Nuprl Lemma : defined-by-rec-comb-loc-program
[Info:Type]. [B:{A:Type| valueall-type(A)} ]. [Ps:eclass-program{i:l}(Info) List].
[F:Id 
k:
||Ps|| bag(eclass-program-type(Ps[k])) bag(B) bag(B)]
defined-class(rec-comb-loc-program(F;B;Ps)) = F|Loc, 
k.defined-class(Ps[k]), Prior(self)|
supposing x:Id. buf:bag(B). ((F x (k.{}) buf) = {})
supposing 0 < ||Ps||
Proof not projected
Definitions occuring in Statement :
rec-comb-loc-program: rec-comb-loc-program(F;B;Ps),
defined-class: defined-class(prg),
eclass-program-type: eclass-program-type(prg),
eclass-program: eclass-program{i:l}(Info),
rec-combined-loc-class: f|Loc, X, Prior(self)|,
eclass: EClass(A[eo; e]),
Id: Id,
select: l[i],
length: ||as||,
int_seg: {i..j
},
uimplies: b supposing a,
uall: [x:A]. B[x],
all: x:A. B[x],
less_than: a < b,
set: {x:A| B[x]} ,
apply: f a,
lambda: x.A[x],
function: x:A B[x],
list: type List,
natural_number: $n,
universe: Type,
equal: s = t,
empty-bag: {},
bag: bag(T),
valueall-type: valueall-type(T)
Definitions :
AssertBY: Error :AssertBY,
all: x:A. B[x],
int_seg: {i..j},
natural_number: $n,
length: ||as||,
implies: P 
Q,
l_member: (x 
l),
union-list2: union-list2(eq;ll),
id-deq: IdDeq,
map: map(f;as),
lambda: x.A[x],
Id: Id,
fpf-domain: fpf-domain(f),
eclass-program-flows: eclass-program-flows(p),
select: l[i],
MaAuto: Error :MaAuto,
RepUR: Error :RepUR,
CollapseTHEN: Error :CollapseTHEN,
CollapseTHENA: Error :CollapseTHENA,
Auto: Error :Auto,
isect: 
x:A. B[x],
eclass-program: eclass-program{i:l}(Info),
eclass-program-type: eclass-program-type(prg),
bag: bag(T),
function: x:A B[x],
member: t T,
uall: [x:A]. B[x],
less_than: a < b,
prop: 
,
uimplies: b supposing a,
list: type List,
universe: Type,
equal: s = t,
eclass: EClass(A[eo; e]),
defined-class: defined-class(prg),
rec-comb-loc-program: rec-comb-loc-program(F;B;Ps),
rec-combined-loc-class: f|Loc, X, Prior(self)|,
axiom: Ax,
so_lambda: 
x y.t[x; y],
subtype_rel: A 
r B,
uiff: uiff(P;Q),
and: P 
Q,
product: x:A 
B[x],
not: 
A,
ge: i 
j ,
le: A 
B,
strong-subtype: strong-subtype(A;B),
fpf: a:A fp-> B[a],
pair: <a, b>,
apply: f a,
top: Top,
limited-type: LimitedType,
empty-bag: {},
int: 
,
subtype: S T,
rationals: 
,
real: 
,
set: {x:A| B[x]} ,
false: False,
void: Void,
lelt: i j < k,
exists: 
x:A. B[x],
cand: A c B,
nat: ,
atom: Atom$n,
dataflow-program: DataflowProgram(A),
df-program-type: df-program-type(dfp),
so_lambda: x.t[x],
iff: P 
Q,
rev_implies: P Q,
combination: Combination(n;T),
listp: A List
,
bool: 
,
fpf-join: f 
g,
fpf-single: x : v,
fpf-cap: f(x)?z,
mk_fpf: mk_fpf(L;f),
fpf-dom: x dom(f),
fpf_ap_pair: fpf_ap_pair{fpf_ap_pair_compseq_tag_def:o}(x; eq; f; d),
spread: spread def,
dataflow-set-class: dataflow-set-class(x.P[x]),
df-program-meaning: df-program-meaning(dfp),
