{ 
[M:Type 
Type]. [r:pRunType(P.M[P])]. [t:
]. [n:].
lg-is-source(run-intransit(r;t);first-choosable(r;t))
supposing lg-is-source(run-intransit(r;t);n) }
{ Proof }
Definitions occuring in Statement :
first-choosable: first-choosable(r;t),
run-intransit: run-intransit(r;t),
pRunType: pRunType(T.M[T]),
lg-is-source: lg-is-source(g;i),
assert: b,
nat_plus: ,
nat: ,
uimplies: b supposing a,
uall: [x:A]. B[x],
so_apply: x[s],
function: x:A B[x],
universe: Type
Definitions :
eclass: EClass(A[eo; e]),
fpf: a:A fp-> B[a],
strong-subtype: strong-subtype(A;B),
void: Void,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
is-dag: is-dag(g),
ge: i 
j ,
uiff: uiff(P;Q),
subtype_rel: A 
r B,
false: False,
not: 
A,
exists: 
x:A. B[x],
rev_implies: P 
Q,
iff: P 
Q,
subtract: n - m,
search: search(k;P),
lt_int: i <z j,
ifthenelse: if b then t else f fi ,
grp_car: |g|,
less_than: a < b,
lelt: i 
j < k,
le: A B,
int: 
,
set: {x:A| B[x]} ,
real: 
,
rationals: 
,
subtype: S T,
bool: 
,
natural_number: $n,
int_seg: {i..j
},
product: x:A 
B[x],
and: P 
Q,
let: let,
first-choosable: first-choosable(r;t),
implies: P Q,
prop: 
,
assert: b,
uimplies: b supposing a,
nat: ,
all: x:A. B[x],
function: x:A B[x],
isect: 
x:A. B[x],
so_lambda: 
x.t[x],
apply: f a,
universe: Type,
uall: [x:A]. B[x],
nat_plus: ,
pRunType: pRunType(T.M[T]),
member: t 
T,
Auto: Error :Auto,
CollapseTHEN: Error :CollapseTHEN,
lg-is-source: lg-is-source(g;i),
lambda: x.A[x],
lg-size: lg-size(g),
D: Error :D,
run-intransit: run-intransit(r;t),
so_apply: x[s],
pInTransit: pInTransit(P.M[P]),
ldag: LabeledDAG(T),
equal: s = t,
CollapseTHENA: Error :CollapseTHENA,
RepUR: Error :RepUR,
axiom: Ax,
tactic: Error :tactic,
it: 
,
unit: Unit,
limited-type: LimitedType,
bfalse: ff,
le_int: i z j,
eq_int: (i =
j),
eq_atom: x =a y,
null: null(as),
set_blt: a <
b,
grp_blt: a < b,
infix_ap: x f y,
dcdr-to-bool: [d],
bl-all: (xL.P[x])_b,
bl-exists: (xL.P[x])_b,
b-exists: (i<n.P[i])_b,
eq_type: eq_type(T;T'),
eq_atom: eq_atom$n(x;y),
qeq: qeq(r;s),
q_less: q_less(r;s),
q_le: q_le(r;s),
deq-member: deq-member(eq;x;L),
deq-disjoint: deq-disjoint(eq;as;bs),
deq-all-disjoint: deq-all-disjoint(eq;ass;bs),
eq_str: Error :eq_str,
eq_id: a = b,
eq_lnk: a = b,
es-eq-E: e = e',
es-bless: e <loc e',
es-ble: e loc e',
bimplies: p q,
band: p q,
bor: p 
q,
bnot: b,
guard: {T},
btrue: tt,
sq_type: SQType(T),
proper-iseg: L1 < L2,
iseg: l1 l2,
gt: i > j,
tag-by: zT,
or: P Q,
labeled-graph: LabeledGraph(T),
record+: record+,
record: record(x.T[x]),
fset: FSet{T},
isect2: T1 T2,
b-union: A 
B,
list: type List,
true: True,
fpf-cap: f(x)?z,
add: n + m,
pair: <a, b>,
top: Top,
union: left + right,
length: ||as||,
SplitOn: Error :SplitOn,
MaAuto: Error :MaAuto,
minus: -n,
inr: inr x ,
es-E-interface: E(X),
l_member: (x l),
inl: inl x
Lemmas :
true_wf,
uiff_inversion,
lg-is-source_wf,
false_wf,
not_wf,
subtype_rel_wf,
nat_properties,
lg-size_wf,
search_wf,
int_seg_properties,
bool_cases,
bool_wf,
subtype_base_sq,
bool_subtype_base,
iff_weakening_uiff,
uiff_transitivity,
eqtt_to_assert,
assert_of_lt_int,
eqff_to_assert,
assert_functionality_wrt_uiff,
bnot_of_lt_int,
assert_of_le_int,
lt_int_wf,
le_int_wf,
bnot_wf,
btrue_neq_bfalse,
assert_elim,
bfalse_wf,
it_wf,
unit_wf,
pRunType_wf,
nat_plus_wf,
run-intransit_wf,
ldag_wf,
search_property,
le_wf,
int_seg_wf,
lg-size_wf_dag,
nat_wf,
member_wf,
assert_wf,
pInTransit_wf,
lg-is-source_wf_dag
\mforall{}[M:Type {}\mrightarrow{} Type]. \mforall{}[r:pRunType(P.M[P])]. \mforall{}[t:\mBbbN{}\msupplus{}]. \mforall{}[n:\mBbbN{}].
\muparrow{}lg-is-source(run-intransit(r;t);first-choosable(r;t))
supposing \muparrow{}lg-is-source(run-intransit(r;t);n)
Date html generated:
2011_08_17-PM-03_43_23
Last ObjectModification:
2011_06_18-AM-11_24_21
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