Nuprl Lemma : Threshold-Combinator-prc_wf
S:{S:
'| valueall-type(S)}
[A:']
B:{B:'| valueall-type(B)}
[X:EClass'(A)]
R:A 
S 
. init_state:Id bag(S). accum:A S S. f:Id A S bag(B).
Xpr:NormalLProgrammable'(A;X).
(Threshold-Combinator-prc(S;B;R;Xpr;init_state;accum;f)
NormalLProgrammable'(B;Threshold-Combinator(R;X;init_state;accum;f)))
Proof not projected
Definitions occuring in Statement :
Threshold-Combinator-prc: Threshold-Combinator-prc(S;B;R;X;init_state;accum;f),
Threshold-Combinator: Threshold-Combinator(R;X;init_state;accum;f),
Message: Message,
normal-locally-programmable: NormalLProgrammable(A;X),
eclass: EClass(A[eo; e]),
Id: Id,
bool: ,
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 :
all: x:A. B[x],
uall: [x:A]. B[x],
eclass: EClass(A[eo; e]),
bag: bag(T),
member: t T,
Threshold-Combinator-prc: Threshold-Combinator-prc(S;B;R;X;init_state;accum;f),
length: ||as||,
select-tuple: x.n,
so_apply: x[s1;s2;s3],
concat-lifting-loc-2: f@Loc,
ifthenelse: if b then t else f fi ,
empty-bag: {},
map: map(f;as),
upto: upto(n),
Threshold-Combinator-locally-programmable,
simple-loc-comb-2-nlp,
simple-loc-comb2-nlp,
simple-loc-comb-locally-programmable1,
select: l[i],
append: as @ bs,
concat-lifting2-loc: concat-lifting2-loc(f;abag;bbag;loc),
concat-lifting-loc: concat-lifting-loc(n;bags;loc;f),
concat-lifting: concat-lifting(n;f;bags),
concat-lifting-list: concat-lifting-list(n;bags),
bag-union: bag-union(bbs),
concat: concat(ll),
reduce: reduce(f;k;as),
btrue: tt,
bfalse: ff,
le_int: i 
z j,
bnot: 
b,
lt_int: i <z j,
from-upto: [n, m),
ycomb: Y,
decidable__equal_int,
feedback-prog: feedback-prog,
lifting-2: lifting-2(f),
bl-all: (xL.P[x])_b,
isl: isl(x),
unit: Unit,
evalall: evalall(t),
let: let,
bag-size: bag-size(bs),
band: p 
q,
eq_int: (i =
j),
it: 
,
primed-class-opt-nlp,
primed-class-opt-locally-programmable,
delay-program: delay-program,
spreadn: spread4,
Accum-class-locally-programmable,
rec-combined-class-opt-1-nlp,
rec-comb-locally-programmable1,
feedback-df-program-case1: feedback-df-program-case1(B;F;dfps;init),
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),
ap2-tuple: ap2-tuple(len;f;x;t),
map-tuple: map-tuple(len;f;t),
pi2: snd(t),
pi1: fst(t),
null: null(as),
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),
lifting2: lifting2(f;abag;bbag),
lifting-gen-rev: lifting-gen-rev(n;f;bags),
prop: 
,
so_lambda: 
x.t[x],
label: ...$L... t,
so_apply: x[s],
spreadn: spread3,
subtype: S 
T
Lemmas :
all_wf,
valueall-type_wf,
uall_wf,
event-ordering+_wf,
Message_wf,
es-E_wf,
event-ordering+_inc,
bag_wf,
bool_wf,
Id_wf,
implies-wf,
normal-locally-programmable_wf,
Threshold-Combinator_wf,
equal_wf,
eclass_wf2
\mforall{}S:\{S:\mBbbU{}'| valueall-type(S)\}
\mforall{}[A:\mBbbU{}']
\mforall{}B:\{B:\mBbbU{}'| valueall-type(B)\}
\mforall{}[X:EClass'(A)]
\mforall{}R:A {}\mrightarrow{} S {}\mrightarrow{} \mBbbB{}. \mforall{}init$_{state}$:Id {}\mrightarrow{} bag(S). \mforall{}accum:A {}\mrightarrow{} S {}\mrightarrow{} S. \mforall{}f:Id \000C{}\mrightarrow{} A {}\mrightarrow{} S {}\mrightarrow{} bag(B).
\mforall{}Xpr:NormalLProgrammable'(A;X).
(Threshold-Combinator-prc(S;B;R;Xpr;init$_{state}$;accum;f)
\mmember{} NormalLProgrammable'(B;Threshold-Combinator(R;X;init$_{state}$;accum\000C;f)))
Date html generated:
2012_01_23-PM-01_06_30
Last ObjectModification:
2011_11_04-PM-07_57_18
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