ifthenelse: if b then t else f fi ,
deq-member: deq-member(eq;x;L),
fpf-ap: f(x),
null-df-program: null-df-program(B),
dataflow: dataflow(A;B),
corec: corec(T.F[T]),
es-E-interface: E(X),
union: left + right,
unit: Unit,
bnot: 
b,
assert: 
b,
bor: p 
q,
band: p q,
bimplies: p q,
es-ble: e loc e',
es-bless: e <loc e',
es-eq-E: e = e',
eq_lnk: a = b,
eq_id: a = b,
deq-all-disjoint: deq-all-disjoint(eq;ass;bs),
deq-disjoint: deq-disjoint(eq;as;bs),
btrue: tt,
bfalse: ff,
sq_type: SQType(T),
guard: {T},
deq: EqDecider(T),
le_int: i z j,
lt_int: i <z j,
nil: [],
cons: [car / cdr],
or: P Q,
so_apply: x[s],
event-ordering+: EO+(Info),
es-E: E,
event_ordering: EO,
quotient: x,y:A//B[x; y],
decide: case b of inl(x) => s[x] | inr(y) => t[y],
true: True,
eqof: eqof(d),
pi1: fst(t),
class-program: ClassProgram(T),
squash: 
T,
feedback-df-program: feedback-df-program(B;F;buf;P;dfps),
bag-size: bag-size(bs),
tactic: Error :tactic,
upto: upto(n),
better-feedback-dataflow: better-feedback-dataflow(n;ds;F;s;x.P[x]),
constant-dataflow: constant-dataflow(b),
Knd: Knd,
locl: locl(a),
rcv: rcv(l,tg),
ma-state: State(ds),
fpf-sub: f g,
b-union: A 
B,
isect2: T1 T2,
fset: FSet{T},
record: record(x.T[x]),
record+: record+,
tag-by: zT,
grp_car: |g|,
dep-isect: Error :dep-isect,
eq_atom: eq_atom$n(x;y),
eq_atom: x =a y,
record-select: r.x,
es-loc: loc(e),
same-thread: same-thread(es;p;e;e'),
decidable: Dec(P),
collect-event: collect-event(es;X;n;v.num[v];L.P[L];e),
cut-order: a (X;f) b,
path-goes-thru: x-f*-y thru i,
es-r-immediate-pred: es-r-immediate-pred(es;R;e';e),
es-fset-loc: i locs(s),
existse-between3: e(e1,e2].P[e],
existse-between2: e[e1,e2].P[e],
alle-between2: e[e1,e2].P[e],
existse-between1: e[e1,e2).P[e],
alle-between1: e[e1,e2).P[e],
alle-le: ee'.P[e],
alle-lt: e<e'.P[e],
existse-le: ee'.P[e],
existse-before: e<e'.P[e],
es-causle: e c e',
es-le: e loc e' ,
es-locl: (e <loc e'),
es-causl: (e < e'),
infix_ap: x f y,
cs-precondition: state s may consider v in inning i,
cs-archive-blocked: in state s, ws' blocks ws from archiving v in inning i,
cs-inning-committable: in state s, inning i could commit v ,
cs-inning-committed: in state s, inning i has committed v,
cs-passed: by state s, a passed inning i without archiving a value,
cs-archived: by state s, a archived v in inning i,
cs-not-completed: in state s, a has not completed inning i,
l_disjoint: l_disjoint(T;l1;l2),
fset-closed: (s closed under fs),
f-subset: xs ys,
fset-member: a s,
p-outcome: Outcome,
i-closed: i-closed(I),
i-finite: i-finite(I),
sq_exists: x:{A| B[x]},
q-rel: q-rel(r;x),
qless: r < s,
qle: r s,
fun-connected: y is f*(x),
l_all: (xL.P[x]),
l_exists: (xL. P[x]),
prime: prime(a),
reducible: reducible(a),
inject: Inj(A;B;f),
