Nuprl Lemma : programmable-iff
Info,A:Type. X:EClass(A).
Programmable(A;X) 
p:eclass-program{i:l}(Info). ((eclass-program-type(p) = A) 
(X = defined-class(p)))
supposing (
Info) valueall-type(A)
Proof not projected
Definitions occuring in Statement :
programmable: Programmable(A;X),
defined-class: defined-class(prg),
eclass-program-type: eclass-program-type(prg),
eclass-program: eclass-program{i:l}(Info),
eclass: EClass(A[eo; e]),
uimplies: b supposing a,
all: x:A. B[x],
exists: x:A. B[x],
iff: P Q,
squash: T,
and: P Q,
universe: Type,
equal: s = t,
valueall-type: valueall-type(T)
Definitions :
set: {x:A| B[x]} ,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
es-E-interface: E(X),
sq_type: SQType(T),
eq_atom: eq_atom$n(x;y),
atom: Atom,
es-base-E: es-base-E(es),
token: "$token",
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
record-select: r.x,
dep-isect: Error :dep-isect,
record+: record+,
cand: A c B,
bool: 
,
Knd: Knd,
IdLnk: IdLnk,
rationals: 
,
list: type List,
apply: f a,
so_apply: x[s],
union: left + right,
or: P 
Q,
guard: {T},
l_member: (x 
l),
assert: 
b,
top: Top,
spread: spread def,
pi1: fst(t),
defined-class: defined-class(prg),
subtype: S 
T,
event_ordering: EO,
es-E: E,
event-ordering+: EO+(Info),
lambda: 
x.A[x],
eclass-program-type: eclass-program-type(prg),
limited-type: LimitedType,
Id: Id,
bag: bag(T),
dataflow: dataflow(A;B),
so_lambda: 
x.t[x],
fpf: a:A fp-> B[a],
member: t T,
fpf-single: x : v,
fpf-join: f 
g,
strong-subtype: strong-subtype(A;B),
le: A 
B,
ge: i 
j ,
not: 
A,
less_than: a < b,
uimplies: b supposing a,
uiff: uiff(P;Q),
subtype_rel: A r B,
isect: 
x:A. B[x],
uall: [x:A]. B[x],
all: x:A. B[x],
iff: P Q,
rev_implies: P Q,
implies: P Q,
function: x:A 
B[x],
so_lambda: x y.t[x; y],
equal: s = t,
eclass-program: eclass-program{i:l}(Info),
prop: 
,
programmable: Programmable(A;X),
eclass: EClass(A[eo; e]),
universe: Type,
exists: x:A. B[x],
product: x:A 
B[x],
and: P Q,
MaAuto: Error :MaAuto,
tactic: Error :tactic,
rec-dataflow: rec-dataflow(s0;s,m.next[s; m]),
null-df-program: null-df-program(B),
spreadn: spread4,
df-program-meaning: df-program-meaning(dfp),
fpf-dom: x dom(f),
false: False,
rcv: rcv(l,tg),
locl: locl(a),
unit: Unit,
corec: corec(T.F[T]),
atom: Atom$n,
df-program-type: df-program-type(dfp),
dataflow-program: DataflowProgram(A),
empty-bag: {},
constant-dataflow: constant-dataflow(b),
id-deq: IdDeq,
fpf-cap: f(x)?z,
dataflow-set-class: dataflow-set-class(x.P[x]),
Auto: Error :Auto,
RepUR: Error :RepUR,
CollapseTHEN: Error :CollapseTHEN,
inl: inl x ,
pair: <a, b>,
dataflow-ap: df(a),
fpf-compose: g o f,
dataflow-history-val: dataflow-history-val(es;e;x.P[x]),
es-le-before: loc(e),
es-info: info(e),
map: map(f;as),
es-loc: loc(e),
data-stream: data-stream(P;L),
true: True,
void: Void,
null: null(as),
last: last(L),
squash: T,
lt_int: i <z j,
le_int: i z j,
