{ 
[A,B,C:
'].
D:{D:'| valueall-type(D)} . F:bag(A)
bag(B)
bag(C)
bag(D)
bag(D). init:Id bag(D).
[X:EClass(A)]. [Y:EClass(B)]. [Z:EClass'(C)].
(((
s:bag(D)
((as:bag(A). bs:bag(B). (F[as;bs;{};s] = {}))
(as:bag(A). cs:bag(C). (F[as;{};cs;s] = {}))
(bs:bag(B). [cs:bag(C)]. (F[{};bs;cs;s] = {}))))
(s:bag(D). (F[{};{};{};s] = {})))
NormalLProgrammable'(A;X)
NormalLProgrammable'(B;Y)
NormalLProgrammable'(C;Z)
NormalLProgrammable'(D;rec-combined-class-opt-3(F;init;X;Y;Z))) }
{ Proof }
Definitions occuring in Statement :
Message: Message,
normal-locally-programmable: NormalLProgrammable(A;X),
rec-combined-class-opt-3: rec-combined-class-opt-3(F;init;X;Y;Z),
eclass: EClass(A[eo; e]),
Id: Id,
uall: [x:A]. B[x],
so_apply: x[s1;s2;s3;s4],
all: x:A. B[x],
squash: T,
implies: P Q,
or: P Q,
and: P Q,
set: {x:A| B[x]} ,
function: x:A B[x],
universe: Type,
equal: s = t,
empty-bag: {},
bag: bag(T),
valueall-type: valueall-type(T)
Lemmas :
rec-combined-class-opt-3_wf,
Message_wf,
Id_wf,
dataflow-program_wf,
local-program-at_wf,
normal-locally-programmable_wf,
squash_wf,
bag_wf,
uall_wf,
eclass_wf,
valueall-type_wf,
empty-bag_wf,
eclass_wf3,
eclass_wf2,
member_wf,
sq_stable__all,
sq_stable__uall,
sq_stable_from_decidable,
es-E_wf,
event-ordering+_wf,
event-ordering+_inc,
rec-comb-locally-programmable1,
subtype_rel_wf,
Message-inhabited,
le_wf,
not_wf,
false_wf,
nat_wf,
int_seg_wf,
select_wf,
int_seg_properties,
length_wf_nat,
length_nil,
length_cons,
non_neg_length,
length_wf1,
top_wf,
decidable__equal_int,
subtype_base_sq,
int_subtype_base,
permutation_wf,
pos_length2
\mforall{}[A,B,C:\mBbbU{}'].
\mforall{}D:\{D:\mBbbU{}'| valueall-type(D)\} . \mforall{}F:bag(A) {}\mrightarrow{} bag(B) {}\mrightarrow{} bag(C) {}\mrightarrow{} bag(D) {}\mrightarrow{} bag(D).
\mforall{}init:Id {}\mrightarrow{} bag(D).
\mforall{}[X:EClass(A)]. \mforall{}[Y:EClass(B)]. \mforall{}[Z:EClass'(C)].
(((\mdownarrow{}\mforall{}s:bag(D)
((\mforall{}as:bag(A). \mforall{}bs:bag(B). (F[as;bs;\{\};s] = \{\}))
\mwedge{} (\mforall{}as:bag(A). \mforall{}cs:bag(C). (F[as;\{\};cs;s] = \{\}))
\mwedge{} (\mforall{}bs:bag(B). \mforall{}[cs:bag(C)]. (F[\{\};bs;cs;s] = \{\}))))
\mvee{} (\mdownarrow{}\mforall{}s:bag(D). (F[\{\};\{\};\{\};s] = \{\})))
{}\mRightarrow{} NormalLProgrammable'(A;X)
{}\mRightarrow{} NormalLProgrammable'(B;Y)
{}\mRightarrow{} NormalLProgrammable'(C;Z)
{}\mRightarrow{} NormalLProgrammable'(D;rec-combined-class-opt-3(F;init;X;Y;Z)))
Date html generated:
2011_08_17-PM-04_10_43
Last ObjectModification:
2011_07_25-PM-05_55_30
Home
Index