{ 
[Info:Type]. [eo:EO+(Info)]. [e,e':E]. first(e) ~ tt supposing e' = e }
{ Proof }
Definitions occuring in Statement :
eo-forward: eo.e,
event-ordering+: EO+(Info),
es-first: first(e),
es-E: E,
btrue: tt,
uimplies: b supposing a,
uall: [x:A]. B[x],
universe: Type,
sqequal: s ~ t,
equal: s = t
Definitions :
void: Void,
top: Top,
lambda: 
x.A[x],
record-update: r[x := v],
eo-restrict: eo-restrict(eo;P),
es-eq: es-eq(es),
apply: f a,
eq_id: a = b,
ifthenelse: if b then t else f fi ,
es-loc: loc(e),
subtype: S 
T,
limited-type: LimitedType,
pair: <a, b>,
fpf: a:A fp-> B[a],
strong-subtype: strong-subtype(A;B),
record-select: r.x,
assert: 
b,
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
set: {x:A| B[x]} ,
dep-isect: Error :dep-isect,
record+: record+,
le: A 
B,
ge: i 
j ,
not: 
A,
less_than: a < b,
product: x:A 
B[x],
and: P 
Q,
uiff: uiff(P;Q),
btrue: tt,
eo-forward: eo.e,
guard: {T},
implies: P 
Q,
sq_type: SQType(T),
bool: 
,
es-first: first(e),
subtype_rel: A r B,
function: x:A 
B[x],
all: x:A. B[x],
prop: 
,
universe: Type,
sqequal: s ~ t,
uall: [x:A]. B[x],
uimplies: b supposing a,
isect: 
x:A. B[x],
member: t 
T,
equal: s = t,
es-E: E,
event-ordering+: EO+(Info),
event_ordering: EO,
atom: Atom$n,
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),
exists: x:A. B[x],
es-r-immediate-pred: es-r-immediate-pred(es;R;e';e),
same-thread: same-thread(es;p;e;e'),
decidable: Dec(P),
es-locl: (e <loc e'),
es-causl: (e < e'),
rev_implies: P 
Q,
es-le: e loc e' ,
union: left + right,
iff: P Q,
or: P 
Q,
eq_lnk: a = b,
es-eq-E: e = e',
es-bless: e <loc e',
bimplies: p 
q,
band: p q,
eqof: eqof(d),
Id: Id,
atom: Atom,
es-base-E: es-base-E(es),
true: True,
false: False,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
bnot: b,
es-ble: e loc e',
bor: p q,
record: record(x.T[x]),
token: "$token",
lt_int: i <z j,
le_int: i z j,
bfalse: ff,
unit: Unit,
int: 
Lemmas :
iff_imp_equal_bool,
iff_functionality_wrt_iff,
assert-es-eq-E-2,
iff_wf,
rev_implies_wf,
es-eq-E_wf,
eqtt_to_assert,
eqff_to_assert,
es-eq_wf,
true_wf,
bor_wf,
false_wf,
assert_wf,
subtype_rel_self,
es-base-E_wf,
es-loc_wf,
eq_id_wf,
bnot_wf,
es-ble_wf,
eo-forward-E,
es-le_wf,
Id_wf,
not_wf,
iff_transitivity,
iff_weakening_uiff,
assert_of_bor,
or_functionality_wrt_iff,
assert-es-ble,
uiff_transitivity,
assert_of_bnot,
not_functionality_wrt_uiff,
assert-eq-id,
decidable__es-le,
atom2_subtype_base,
es-le_weakening_eq,
subtype_base_sq,
bool_subtype_base,
event-ordering+_inc,
event-ordering+_wf,
eo-forward-first,
eo-forward-loc,
member_wf,
eo-forward_wf,
es-E_wf,
subtype_rel_wf,
es-first_wf,
bool_wf,
ifthenelse_wf,
btrue_wf
\mforall{}[Info:Type]. \mforall{}[eo:EO+(Info)]. \mforall{}[e,e':E]. first(e) \msim{} tt supposing e' = e
Date html generated:
2011_08_16-AM-11_24_40
Last ObjectModification:
2010_12_10-PM-12_13_48
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