functionality_wrt_iff,
nil_member,
cons_member
\mforall{}[T:Type]. \mforall{}[g:LabeledGraph(T)]. \mforall{}[i:\mBbbN{}lg-size(g)].
uiff(\muparrow{}lg-is-source(g;i);\mforall{}[j:\mBbbN{}lg-size(g)]. (\mneg{}lg-edge(g;j;i)))
Date html generated:
2011_08_16-PM-06_41_47
Last ObjectModification:
2011_06_20-AM-02_00_53
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