bfalse: ff,
nat: 
,
deq: EqDecider(T),
btrue: tt,
deq-disjoint: deq-disjoint(eq;as;bs),
deq-all-disjoint: deq-all-disjoint(eq;ass;bs),
eq_id: a = b,
eq_lnk: a = b,
es-eq-E: e = e',
es-bless: e <loc e',
es-ble: e loc e',
bimplies: p 
q,
band: p q,
bor: p q,
deq-member: deq-member(eq;x;L),
bnot: b,
int: 
,
compose: f o g,
fpf_ap_pair: fpf_ap_pair{fpf_ap_pair_compseq_tag_def:o}(x; eq; f; d),
es-le: e loc e' ,
listp: A List
,
combination: Combination(n;T),
tl: tl(l),
hd: hd(l),
cons: [car / cdr],
data_stream_nil: data_stream_nil{data_stream_nil_compseq_tag_def:o}(P),
nil: [],
quotient: x,y:A//B[x; y],
rec_dataflow_ap: rec_dataflow_ap{rec_dataflow_ap_compseq_tag_def:o}(a; v21,v22.next[v21; v22]; s0),
pi2: snd(t),
sqequal: s ~ t,
BHyp: Error :BHyp,
D: Error :D,
CollapseTHENA: Error :CollapseTHENA,
length: ||as||,
upto: upto(n),
lelt: i j < k,
real: 
,
grp_car: |g|,
select: l[i],
natural_number: $n,
int_seg: {i..j
},
sq_stable: SqStable(P),
fpf-sub: f g,
class-program: ClassProgram(T),
ma-state: State(ds),
b-union: A 
B,
isect2: T1 T2,
fset: FSet{T},
record: record(x.T[x]),
tag-by: zT,
permutation: permutation(T;L1;L2),
add: n + m,
subtract: n - m,
label: ...$L... t,
gt: i > j,
iseg: l1 l2,
proper-iseg: L1 < L2
Lemmas :
ge_wf,
non_neg_length,
nat_properties,
data-stream_wf,
permutation_wf,
sq_stable__subtype_rel,
dataflow_subtype,
constant-dataflow_wf,
df-program-meaning_wf,
bool_subtype_base,
subtype_base_sq,
es-le-before-not-null,
null-map,
null-data-stream,
bfalse_wf,
int_seg_wf,
le_wf,
upto_wf,
length_wf_nat,
select-map,
length_upto,
empty-bag_wf,
length_wf,
list_extensionality,
length-map,
map-map,
es-le-before_wf2,
es-le_wf,
data-stream-null-df-program,
constant-data-stream,
data-stream-cons,
nat_wf,
bool_wf,
es-loc_wf,
id-deq_wf,
deq-member_wf,
l_member_wf,
bnot_wf,
assert-deq-member,
not_functionality_wrt_iff,
assert_of_bnot,
iff_weakening_uiff,
iff_transitivity,
eqff_to_assert,
eqtt_to_assert,
last_wf,
squash_wf,
null_wf3,
top_wf,
not_wf,
false_wf,
assert_wf,
es-info_wf,
es-le-before_wf,
map_wf,
dataflow-program_wf,
df-program-type_wf,
fpf-compose_wf,
dataflow-set-class_wf,
fpf-cap_wf,
unit_wf,
dataflow-ap_wf,
member_wf,
Error :eclass_wf,
defined-class_wf,
event-ordering+_wf,
event-ordering+_inc,
es-E_wf,
eclass-program-type_wf,
eclass-program_wf,
fpf_wf,
Id_wf,
dataflow_wf,
bag_wf,
programmable_wf,
subtype_rel_wf,
es-interface-top,
iff_wf,
rev_implies_wf,
es-base-E_wf,
subtype_rel_self,
es-interface-subtype_rel2
\mforall{}Info,A:Type. \mforall{}X:EClass(A).
Programmable(A;X)
\mLeftarrow{}{}\mRightarrow{} \mexists{}p:eclass-program\{i:l\}(Info). ((eclass-program-type(p) = A) \mwedge{} (X = defined-class(p)))
supposing (\mdownarrow{}Info) \mwedge{} valueall-type(A)
Date html generated:
2012_01_23-PM-12_30_44
Last ObjectModification:
2011_12_19-PM-06_33_43
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