Nuprl Lemma : parallel-class-locally-programmable
[Info:{Info:Type| 
Info} ]
A:{A:Type| valueall-type(A)}
[X,Y:EClass(A)]. (NormalLProgrammable(A;X) 
NormalLProgrammable(A;Y) NormalLProgrammable(A;X || Y))
Proof not projected
Definitions occuring in Statement :
normal-locally-programmable: NormalLProgrammable(A;X),
parallel-class: X || Y,
eclass: EClass(A[eo; e]),
uall: [x:A]. B[x],
all: x:A. B[x],
squash: T,
implies: P Q,
set: {x:A| B[x]} ,
universe: Type,
valueall-type: valueall-type(T)
Definitions :
uall: [x:A]. B[x],
all: x:A. B[x],
implies: P Q,
normal-locally-programmable: NormalLProgrammable(A;X),
sq_exists: 
x:{A| B[x]},
local-program-at: local-program-at{i:l}(Info;A;X;dfp;x),
exists: x:A. B[x],
member: t 
T,
prop: 
,
and: P 
Q,
le: A 
B,
not: 
A,
false: False,
so_lambda: 
x y.t[x; y],
squash: T,
true: True,
int_seg: {i..j
},
length: ||as||,
select: l[i],
ycomb: Y,
ifthenelse: if b then t else f fi ,
le_int: i z j,
bnot: 
b,
lt_int: i <z j,
bfalse: ff,
btrue: tt,
lelt: i j < k,
df-program-type: df-program-type(dfp),
parallel-df-program-case1: parallel-df-program-case1(B;F;dfps),
parallel-df-prog: parallel-df-prog,
has-valueall: has-valueall(a),
so_lambda: x.t[x],
pi1: fst(t),
top: Top,
subtype: S 
T,
assert: 
b,
parallel-class: X || Y,
eclass-compose2: eclass-compose2(f;X;Y),
uimplies: b supposing a,
so_apply: x[s1;s2],
so_apply: x[s],
uiff: uiff(P;Q),
sq_type: SQType(T),
guard: {T}
Lemmas :
Id_wf,
dataflow-program_wf,
local-program-at_wf,
es-loc_wf,
event-ordering+_inc,
es-E_wf,
parallel-df-program-case1_wf,
bag-append_wf,
int_seg_wf,
length_wf1,
bag_wf,
df-program-type_wf,
select_wf,
parallel-class_wf,
normal-locally-programmable_wf,
eclass_wf,
event-ordering+_wf,
valueall-type_wf,
squash_wf,
le_wf,
subtype_rel_bag,
subtype_rel-equal,
list-valueall-type,
set-valueall-type,
int-valueall-type,
last-stream-parallel-df-program-case1-meaning,
map_wf,
es-le-before_wf,
es-info_wf,
empty-bag_wf,
length-map,
non_null_iff_length,
es-le-before_wf2,
top_wf,
es-le_wf,
es-le-before-not-null,
subtype_base_sq,
bool_wf,
bool_subtype_base,
false_wf,
bfalse_wf,
true_wf
\mforall{}[Info:\{Info:Type| \mdownarrow{}Info\} ]
\mforall{}A:\{A:Type| valueall-type(A)\}
\mforall{}[X,Y:EClass(A)].
(NormalLProgrammable(A;X) {}\mRightarrow{} NormalLProgrammable(A;Y) {}\mRightarrow{} NormalLProgrammable(A;X || Y))
Date html generated:
2011_10_20-PM-03_24_47
Last ObjectModification:
2011_09_22-AM-00_57_24
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