Nuprl Lemma : lg-acyclic-has-source
[T:Type]. g:LabeledGraph(T). (
i:
lg-size(g). (
lg-is-source(g;i))) supposing (lg-acyclic(g) and (0 < lg-size(g)))
Proof not projected
Definitions occuring in Statement :
lg-is-source: lg-is-source(g;i),
lg-acyclic: lg-acyclic(g),
lg-size: lg-size(g),
labeled-graph: LabeledGraph(T),
assert: b,
int_seg: {i..j
},
uimplies: b supposing a,
uall: [x:A]. B[x],
all: x:A. B[x],
exists: x:A. B[x],
less_than: a < b,
natural_number: $n,
universe: Type
Definitions :
subtype: S 
T,
true: True,
btrue: tt,
bfalse: ff,
null: null(as),
ifthenelse: if b then t else f fi ,
lg-edge: lg-edge(g;a;b),
or: P 
Q,
so_lambda: 
x.t[x],
nat: ,
false: False,
implies: P 
Q,
not: 
A,
member: t 
T,
lg-is-source: lg-is-source(g;i),
assert: b,
exists: x:A. B[x],
lg-acyclic: lg-acyclic(g),
uimplies: b supposing a,
all: x:A. B[x],
uall: [x:A]. B[x],
pi1: fst(t),
and: P 
Q,
lelt: i 
j < k,
le: A B,
int_seg: {i..j},
nat_plus: 
,
squash: 
T,
guard: {T},
rev_implies: P 
Q,
iff: P Q,
uiff: uiff(P;Q),
unit: Unit,
bool: 
,
so_apply: x[s],
decidable: Dec(P),
prop: 
,
sq_exists: x:{A| B[x]},
sq_type: SQType(T),
it: 
Lemmas :
labeled-graph_wf,
lg-acyclic_wf,
assert_of_le_int,
bnot_of_lt_int,
assert_functionality_wrt_uiff,
eqff_to_assert,
bnot_wf,
le_int_wf,
cons_member,
l_member_wf,
exists_wf,
not_wf,
lg-in-edges_wf,
assert_of_lt_int,
eqtt_to_assert,
less_than_wf,
equal_wf,
uiff_transitivity,
bool_wf,
lt_int_wf,
decidable__lg-edge,
lg-edge_wf,
decidable__assert,
le_wf,
lg-is-source_wf,
assert_wf,
decidable__ex_int_seg,
nat_wf,
lg-size_wf,
int_seg_wf,
lg-connected_wf,
all_wf,
sq_stable__equal,
lelt_wf,
fun_exp_wf,
pigeon-hole-implies,
decidable__lt,
true_wf,
squash_wf,
int_subtype_base,
subtype_base_sq,
and_wf
\mforall{}[T:Type]
\mforall{}g:LabeledGraph(T)
(\mexists{}i:\mBbbN{}lg-size(g). (\muparrow{}lg-is-source(g;i))) supposing (lg-acyclic(g) and (0 < lg-size(g)))
Date html generated:
2012_01_23-PM-12_38_31
Last ObjectModification:
2011_12_14-PM-11_31_20
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