{ 
[T:Type]
g:LabeledGraph(T). (lg-acyclic(g) 
SWellFounded(lg-edge(g;a;b))) }
{ Proof }
Definitions occuring in Statement :
lg-acyclic: lg-acyclic(g),
lg-edge: lg-edge(g;a;b),
lg-size: lg-size(g),
labeled-graph: LabeledGraph(T),
int_seg: {i..j
},
uall: [x:A]. B[x],
all: x:A. B[x],
iff: P Q,
natural_number: $n,
universe: Type,
strongwellfounded: SWellFounded(R[x; y])
Definitions :
uall: [x:A]. B[x],
member: t 
T,
all: x:A. B[x],
implies: P Q,
lg-acyclic: lg-acyclic(g),
not: 
A,
false: False,
prop: 
,
ge: i 
j ,
le: A 
B,
nat: 
,
so_lambda: 
x.t[x],
rev_implies: P Q,
iff: P Q,
and: P 
Q,
strongwellfounded: SWellFounded(R[x; y]),
exists: 
x:A. B[x],
int_seg: {i..j},
ifthenelse: if b then t else f fi ,
btrue: tt,
lelt: i j < k,
bfalse: ff,
squash: 
T,
true: True,
so_lambda: x y.t[x; y],
infix_ap: x f y,
decidable: Dec(P),
or: P 
Q,
uimplies: b supposing a,
so_apply: x[s],
bool: 
,
unit: Unit,
sq_type: SQType(T),
guard: {T},
so_apply: x[s1;s2],
it: 
,
lg-connected: lg-connected(g;a;b)
Lemmas :
nat_wf,
lg-connected_wf,
int_seg_wf,
lg-size_wf,
lg-acyclic_wf,
labeled-graph_wf,
nat_properties,
ge_wf,
decidable__lt,
lg-acyclic-has-source,
iff_weakening_uiff,
assert_wf,
lg-is-source_wf,
le_wf,
uall_wf,
not_wf,
lg-edge_wf,
assert-lg-is-source,
lg-remove_wf,
lg-size-remove,
lg-acyclic-remove,
lt_int_wf,
bool_wf,
uiff_transitivity,
eqtt_to_assert,
assert_of_lt_int,
add-nat,
le_int_wf,
bnot_wf,
eqff_to_assert,
assert_functionality_wrt_uiff,
bnot_of_lt_int,
assert_of_le_int,
eq_int_wf,
assert_of_eq_int,
assert_of_bnot,
not_functionality_wrt_uiff,
ifthenelse_wf,
squash_wf,
true_wf,
lg-edge-remove,
subtype_base_sq,
int_subtype_base,
strongwellfounded_wf,
rel_plus_strongwellfounded
\mforall{}[T:Type]. \mforall{}g:LabeledGraph(T). (lg-acyclic(g) \mLeftarrow{}{}\mRightarrow{} SWellFounded(lg-edge(g;a;b)))
Date html generated:
2011_08_16-PM-06_42_21
Last ObjectModification:
2011_06_20-AM-02_01_12
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