{ 
[Info:Type]. [es:EO+(Info)]. [X:EClass(Top)]. [e:E].
(
(X)(e) ~ if e 
prior(X) then (X)(prior(X)(e)) else [] fi
@ if e X then [e] else [] fi ) }
{ Proof }
Definitions occuring in Statement :
es-prior-interface: prior(X),
es-interface-predecessors: (X)(e),
eclass-val: X(e),
in-eclass: e X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
append: as @ bs,
ifthenelse: if b then t else f fi ,
uall: [x:A]. B[x],
top: Top,
cons: [car / cdr],
nil: [],
universe: Type,
sqequal: s ~ t
Definitions :
sqequal: s ~ t,
subtype: S 
T,
top: Top,
event_ordering: EO,
es-E: E,
lambda: 
x.A[x],
event-ordering+: EO+(Info),
universe: Type,
eclass: EClass(A[eo; e]),
all: x:A. B[x],
function: x:A 
B[x],
member: t T,
equal: s = t,
so_lambda: 
x y.t[x; y],
uall: [x:A]. B[x],
isect: 
x:A. B[x],
Repeat: Error :Repeat,
CollapseTHEN: Error :CollapseTHEN,
tactic: Error :tactic,
true: True,
squash: 
T,
es-causl: (e < e'),
apply: f a,
limited-type: LimitedType,
real: 
,
grp_car: |g|,
minus: -n,
add: n + m,
subtract: n - m,
void: Void,
false: False,
not: 
A,
natural_number: $n,
prop: 
,
le: A B,
ge: i 
j ,
int: 
,
set: {x:A| B[x]} ,
less_than: a < b,
nat: 
,
implies: P 
Q,
product: x:A 
B[x],
exists: 
x:A. B[x],
strongwellfounded: SWellFounded(R[x; y]),
nil: [],
cons: [car / cdr],
append: as @ bs,
tl: tl(l),
hd: hd(l),
so_lambda: x.t[x],
sq_type: SQType(T),
Id: Id,
es-interface-predecessors: (X)(e),
fpf: a:A fp-> B[a],
strong-subtype: strong-subtype(A;B),
list: type List,
uimplies: b supposing a,
record-select: r.x,
dep-isect: Error :dep-isect,
record+: record+,
subtype_rel: A r B,
es-E-interface: E(X),
bfalse: ff,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
ifthenelse: if b then t else f fi ,
btrue: tt,
uiff: uiff(P;Q),
and: P 
Q,
iff: P 
Q,
eq_bool: p =b q,
lt_int: i <z j,
le_int: i z j,
eq_int: (i =
j),
eq_atom: x =a y,
null: null(as),
set_blt: a < b,
grp_blt: a < b,
infix_ap: x f y,
dcdr-to-bool: [d],
bl-all: (xL.P[x])_b,
bl-exists: (xL.P[x])_b,
b-exists: (i<n.P[i])_b,
eq_type: eq_type(T;T'),
eq_atom: eq_atom$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',
bimplies: p q,
band: p q,
bor: p 
q,
assert: 
b,
bnot: b,
unit: Unit,
union: left + right,
bool: 
,
es-prior-interface: prior(X),
in-eclass: e X,
atom: Atom,
token: "$token",
eclass-val: X(e),
es-pred: pred(e),
or: P Q,
es-first: first(e),
es-loc: loc(e),
es-le: e loc e' ,
es-locl: (e <loc e'),
es-p-le: e p e',
es-causle: e c e',
es-p-locl: e p< e',
causal-predecessor: causal-predecessor(es;p),
record: record(x.T[x])
Lemmas :
iff_transitivity,
es-interface-predecessors-nil,
eclass-val_wf2,
eclass-val_wf,
es-E-interface-subtype_rel,
es-pred-causl,
append-nil,
es-loc_wf,
es-pred_wf,
es-prior-interface-cases-sq,
es-first_wf,
es-interface-subtype_rel2,
subtype_rel_self,
ifthenelse_wf,
es-E-interface_wf,
Id_wf,
es-interface-predecessors_wf,
set_subtype_base,
assert_wf,
list_subtype_base,
subtype_base_sq,
bool_wf,
es-prior-interface_wf,
subtype_rel_wf,
es-prior-interface_wf1,
es-prior-interface_wf0,
in-eclass_wf,
bnot_wf,
not_wf,
assert_of_bnot,
eqff_to_assert,
uiff_transitivity,
iff_weakening_uiff,
eqtt_to_assert,
es-interface-predecessors-cases,
append_wf,
nat_wf,
ge_wf,
nat_properties,
es-causl-swellfnd,
le_wf,
member_wf,
es-causl_wf,
eclass_wf,
event-ordering+_wf,
top_wf,
es-E_wf,
event-ordering+_inc
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(Top)]. \mforall{}[e:E].
(\mleq{}(X)(e) \msim{} if e \mmember{}\msubb{} prior(X) then \mleq{}(X)(prior(X)(e)) else [] fi @ if e \mmember{}\msubb{} X then [e] else [] fi )
Date html generated:
2011_08_16-PM-05_16_28
Last ObjectModification:
2011_06_20-AM-01_18_35
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