Nuprl Lemma : prior-classrel-list-append
[A:
']. [X:EClass'(A)]. [es:EO']. [e1,e2:E].
L1,L2:(A 
E) List.
[a:A]
(single-valued-classrel(es;X;A)
prior-classrel-list(es;A;X;L1;e1)
prior-classrel-list(es;A;X;L2;e2)
a 
X(e1)
(e1 <loc e2)
(
L:(A E) List. (L2 = ((L1 @ [<a, e1>]) @ L))))
Proof not projected
Definitions occuring in Statement :
prior-classrel-list: prior-classrel-list(es;A;X;L;e),
single-valued-classrel: single-valued-classrel(es;X;T),
Message: Message,
classrel: v X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-locl: (e <loc e'),
es-E: E,
append: as @ bs,
uall: [x:A]. B[x],
all: x:A. B[x],
exists: x:A. B[x],
implies: P Q,
pair: <a, b>,
product: x:A B[x],
cons: [car / cdr],
nil: [],
list: type List,
universe: Type,
equal: s = t
Definitions :
uall: [x:A]. B[x],
all: x:A. B[x],
implies: P Q,
exists: x:A. B[x],
member: t T,
and: P 
Q,
prop: 
,
label: ...$L... t,
iff: P 
Q,
length: ||as||,
rev_implies: P Q,
subtype: S 
T,
nat: 
,
top: Top,
ycomb: Y,
so_lambda: 
x.t[x],
guard: {T},
l_disjoint: l_disjoint(T;l1;l2),
not: 
A,
false: False,
l_all: (xL.P[x]),
l_contains: A B,
cand: A c B,
lastn: lastn(n;L),
squash: 
T,
true: True,
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff,
le: A 
B,
int_seg: {i..j
},
lelt: i j < k,
or: P 
Q,
gt: i > j,
decidable: Dec(P),
it: 
,
int_iseg: {i...j},
select: l[i],
le_int: i z j,
bnot: 
b,
lt_int: i <z j,
so_lambda: x y.t[x; y],
ge: i 
j ,
prior-classrel-list: prior-classrel-list(es;A;X;L;e),
uimplies: b supposing a,
so_apply: x[s],
rev_uimplies: rev_uimplies(P;Q),
uiff: uiff(P;Q),
bool: 
,
unit: Unit,
l_member: (x l),
sorted-by: sorted-by(R;L),
deq: EqDecider(T),
sq_type: SQType(T),
single-valued-classrel: single-valued-classrel(es;X;T),
so_apply: x[s1;s2],
pi2: snd(t),
pi1: fst(t)
Lemmas :
lastn_wf,
length_wf1,
classrel_wf,
append_wf,
es-locl_wf,
event-ordering+_inc,
Message_wf,
prior-classrel-list_wf,
single-valued-classrel_wf,
es-E_wf,
event-ordering+_wf,
eclass_wf2,
list_extensionality,
nat_wf,
length_append,
length-map,
length-append,
map_wf,
top_wf,
l_contains-no_repeats-length,
pi2_wf,
non_neg_length,
length_wf_nat,
add_functionality_wrt_eq,
length-lastn,
no_repeats-append,
no_repeats-single,
member_singleton,
l_member_wf,
es-locl_irreflexivity,
member_append,
es-locl_transitivity2,
es-le_weakening,
select-append,
lt_int_wf,
bool_wf,
assert_wf,
le_int_wf,
le_wf,
bnot_wf,
select-nth_tl,
select_wf,
squash_wf,
uiff_transitivity,
eqtt_to_assert,
assert_of_lt_int,
eqff_to_assert,
assert_functionality_wrt_uiff,
bnot_of_lt_int,
assert_of_le_int,
member_map,
select_member,
nat_properties,
longer-list-not-member,
es-eq_wf,
deq_wf,
assert-deq,
inl_wf,
not_wf,
assert_of_bnot,
not_functionality_wrt_uiff,
inr_wf,
firstn_wf,
no_repeats-firstn,
length_firstn,
subtype_base_sq,
int_subtype_base,
member_firstn,
select-map,
es-locl_transitivity1,
es-le_weakening_eq,
decidable__lt,
add_wf,
pi1_wf_top,
pair-eta,
true_wf,
eclass_wf,
length-eq-lists-diff-elts
\mforall{}[A:\mBbbU{}']. \mforall{}[X:EClass'(A)]. \mforall{}[es:EO']. \mforall{}[e1,e2:E].
\mforall{}L1,L2:(A \mtimes{} E) List.
\mforall{}[a:A]
(single-valued-classrel(es;X;A)
{}\mRightarrow{} prior-classrel-list(es;A;X;L1;e1)
{}\mRightarrow{} prior-classrel-list(es;A;X;L2;e2)
{}\mRightarrow{} a \mmember{} X(e1)
{}\mRightarrow{} (e1 <loc e2)
{}\mRightarrow{} (\mexists{}L:(A \mtimes{} E) List. (L2 = ((L1 @ [<a, e1>]) @ L))))
Date html generated:
2011_10_20-PM-03_45_03
Last ObjectModification:
2011_08_30-PM-08_49_57
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