{ 
[Info:Type]. [B:{B:Type| valueall-type(B)} ].
[Ps:eclass-program{i:l}(Info) List].
[F:Id 
k:
||Ps|| bag(eclass-program-type(Ps[k])) bag(B)]
defined-class(simple-loc-comb-program(F;B;Ps))
= F|Loc; 
k.defined-class(Ps[k])|
supposing x:Id. ((F x (k.{})) = {})
supposing 0 < ||Ps|| }
{ Proof }
Definitions occuring in Statement :
simple-loc-comb-program: simple-loc-comb-program(F;B;Ps),
defined-class: defined-class(prg),
eclass-program-type: eclass-program-type(prg),
eclass-program: eclass-program{i:l}(Info),
simple-loc-comb: F|Loc; Xs|,
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: $n,
universe: Type,
equal: s = t,
empty-bag: {},
bag: bag(T),
valueall-type: valueall-type(T)
Definitions :
es-le-before: 
loc(e),
es-info: info(e),
pi1: fst(t),
fpf-ap: f(x),
null-df-program: null-df-program(B),
parallel-df-program: parallel-df-program(B;F;dfps),
df-program-meaning: df-program-meaning(dfp),
data-stream: data-stream(P;L),
last: last(L),
lt_int: i <z j,
le_int: i z j,
bfalse: ff,
btrue: tt,
deq-disjoint: deq-disjoint(eq;as;bs),
deq-all-disjoint: deq-all-disjoint(eq;ass;bs),
name_eq: name_eq(x;y),
eq_id: a = b,
eq_lnk: a = b,
es-eq-E: e = e',
es-bless: e <loc e',
es-ble: e loc e',
bimplies: p 
q,
band: p 
q,
bor: p 
q,
es-loc: loc(e),
deq-member: deq-member(eq;x;L),
bnot: 
b,
unit: Unit,
union: left + right,
fpf-dom: x 
dom(f),
fpf_ap_pair: fpf_ap_pair{fpf_ap_pair_compseq_tag_def:o}(x; eq; f; d),
dataflow-history-val: dataflow-history-val(es;e;x.P[x]),
fpf-cap: f(x)?z,
bool: 
,
listp: A List
,
combination: Combination(n;T),
rev_implies: P 
Q,
iff: P Q,
so_lambda: 
x.t[x],
df-program-type: df-program-type(dfp),
dataflow-program: DataflowProgram(A),
record-select: r.x,
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
atom: Atom$n,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
ifthenelse: if b then t else f fi ,
assert: 
b,
dep-isect: Error :dep-isect,
record+: record+,
nat: ,
cand: A c B,
exists: 
x:A. B[x],
event_ordering: EO,
es-E: E,
event-ordering+: EO+(Info),
spread: spread def,
dataflow-set-class: dataflow-set-class(x.P[x]),
fpf-single: x : v,
mk_fpf: mk_fpf(L;f),
fpf-join: f 
g,
lelt: i j < k,
void: Void,
false: False,
real: 
,
rationals: 
,
subtype: S 
T,
int: 
,
empty-bag: {},
limited-type: LimitedType,
top: Top,
apply: f a,
pair: <a, b>,
fpf: a:A fp-> B[a],
strong-subtype: strong-subtype(A;B),
le: A B,
ge: i 
j ,
not: A,
product: x:A 
B[x],
and: P Q,
uiff: uiff(P;Q),
subtype_rel: A r B,
so_lambda: x y.t[x; y],
axiom: Ax,
simple-loc-comb: F|Loc; Xs|,
simple-loc-comb-program: simple-loc-comb-program(F;B;Ps),
defined-class: defined-class(prg),
eclass: EClass(A[eo; e]),
eclass-program-type: eclass-program-type(prg),
equal: s = t,
valueall-type: valueall-type(T),
eclass-program: eclass-program{i:l}(Info),
list: type List,
uimplies: b supposing a,
prop: 
,
less_than: a < b,
uall: [x:A]. B[x],
isect: 
x:A. B[x],
member: t T,
set: {x:A| B[x]} ,
universe: Type,
function: x:A B[x],
bag: bag(T),
select: l[i],
eclass-program-flows: eclass-program-flows(p),
fpf-domain: fpf-domain(f),
Id: Id,
lambda: x.A[x],
map: map(f;as),
id-deq: IdDeq,
union-list2: union-list2(eq;ll),
l_member: (x l),
implies: P Q,
length: ||as||,