cmp-le: cmp-le(cmp;x;y),
l_contains: A B,
consensus-rcv: consensus-rcv(V;A),
consensus-state3: consensus-state3(T),
MaName: MaName,
IdLnk: IdLnk,
primed-class: Prior(X),
strongwellfounded: SWellFounded(R[x; y]),
subtract: n - m,
add: n + m,
minus: -n,
sqequal: s ~ t,
atom: Atom,
es-before: before(e),
es-info: info(e),
append: as @ bs,
data-stream: data-stream(P;L),
filter: filter(P;l),
null: null(as),
last: last(L),
es-le-before: loc(e),
dataflow-history-val: dataflow-history-val(es;e;x.P[x]),
base: Base,
D: Error :D,
iterate-dataflow: P*(inputs),
dataflow-ap: df(a),
pi2: snd(t),
data_stream_nil: data_stream_nil{data_stream_nil_compseq_tag_def:o}(P),
suptype: suptype(S; T),
permutation: permutation(T;L1;L2),
equiv_rel: EquivRel(T;x,y.E[x; y]),
trans: Trans(T;x,y.E[x; y]),
sym: Sym(T;x,y.E[x; y]),
refl: Refl(T;x,y.E[x; y]),
intensional-universe: IType,
firstn: firstn(n;as),
iter_df_nil: iter_df_nil{iter_df_nil_compseq_tag_def:o}(P),
iter_df_cons: iter_df_cons{iter_df_cons_compseq_tag_def:o}(as; a; P),
hd: hd(l),
tl: tl(l),
rec_dataflow_ap: rec_dataflow_ap{rec_dataflow_ap_compseq_tag_def:o}(a; v21,v22.next[v21; v22]; s0),
eval-parallel-dataflow: eval-parallel-dataflow(n;s;m),
dataflow-out: dataflow-out(df;a),
primrec: primrec(n;b;c),
rec-dataflow: rec-dataflow(s0;s,m.next[s; m]),
let: let,
q_le: q_le(r;s),
q_less: q_less(r;s),
qeq: qeq(r;s),
eq_type: eq_type(T;T'),
b-exists: (i<n.P[i])_b,
bl-exists: (xL.P[x])_b,
bl-all: (xL.P[x])_b,
dcdr-to-bool: [d],
grp_blt: a < b,
set_blt: a < b,
eq_int: (i =
j),
es-interface-prior-vals: X(e),
token: "$token",
es-base-E: es-base-E(es),
RepeatFor: Error :RepeatFor,
rev_uimplies: rev_uimplies(P;Q),
label: ...$L... t,
es-first: first(e),
eq_bool: p =b q,
es-pred: pred(e),
causal-predecessor: causal-predecessor(es;p),
es-p-locl: e p< e',
es-p-le: e p e',
name_eq: name_eq(x;y),
compose: f o g,
sq_stable: SqStable(P),
gt: i > j,
multiply: n * m,
iseg: l1 l2,
proper-iseg: L1 < L2,
list_ind: list_ind def,
it: 
,
inr: inr x
Lemmas :
it_wf,
equal-nil-sq-nil,
pos-length,
feedback-df-program-type,
sq_stable__subtype_rel,
length-map-sq,
list_extensionality,
map-map,
select_upto,
int_subtype_base,
select-map,
feedback-df-program-meaning,
dataflow-history-val_wf,
feedback-df-program_wf,
length_upto,
constant-data-stream,
es-le_weakening,
es-locl_transitivity2,
es-pred-locl,
es-loc-pred,
es-le-loc,
es-causl_transitivity2,
es-causle_weakening_locl,
es-pred-causl,
es-pred_wf,
es-first_wf,
primed-class-cases,
nat_ind_tp,
guard_wf,
primed-class_wf,
last-map,
data-stream-null-df-program,
length_append,
length_cons,
non_neg_length,
length_nil,
length-data-stream,
length-map,
non_null_iff_length,
iff_wf,
rev_implies_wf,
bfalse_wf,
es-le-before-not-null,
es-le_wf,
es-le-before_wf2,
null-map,
member_null,
