Nuprl Lemma : simple-loc-comb-3-nlp
[A,B,C:
'].
D:{D:'| valueall-type(D)} . F:Id 
bag(A) bag(B) (bag(C) 
bag(D)).
[X:EClass(A)]. [Y:EClass(B)]. [Z:EClass(C)].
(((
l:Id
((bs:bag(B). cs:bag(C). ((F l {} bs cs) = {}))
(as:bag(A). cs:bag(C). ((F l as {} cs) = {}))
(as:bag(A). bs:bag(B). ((F l as bs {}) = {}))))
(l:Id. ((F l {} {} {}) = {})))
NormalLProgrammable'(A;X)
NormalLProgrammable'(B;Y)
NormalLProgrammable'(C;Z)
NormalLProgrammable'(D;F|Loc, X, Y, Z|))
Proof not projected
Definitions occuring in Statement :
Message: Message,
normal-locally-programmable: NormalLProgrammable(A;X),
simple-loc-comb-3: F|Loc, X, Y, Z|,
eclass: EClass(A[eo; e]),
Id: Id,
uall: [x:A]. B[x],
all: x:A. B[x],
squash: T,
implies: P Q,
or: P Q,
and: P Q,
set: {x:A| B[x]} ,
apply: f a,
function: x:A B[x],
universe: Type,
equal: s = t,
empty-bag: {},
bag: bag(T),
valueall-type: valueall-type(T)
Definitions :
uall: [x:A]. B[x],
all: x:A. B[x],
implies: P Q,
eclass: EClass(A[eo; e]),
and: P Q,
simple-loc-comb-3: F|Loc, X, Y, Z|,
member: t 
T,
prop: 
,
so_lambda: 
x.t[x],
cand: A c B,
select: l[i],
nat: 
,
exists: 
x:A. B[x],
le: A 
B,
not: 
A,
false: False,
length: ||as||,
ge: i 
j ,
label: ...$L... t,
ycomb: Y,
top: Top,
ifthenelse: if b then t else f fi ,
le_int: i z j,
bnot: 
b,
lt_int: i <z j,
bfalse: ff,
btrue: tt,
int_seg: {i..j
},
lelt: i j < k,
or: P Q,
so_apply: x[s],
squash: T,
uimplies: b supposing a,
decidable: Dec(P),
sq_type: SQType(T),
guard: {T},
subtype: S 
T
Lemmas :
normal-locally-programmable_wf,
Message_wf,
or_wf,
squash_wf,
all_wf,
Id_wf,
bag_wf,
equal_wf,
empty-bag_wf,
implies-wf,
event-ordering+_wf,
es-E_wf,
event-ordering+_inc,
valueall-type_wf,
simple-loc-comb-locally-programmable2,
Message-inhabited,
le_wf,
select_wf,
length_wf,
length_nil,
length_wf_nat,
top_wf,
length_cons,
non_neg_length,
int_seg_wf,
decidable__equal_int,
subtype_base_sq,
int_subtype_base,
eclass_wf2,
exists_wf,
lelt_wf,
simple-loc-comb-locally-programmable1
\mforall{}[A,B,C:\mBbbU{}'].
\mforall{}D:\{D:\mBbbU{}'| valueall-type(D)\} . \mforall{}F:Id {}\mrightarrow{} bag(A) {}\mrightarrow{} bag(B) {}\mrightarrow{} (bag(C) {}\mRightarrow{} bag(D)).
\mforall{}[X:EClass(A)]. \mforall{}[Y:EClass(B)]. \mforall{}[Z:EClass(C)].
(((\mdownarrow{}\mforall{}l:Id
((\mforall{}bs:bag(B). \mforall{}cs:bag(C). ((F l \{\} bs cs) = \{\}))
\mwedge{} (\mforall{}as:bag(A). \mforall{}cs:bag(C). ((F l as \{\} cs) = \{\}))
\mwedge{} (\mforall{}as:bag(A). \mforall{}bs:bag(B). ((F l as bs \{\}) = \{\}))))
\mvee{} (\mdownarrow{}\mforall{}l:Id. ((F l \{\} \{\} \{\}) = \{\})))
{}\mRightarrow{} NormalLProgrammable'(A;X)
{}\mRightarrow{} NormalLProgrammable'(B;Y)
{}\mRightarrow{} NormalLProgrammable'(C;Z)
{}\mRightarrow{} NormalLProgrammable'(D;F|Loc, X, Y, Z|))
Date html generated:
2012_01_23-PM-12_50_57
Last ObjectModification:
2011_11_10-AM-11_06_28
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