{ 
[Info:Type]
X:EClass(Top). es:EO+(Info). e:E.
(
first(e))
(((pred(e) 
X) (prior(X)(e) ~ pred(e)))
((pred(e) X)
(pred(e) prior(X))
(prior(X)(e) ~ prior(X)(pred(e)))))
supposing e prior(X) }
{ Proof }
Definitions occuring in Statement :
es-prior-interface: prior(X),
eclass-val: X(e),
in-eclass: e X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-pred: pred(e),
es-first: first(e),
es-E: E,
assert: b,
uimplies: b supposing a,
uall: [x:A]. B[x],
top: Top,
all: x:A. B[x],
not: A,
or: P Q,
and: P Q,
universe: Type,
sqequal: s ~ t
Definitions :
divides: b | a,
assoced: a ~ b,
set_leq: a 
b,
set_lt: a <p b,
grp_lt: a < b,
l_member: (x l),
l_contains: A 
B,
inject: Inj(A;B;f),
reducible: reducible(a),
prime: prime(a),
squash: 
T,
l_exists: (
xL. P[x]),
l_all: (xL.P[x]),
fun-connected: y is f*(x),
qle: r s,
qless: r < s,
q-rel: q-rel(r;x),
sq_exists: x:{A| B[x]},
i-finite: i-finite(I),
i-closed: i-closed(I),
p-outcome: Outcome,
fset-member: a s,
f-subset: xs ys,
fset-closed: (s closed under fs),
l_disjoint: l_disjoint(T;l1;l2),
cs-not-completed: in state s, a has not completed inning i,
cs-archived: by state s, a archived v in inning i,
cs-passed: by state s, a passed inning i without archiving a value,
cs-inning-committed: in state s, inning i has committed v,
cs-inning-committable: in state s, inning i could commit v ,
cs-archive-blocked: in state s, ws' blocks ws from archiving v in inning i,
cs-precondition: state s may consider v in inning i,
es-le: e loc e' ,
es-causle: e c e',
existse-before: e<e'.P[e],
existse-le: ee'.P[e],
alle-lt: e<e'.P[e],
alle-le: ee'.P[e],
alle-between1: e[e1,e2).P[e],
existse-between1: e[e1,e2).P[e],
alle-between2: e[e1,e2].P[e],
existse-between2: e[e1,e2].P[e],
existse-between3: e(e1,e2].P[e],
es-fset-loc: i locs(s),
es-r-immediate-pred: es-r-immediate-pred(es;R;e';e),
same-thread: same-thread(es;p;e;e'),
decidable: Dec(P),
strong-subtype: strong-subtype(A;B),
sqequal: s ~ t,
guard: {T},
bfalse: ff,
sq_type: SQType(T),
bool: 
,
infix_ap: x f y,
es-causl: (e < e'),
le: A B,
ge: i 
j ,
null: null(as),
less_than: a < b,
uiff: uiff(P;Q),
es-locl: (e <loc e'),
cand: A c B,
exists: x:A. B[x],
iff: P 
Q,
subtype: S T,
atom: Atom,
apply: f a,
es-base-E: es-base-E(es),
token: "$token",
lambda: 
x.A[x],
subtype_rel: A r B,
quotient: x,y:A//B[x; y],
es-E-interface: E(X),
bag: bag(T),
dep-isect: Error :dep-isect,
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
record+: record+,
set: {x:A| B[x]} ,
record-select: r.x,
top: Top,
es-prior-interface: prior(X),
universe: Type,
eclass: EClass(A[eo; e]),
so_lambda: 
x y.t[x; y],
all: x:A. B[x],
es-E: E,
event-ordering+: EO+(Info),
event_ordering: EO,
uimplies: b supposing a,
prop: 
,
product: x:A 
B[x],
or: P Q,
union: left + right,
ifthenelse: if b then t else f fi ,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
true: True,
false: False,
void: Void,
uall: [x:A]. B[x],
isect: 
x:A. B[x],
implies: P Q,
function: x:A 
B[x],
member: t T,
equal: s = t,
and: P Q,
MaAuto: Error :MaAuto,
es-pred: pred(e),
in-eclass: e X,
assert: b,
Decide: Error :Decide,
CollapseTHENA: Error :CollapseTHENA,
Auto: Error :Auto,
CollapseTHEN: Error :CollapseTHEN,
D: Error :D,
es-first: first(e),
not: A,
AssertBY: Error :AssertBY,
tactic: Error :tactic,
Try: Error :Try,
bag_only_single: bag_only_single{bag_only_single_compseq_tag_def:o}(x),
record: record(x.T[x]),
so_lambda: x.t[x],
single-bag: {x},
bag-only: only(bs),
limited-type: LimitedType,
btrue: tt,
eq_bool: p =b q,
lt_int: i <z j,
le_int: i z j,
eq_int: (i =
j),
set_blt: a < b,
grp_blt: a < b,
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'),
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_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,
eclass-val: X(e),
local-pred-class: local-pred-class(P),
es-local-pred: last(P),
unit: Unit,
int: 
,
RepeatFor: Error :RepeatFor,
bag_size_single: bag_size_single{bag_size_single_compseq_tag_def:o}(x),
Id: Id,
inr: inr x ,
fpf: a:A fp-> B[a],
real: 
,
grp_car: |g|,
nat: 
,
inl: inl x ,
empty-bag: {},
natural_number: $n,
bag-size: bag-size(bs),
bag_size_empty: bag_size_empty{bag_size_empty_compseq_tag_def:o},
Unfold: Error :Unfold,
intensional-universe: IType,
so_apply: x[s],
eq_knd: a = b,
fpf-dom: x dom(f)
Lemmas :
union_subtype_base,
intensional-universe_wf,
eq_int_eq_true,
eq_int_wf,
nat_wf,
bag-size_wf,
true_wf,
empty-bag_wf,
bag_wf,
es-causl_wf,
Id_wf,
assert_of_eq_int,
not_functionality_wrt_uiff,
es-local-pred_wf,
ifthenelse_wf,
single-bag_wf,
bag-only_wf,
es-locl_wf,
set_subtype_base,
eqtt_to_assert,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
bnot_wf,
event-ordering+_wf,
event-ordering+_inc,
subtype_rel_self,
es-base-E_wf,
es-E_wf,
es-E-interface_wf,
es-prior-interface_wf,
es-interface-subtype_rel2,
member_wf,
eclass_wf,
es-prior-interface_wf1,
top_wf,
es-prior-interface_wf0,
in-eclass_wf,
assert_wf,
subtype_rel_wf,
assert_witness,
is-prior-interface,
not_wf,
false_wf,
bool_wf,
subtype_base_sq,
bool_subtype_base,
es-locl-first,
es-first_wf,
decidable__assert,
es-pred_wf
\mforall{}[Info:Type]
\mforall{}X:EClass(Top). \mforall{}es:EO+(Info). \mforall{}e:E.
(\mneg{}\muparrow{}first(e))
\mwedge{} (((\muparrow{}pred(e) \mmember{}\msubb{} X) \mwedge{} (prior(X)(e) \msim{} pred(e)))
\mvee{} ((\mneg{}\muparrow{}pred(e) \mmember{}\msubb{} X) \mwedge{} (\muparrow{}pred(e) \mmember{}\msubb{} prior(X)) \mwedge{} (prior(X)(e) \msim{} prior(X)(pred(e)))))
supposing \muparrow{}e \mmember{}\msubb{} prior(X)
Date html generated:
2011_08_16-PM-04_45_49
Last ObjectModification:
2011_06_20-AM-01_03_54
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