null-data-stream,
es-base-E_wf,
es-le-before_wf,
subtype_rel_list,
list-subtype,
not_functionality_wrt_uiff,
assert_of_null,
last-cons,
pos_length2,
null_wf3,
filter_wf,
le_int_wf,
assert_of_le_int,
bnot_of_lt_int,
assert_functionality_wrt_uiff,
assert_of_lt_int,
uiff_transitivity,
append_wf,
last_wf,
Error :pi1_wf,
iterate-dataflow_wf,
rec-dataflow_wf,
eval-parallel-dataflow_wf,
dataflow-out_wf,
isect_subtype_base,
primrec_wf,
product_subtype_base,
Error :pi2_wf,
dataflow-ap_wf,
eval-parallel-dataflow-property,
firstn_wf,
upto_wf,
inject_wf,
intensional-universe_wf,
refl_wf,
sym_wf,
trans_wf,
equiv_rel_wf,
quotient_wf,
permutation_wf,
subtype_rel_function,
last_append,
data-stream_wf,
data-stream-cons,
data-stream-append,
es-info_wf,
es-before_wf,
es-before_wf3,
map_append_sq,
prior-dataflow-set-class,
atom2_subtype_base,
primed-class-equal,
es-locl_wf,
es-causl_wf,
le_wf,
es-causl-swellfnd,
nat_properties,
ge_wf,
es-loc_wf,
decidable__equal_Id,
decidable__l_member,
constant-dataflow_wf,
bag-size_wf,
lt_int_wf,
eclass-ext,
better-feedback-dataflow_wf,
unit_wf,
pi1_wf_top,
subtype_rel_bag,
bool_cases,
subtype_base_sq,
bool_subtype_base,
int_seg_properties,
null-df-program_wf,
event-ordering+_inc,
rec-combined-loc-class_wf,
squash_wf,
subtype_rel_self,
dataflow_subtype,
false_wf,
fpf-dom_wf,
true_wf,
member-fpf-dom,
es-interface-top,
event-ordering+_wf,
es-E_wf,
df-program-meaning_wf_null,
deq-member_wf,
fpf-domain_wf2,
bnot_wf,
not_functionality_wrt_iff,
assert_of_bnot,
eqff_to_assert,
not_wf,
assert-deq-member,
eqtt_to_assert,
iff_weakening_uiff,
assert_wf,
iff_transitivity,
bool_wf,
dataflow_wf,
dataflow-set-class_wf,
ifthenelse_wf,
fpf-ap_wf,
df-program-meaning_wf,
union-list2_wf,
select_member,
length_wf_nat,
member_map,
map_wf,
id-deq_wf,
member-union-list2,
df-program-type_wf,
fpf-trivial-subtype-top,
subtype_rel_wf,
member_wf,
top_wf,
fpf_wf,
dataflow-program_wf,
eclass-program-flows_wf,
fpf-domain_wf,
nat_wf,
l_member_wf,
Error :eclass_wf,
rec-comb-loc-program_wf,
defined-class_wf,
bag_wf,
eclass-program-type_wf,
select_wf,
empty-bag_wf,
Id_wf,
int_seg_wf,
eclass-program_wf,
length_wf
\mforall{}[Info:Type]. \mforall{}[B:\{A:Type| valueall-type(A)\} ]. \mforall{}[Ps:eclass-program\{i:l\}(Info) List].
\mforall{}[F:Id {}\mrightarrow{} k:\mBbbN{}||Ps|| {}\mrightarrow{} bag(eclass-program-type(Ps[k])) {}\mrightarrow{} bag(B) {}\mrightarrow{} bag(B)]
defined-class(rec-comb-loc-program(F;B;Ps)) = F|Loc, \mlambda{}k.defined-class(Ps[k]), Prior(self)|
supposing \mforall{}x:Id. \mforall{}buf:bag(B). ((F x (\mlambda{}k.\{\}) buf) = \{\})
supposing 0 < ||Ps||
Date html generated:
2012_02_20-PM-02_50_52
Last ObjectModification:
2012_01_07-PM-02_00_05
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