natural_number: $n,
int_seg: {i..j},
all: x:A. B[x],
proper-iseg: L1 < L2,
iseg: l1 l2,
multiply: n * m,
gt: i > j,
divides: b | a,
assoced: a ~ b,
set_leq: a b,
set_lt: a <p b,
grp_lt: a < b,
l_contains: A B,
cmp-le: cmp-le(cmp;x;y),
reducible: reducible(a),
prime: prime(a),
l_exists: (xL. P[x]),
l_all: (xL.P[x]),
fun-connected: y is f*(x),
qle: r s,
qless: r < s,
q-rel: q-rel(r;x),
sq_exists: x:{A| B[x]},
i-finite: i-finite(I),
i-closed: i-closed(I),
p-outcome: Outcome,
fset-member: a s,
f-subset: xs ys,
fset-closed: (s closed under fs),
l_disjoint: l_disjoint(T;l1;l2),
cs-not-completed: in state s, a has not completed inning i,
cs-archived: by state s, a archived v in inning i,
cs-passed: by state s, a passed inning i without archiving a value,
cs-inning-committed: in state s, inning i has committed v,
cs-inning-committable: in state s, inning i could commit v ,
cs-archive-blocked: in state s, ws' blocks ws from archiving v in inning i,
cs-precondition: state s may consider v in inning i,
infix_ap: x f y,
es-causl: (e < e'),
es-locl: (e <loc e'),
es-causle: e c e',
existse-before: e<e'.P[e],
existse-le: ee'.P[e],
alle-lt: e<e'.P[e],
alle-le: ee'.P[e],
alle-between1: e[e1,e2).P[e],
existse-between1: e[e1,e2).P[e],
alle-between2: e[e1,e2].P[e],
existse-between2: e[e1,e2].P[e],
existse-between3: e(e1,e2].P[e],
es-fset-loc: i locs(s),
es-r-immediate-pred: es-r-immediate-pred(es;R;e';e),
same-thread: same-thread(es;p;e;e'),
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,
decidable: Dec(P),
uni_sat: a = !x:T. Q[x],
inv_funs: InvFuns(A;B;f;g),
inject: Inj(A;B;f),
eqfun_p: IsEqFun(T;eq),
refl: Refl(T;x,y.E[x; y]),
urefl: UniformlyRefl(T;x,y.E[x; y]),
sym: Sym(T;x,y.E[x; y]),
usym: UniformlySym(T;x,y.E[x; y]),
trans: Trans(T;x,y.E[x; y]),
utrans: UniformlyTrans(T;x,y.E[x; y]),
anti_sym: AntiSym(T;x,y.R[x; y]),
uanti_sym: UniformlyAntiSym(T;x,y.R[x; y]),
connex: Connex(T;x,y.R[x; y]),
uconnex: uconnex(T; x,y.R[x; y]),
coprime: CoPrime(a,b),
ident: Ident(T;op;id),
assoc: Assoc(T;op),
comm: Comm(T;op),
inverse: Inverse(T;op;id;inv),
bilinear: BiLinear(T;pl;tm),
bilinear_p: IsBilinear(A;B;C;+a;+b;+c;f),
action_p: IsAction(A;x;e;S;f),
dist_1op_2op_lr: Dist1op2opLR(A;1op;2op),
fun_thru_1op: fun_thru_1op(A;B;opa;opb;f),
fun_thru_2op: FunThru2op(A;B;opa;opb;f),
cancel: Cancel(T;S;op),
monot: monot(T;x,y.R[x; y];f),
monoid_p: IsMonoid(T;op;id),
group_p: IsGroup(T;op;id;inv),
monoid_hom_p: IsMonHom{M1,M2}(f),
grp_leq: a b,
integ_dom_p: IsIntegDom(r),
prime_ideal_p: IsPrimeIdeal(R;P),
no_repeats: no_repeats(T;l),
value-type: value-type(T),
is_list_splitting: is_list_splitting(T;L;LL;L2;f),
is_accum_splitting: is_accum_splitting(T;A;L;LL;L2;f;g;x),
bag-member: bag-member(T;x;bs),
req: x = y,
rnonneg: rnonneg(r),
rleq: x y,
i-member: r I,
partitions: partitions(I;p),
modulus-of-ccontinuity: modulus-of-ccontinuity(omega;I;f),
null: null(as),
es-le: e loc e' ,
tag-by: zT,
record: record(x.T[x]),
fset: FSet{T},
isect2: T1 T2,
permutation: permutation(T;L1;L2),
quotient: x,y:A//B[x; y],
stream: stream(A),
dataflow: dataflow(A;B),
b-union: A 
B,
intensional-universe: IType,
ma-state: State(ds),
class-program: ClassProgram(T),
fpf-sub: f g,
