Nuprl Lemma : Memory4-prc_wf
A1,A2,A3,A4,B:{T:
'| valueall-type(T)} . init:Id 
bag(B). tr1:Id A1 B B.
[X1:EClass'(A1)]
tr2:Id A2 B B
[X2:EClass'(A2)]
tr3:Id A3 B B
[X3:EClass'(A3)]
tr4:Id A4 B B
[X4:EClass'(A4)]
Xpr1:NormalLProgrammable'(A1;X1). Xpr2:NormalLProgrammable'(A2;X2). Xpr3:NormalLProgrammable'(A3;X3).
Xpr4:NormalLProgrammable'(A4;X4).
(Memory4-prc(A1;A2;A3;A4;B;init;tr1;Xpr1;tr2;Xpr2;tr3;Xpr3;tr4;Xpr4)
NormalLProgrammable'(B;Memory4(init;tr1;X1;tr2;X2;tr3;X3;tr4;X4)))
Proof not projected
Definitions occuring in Statement :
Memory4-prc: Memory4-prc(A1;A2;A3;A4;B;init;tr1;Xpr1;tr2;Xpr2;tr3;Xpr3;tr4;Xpr4),
Memory4: Memory4(init;tr1;X1;tr2;X2;tr3;X3;tr4;X4),
Message: Message,
normal-locally-programmable: NormalLProgrammable(A;X),
eclass: EClass(A[eo; e]),
Id: Id,
uall: [x:A]. B[x],
all: x:A. B[x],
member: t T,
set: {x:A| B[x]} ,
function: x:A B[x],
universe: Type,
bag: bag(T),
valueall-type: valueall-type(T)
Definitions :
label: ...$L... t,
member: t T,
all: x:A. B[x],
bag: bag(T),
uall: [x:A]. B[x],
eclass: EClass(A[eo; e]),
Memory4-prc: Memory4-prc(A1;A2;A3;A4;B;init;tr1;Xpr1;tr2;Xpr2;tr3;Xpr3;tr4;Xpr4),
length: ||as||,
select-tuple: x.n,
delay-program: delay-program,
lifting-loc-2: lifting-loc-2(f),
disjoint-union-tr: tr1 + tr2,
Memory4-locally-programmable,
primed-class-opt-nlp,
primed-class-opt-locally-programmable,
upto: upto(n),
feedback-prog: feedback-prog,
bl-all: (xL.P[x])_b,
bnot: 
b,
isl: isl(x),
map: map(f;as),
unit: Unit,
evalall: evalall(t),
let: let,
ifthenelse: if b then t else f fi ,
lt_int: i <z j,
bag-size: bag-size(bs),
band: p 
q,
eq_int: (i =
j),
it: 
,
spreadn: spread4,
rec-combined-loc-class-opt-1-nlp,
rec-comb-locally-programmable1,
feedback-df-program-case1: feedback-df-program-case1(B;F;dfps;init),
ycomb: Y,
from-upto: [n, m),
btrue: tt,
bfalse: ff,
tuple-type: tuple-type(L),
df-program-statetype: df-program-statetype(dfp),
tuple: tuple(n;i.F[i]),
df-program-state: df-program-state(dfp),
select: l[i],
empty-bag: {},
ap2-tuple: ap2-tuple(len;f;x;t),
map-tuple: map-tuple(len;f;t),
pi2: snd(t),
pi1: fst(t),
null: null(as),
so_apply: x[s1;s2],
bag-append: as + bs,
lifting-1: lifting-1(f),
decidable__equal_int,
disjoint-union-comb-nlp,
parallel-class-nlp,
simple-comb-2-nlp,
simple-comb2-nlp,
simple-comb-locally-programmable1,
append: as @ bs,
so_apply: x[s],
simple-comb-1-nlp,
simple-comb1-nlp,
lifting1: lifting1(f;b),
lifting-gen-rev: lifting-gen-rev(n;f;bags),
permutation: permutation(T;L1;L2),
int_seg: {i..j
},
and: P Q,
inject: Inj(A;B;f),
permute_list: (L o f),
exists: 
x:A. B[x],
lelt: i 
j < k,
le: A B,
false: False,
not: A,
implies: P 
Q,
mklist: mklist(n;f),
le_int: i z j,
reduce: reduce(f;k;as),
lifting2-loc: lifting2-loc(f;loc;abag;bbag),
lifting-loc-gen-rev: lifting-loc-gen-rev(n;bags;loc;f),
outl: outl(x),
outr: outr(x),
prop: 
,
so_lambda: 
x.t[x],
spreadn: spread3,
subtype: S 
T
Lemmas :
all_wf,
valueall-type_wf,
Id_wf,
bag_wf,
uall_wf,
event-ordering+_wf,
Message_wf,
es-E_wf,
event-ordering+_inc,
normal-locally-programmable_wf,
Memory4_wf,
equal_wf,
eclass_wf2
\mforall{}A1,A2,A3,A4,B:\{T:\mBbbU{}'| valueall-type(T)\} . \mforall{}init:Id {}\mrightarrow{} bag(B). \mforall{}tr1:Id {}\mrightarrow{} A1 {}\mrightarrow{} B {}\mrightarrow{} B.
\mforall{}[X1:EClass'(A1)]
\mforall{}tr2:Id {}\mrightarrow{} A2 {}\mrightarrow{} B {}\mrightarrow{} B
\mforall{}[X2:EClass'(A2)]
\mforall{}tr3:Id {}\mrightarrow{} A3 {}\mrightarrow{} B {}\mrightarrow{} B
\mforall{}[X3:EClass'(A3)]
\mforall{}tr4:Id {}\mrightarrow{} A4 {}\mrightarrow{} B {}\mrightarrow{} B
\mforall{}[X4:EClass'(A4)]
\mforall{}Xpr1:NormalLProgrammable'(A1;X1). \mforall{}Xpr2:NormalLProgrammable'(A2;X2).
\mforall{}Xpr3:NormalLProgrammable'(A3;X3). \mforall{}Xpr4:NormalLProgrammable'(A4;X4).
(Memory4-prc(A1;A2;A3;A4;B;init;tr1;Xpr1;tr2;Xpr2;tr3;Xpr3;tr4;Xpr4)
\mmember{} NormalLProgrammable'(B;Memory4(init;tr1;X1;tr2;X2;tr3;X3;tr4;X4)))
Date html generated:
2012_01_23-PM-01_32_05
Last ObjectModification:
2012_01_12-AM-11_41_04
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