{ 
[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,
equal: s = t
Definitions :
local-pred-class: local-pred-class(P),
prop: 
,
subtype: S 
T,
do-apply: do-apply(f;x),
apply: f a,
es-local-pred: last(P),
can-apply: can-apply(f;x),
bool: 
,
es-locl: (e <loc e'),
set: {x:A| B[x]} ,
eclass-val: X(e),
es-pred: pred(e),
es-first: first(e),
es-prior-interface: prior(X),
top: Top,
member: t T,
void: Void,
false: False,
implies: P 
Q,
universe: Type,
so_lambda: 
x y.t[x; y],
eclass: EClass(A[eo; e]),
uall: [x:A]. B[x],
so_lambda: x.t[x],
all: x:A. B[x],
function: x:A 
B[x],
uimplies: b supposing a,
isect: 
x:A. B[x],
or: P Q,
union: left + right,
and: P Q,
product: x:A 
B[x],
equal: s = t,
not: A,
assert: b,
es-E: E,
event-ordering+: EO+(Info),
event_ordering: EO,
CollapseTHEN: Error :CollapseTHEN,
Auto: Error :Auto,
in-eclass: e X,
lambda: x.A[x],
CollapseTHENA: Error :CollapseTHENA,
ParallelOp: Error :ParallelOp,
D: Error :D,
bag_size_empty: bag_size_empty{bag_size_empty_compseq_tag_def:o},
bag_only_single: bag_only_single{bag_only_single_compseq_tag_def:o}(x),
bag_size_single: bag_size_single{bag_size_single_compseq_tag_def:o}(x),
cand: A c B,
atom: Atom,
es-base-E: es-base-E(es),
token: "$token",
infix_ap: x f y,
es-causl: (e < e'),
fpf: a:A fp-> B[a],
strong-subtype: strong-subtype(A;B),
record-select: r.x,
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
decide: case b of inl(x) => s[x] | inr(y) => t[y],
ifthenelse: if b then t else f fi ,
dep-isect: Error :dep-isect,
record+: record+,
le: A 
B,
ge: i 
j ,
less_than: a < b,
uiff: uiff(P;Q),
subtype_rel: A r B,
bag: bag(T),
natural_number: $n,
real: 
,
grp_car: |g|,
int: 
,
nat: 
,
bag-size: bag-size(bs),
eq_int: (i =
j),
sq_exists: 
x:{A| B[x]},
MaAuto: Error :MaAuto,
outl: outl(x),
isl: isl(x),
axiom: Ax,
true: True,
limited-type: LimitedType,
inl: inl x ,
bfalse: ff,
btrue: tt,
eq_bool: p =b q,
lt_int: i <z j,
le_int: i z j,
null: null(as),
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,
unit: Unit,
pair: <a, b>,
Knd: Knd,
IdLnk: IdLnk,
Id: Id,
rationals: 
,
so_apply: x[s],
guard: {T},
eq_knd: a = b,
list: type List,
l_member: (x l),
fpf-dom: x dom(f),
tactic: Error :tactic,
empty-bag: {},
bag-only: only(bs),
inr: inr x ,
RepeatFor: Error :RepeatFor,
Complete: Error :Complete,
ORELSE: Error :ORELSE,
THENL_cons: Error :THENL_nil,
THENL_cons: Error :THENL_cons,
THENL_v2: Error :THENL
Lemmas :
bag-only_wf,
empty-bag_wf,
es-pred_wf,
true_wf,
false_wf,
es-first_wf,
bnot_wf,
assert_of_bnot,
eqff_to_assert,
uiff_transitivity,
eqtt_to_assert,
isl_wf,
outl_wf,
ifthenelse_wf,
eq_int_wf,
bag_wf,
member_wf,
nat_wf,
bag-size_wf,
es-local-pred_wf,
bool_wf,
es-base-E_wf,
subtype_rel_self,
not_wf,
assert_wf,
es-E_wf,
event-ordering+_wf,
event-ordering+_inc,
top_wf,
eclass_wf,
uall_wf,
es-local-pred-cases,
es-locl_wf,
in-eclass_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) = pred(e)))
\mvee{} ((\mneg{}\muparrow{}pred(e) \mmember{}\msubb{} X) \mwedge{} (\muparrow{}pred(e) \mmember{}\msubb{} prior(X)) \mwedge{} (prior(X)(e) = prior(X)(pred(e)))))
supposing \muparrow{}e \mmember{}\msubb{} prior(X)
Date html generated:
2011_08_16-PM-04_45_27
Last ObjectModification:
2011_06_20-AM-01_03_47
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