{ 
[the_es:EO]. [e:E]. [n:
].
firstn(n;before(e)) ~ before(before(e)[n]) supposing n < ||before(e)|| }
{ Proof }
Definitions occuring in Statement :
es-before: before(e),
es-E: E,
event_ordering: EO,
select: l[i],
firstn: firstn(n;as),
length: ||as||,
nat: ,
uimplies: b supposing a,
uall: [x:A]. B[x],
less_than: a < b,
sqequal: s ~ t
Definitions :
implies: P 
Q,
sqequal: s ~ t,
es-before: before(e),
length: ||as||,
set: {x:A| B[x]} ,
real: 
,
grp_car: |g|,
subtype: S 
T,
int: 
,
all: x:A. B[x],
function: x:A 
B[x],
isect: 
x:A. B[x],
uall: [x:A]. B[x],
event_ordering: EO,
uimplies: b supposing a,
less_than: a < b,
prop: 
,
nat: ,
equal: s = t,
es-E: E,
member: t 
T,
Repeat: Error :Repeat,
CollapseTHEN: Error :CollapseTHEN,
tactic: Error :tactic,
lelt: i 
j < k,
int_seg: {i..j
},
es-le: e loc e' ,
es-causle: e c e',
es-locl: (e <loc e'),
record: record(x.T[x]),
es-loc: loc(e),
Id: Id,
top: Top,
strong-subtype: strong-subtype(A;B),
tl: tl(l),
hd: hd(l),
dep-isect: Error :dep-isect,
record+: record+,
record-select: r.x,
sq_type: SQType(T),
list: type List,
subtype_rel: A r B,
firstn: firstn(n;as),
select: l[i],
bfalse: ff,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
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: 
,
true: True,
squash: 
T,
es-causl: (e < e'),
apply: f a,
limited-type: LimitedType,
universe: Type,
minus: -n,
add: n + m,
subtract: n - m,
void: Void,
false: False,
not: A,
natural_number: $n,
le: A B,
ge: i 
j ,
strongwellfounded: SWellFounded(R[x; y]),
exists: x:A. B[x],
product: x:A 
B[x],
es-pred: pred(e),
nil: [],
cons: [car / cdr],
append: as @ bs,
es-first: first(e),
ifthenelse: if b then t else f fi ,
guard: {T}
Lemmas :
int_subtype_base,
firstn_all,
lt_int_wf,
le_int_wf,
assert_of_le_int,
bnot_of_lt_int,
assert_functionality_wrt_uiff,
assert_of_lt_int,
select-append,
ge_wf,
nat_properties,
es-causl-swellfnd,
le_wf,
member_wf,
es-causl_wf,
bool_wf,
assert_wf,
iff_weakening_uiff,
eqtt_to_assert,
not_wf,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
bnot_wf,
es-first_wf,
es-pred_wf,
append_wf,
firstn_wf,
subtype_base_sq,
list_subtype_base,
length-append,
es-before_wf2,
Id_wf,
top_wf,
es-loc_wf,
length_wf_nat,
es-pred-causl,
firstn_append,
false_wf,
event_ordering_wf,
nat_wf,
es-E_wf,
length_wf1,
es-before_wf
\mforall{}[the$_{es}$:EO]. \mforall{}[e:E]. \mforall{}[n:\mBbbN{}]. firstn(n;before(e)) \msim{} before(before(e)[n]) su\000Cpposing n < ||before(e)||
Date html generated:
2011_08_16-AM-10_43_13
Last ObjectModification:
2011_06_18-AM-09_19_40
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