classrel: v X(e),
squash: 
T,
sq_stable: SqStable(P),
es-E-interface: E(X),
grp_car: |g|,
suptype: suptype(S; T),
sqequal: s ~ t,
inr: inr x ,
it: 
,
eqof: eqof(d),
true: True,
cons: [car / cdr],
nil: [],
deq: EqDecider(T),
sq_type: SQType(T),
so_apply: x[s],
or: P Q,
guard: {T},
filter: filter(P;l),
atom: Atom,
es-base-E: es-base-E(es),
token: "$token",
MaAuto: Error :MaAuto,
Auto: Error :Auto,
CollapseTHENA: Error :CollapseTHENA,
CollapseTHEN: Error :CollapseTHEN,
tactic: Error :tactic,
in-eclass: e X,
eq_knd: a = b,
eq_bool: p =b q,
eq_int: (i =
j),
set_blt: a < b,
grp_blt: a < b,
dcdr-to-bool: [d],
bl-all: (xL.P[x])_b,
bl-exists: (xL.P[x])_b,
b-exists: (i<n.P[i])_b,
eq_type: eq_type(T;T'),
qeq: qeq(r;s),
q_less: q_less(r;s),
q_le: q_le(r;s),
D: Error :D,
label: ...$L... t,
tl: tl(l),
hd: hd(l),
es-before: before(e),
append: as @ bs,
Unfold: Error :Unfold,
THENM: Error :THENM,
corec: corec(T.F[T]),
rcv: rcv(l,tg),
locl: locl(a),
Knd: Knd,
primrec: primrec(n;b;c),
es-interface-prior-vals: X(e)
Lemmas :
last-map,
data-stream-null-df-program,
null-map,
es-le-before_wf2,
es-le_wf,
es-le-before-not-null,
subtype_base_sq,
bool_subtype_base,
bfalse_wf,
length-data-stream,
data-stream_wf,
non_null_iff_length,
last_wf,
subtype_rel_list,
df-program-meaning_wf,
df-program-meaning_wf_null,
dataflow_wf,
es-locl_wf,
es-before_wf3,
append_wf,
es-before_wf,
length_append,
length_cons,
length_nil,
map_length,
non_neg_length,
ge_wf,
uiff_transitivity,
select-map,
null-df-program_wf,
subtype_rel_self,
es-base-E_wf,
fpf-ap_wf,
pi1_wf_top,
ifthenelse_wf,
last-stream-parallel-df-program-meaning,
false_wf,
fpf-dom_wf,
true_wf,
member-fpf-dom,
unit_wf,
it_wf,
length-map,
le_wf,
sq_stable__subtype_rel,
subtype_rel_function,
intensional-universe_wf,
nat_properties,
int_seg_properties,
subtype_rel_dep_function,
squash_wf,
subtype_rel_bag,
permutation_wf,
pos_length2,
member_null,
sq_stable__and,
sq_stable_from_decidable,
decidable__lt,
sq_stable__equal,
pos-length,
equal-nil-sq-nil,
l_member_length,
eclass-program-type_wf,
select_wf,
eclass-program_wf,
bag_wf,
length_wf1,
int_seg_wf,
Id_wf,
empty-bag_wf,
defined-class_wf,
simple-loc-comb-program_wf,
eclass_wf,
valueall-type_wf,
event-ordering+_wf,
es-E_wf,
event-ordering+_inc,
l_member_wf,
nat_wf,
fpf-domain_wf,
eclass-program-flows_wf,
dataflow-program_wf,
fpf_wf,
top_wf,
member_wf,
subtype_rel_wf,
fpf-trivial-subtype-top,
df-program-type_wf,
member-union-list2,
id-deq_wf,
map_wf,
member_map,
length_wf_nat,
select_member,
union-list2_wf,
bool_wf,
es-loc_wf,
iff_transitivity,
assert_wf,
iff_weakening_uiff,
eqtt_to_assert,
assert-deq-member,
not_wf,
eqff_to_assert,
assert_of_bnot,
not_functionality_wrt_iff,
bnot_wf,
deq-member_wf,
es-info_wf,
es-le-before_wf
\mforall{}[Info:Type]. \mforall{}[B:\{B:Type| valueall-type(B)\} ]. \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)]
defined-class(simple-loc-comb-program(F;B;Ps)) = F|Loc; \mlambda{}k.defined-class(Ps[k])|
supposing \mforall{}x:Id. ((F x (\mlambda{}k.\{\})) = \{\})
supposing 0 < ||Ps||
Date html generated:
2011_08_16-PM-06_24_44
Last ObjectModification:
2011_06_20-AM-01_52_08
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