{ 
[Info:Type]. [P:eclass-program{i:l}(Info)].
(defined-class(delay-program(P)) = Prior(defined-class(P))) }
{ Proof }
Definitions occuring in Statement :
delay-program: delay-program(P),
defined-class: defined-class(prg),
eclass-program-type: eclass-program-type(prg),
eclass-program: eclass-program{i:l}(Info),
primed-class: Prior(X),
eclass: EClass(A[eo; e]),
uall: [x:A]. B[x],
universe: Type,
equal: s = t
Definitions :
union: left + right,
or: P 
Q,
divides: b | a,
assoced: a ~ b,
set_leq: a 
b,
set_lt: a <p b,
grp_lt: a < b,
cand: A c
B,
l_member: (x 
l),
l_contains: A 
B,
cmp-le: cmp-le(cmp;x;y),
inject: Inj(A;B;f),
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-locl: (e <loc e'),
es-le: 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),
true: True,
squash: 
T,
es-causl: (e < e'),
limited-type: LimitedType,
real: 
,
grp_car: |g|,
minus: -n,
add: n + m,
subtract: n - m,
void: Void,
false: False,
natural_number: $n,
prop: 
,
int: 
,
nat: 
,
implies: P 
Q,
exists: x:A. B[x],
strongwellfounded: SWellFounded(R[x; y]),
df-program-type: df-program-type(dfp),
dataflow: dataflow(A;B),
id-deq: IdDeq,
Id: Id,
dataflow-program: DataflowProgram(A),
delay-df-program: delay-df-program(dfp),
null-df-program: null-df-program(B),
df-program-meaning: df-program-meaning(dfp),
so_lambda: 
x.t[x],
apply: f a,
record-select: r.x,
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
decide: case b of inl(x) => s[x] | inr(y) => t[y],
ifthenelse: if b then t else f fi ,
dep-isect: Error :dep-isect,
record+: record+,
bag: bag(T),
dataflow-set-class: dataflow-set-class(x.P[x]),
fpf-compose: g o f,
fpf-single: x : v,
fpf-join: f 
g,
fpf-cap: f(x)?z,
spread: spread def,
pi1: fst(t),
subtype: S T,
valueall-type: valueall-type(T),
event_ordering: EO,
es-E: E,
event-ordering+: EO+(Info),
lambda: x.A[x],
top: Top,
set: {x:A| B[x]} ,
pair: <a, b>,
fpf: a:A fp-> B[a],
strong-subtype: strong-subtype(A;B),
le: A B,
ge: i 
j ,
not: 
A,
less_than: a < b,
uimplies: b supposing a,
product: x:A 
B[x],
and: P Q,
uiff: uiff(P;Q),
eclass-program-type: eclass-program-type(prg),
delay-program: delay-program(P),
primed-class: Prior(X),
defined-class: defined-class(prg),
member: t T,
axiom: Ax,
eclass-program: eclass-program{i:l}(Info),
universe: Type,
eclass: EClass(A[eo; e]),
so_lambda: x y.t[x; y],
equal: s = t,
all: x:A. B[x],
function: x:A 
B[x],
uall: [x:A]. B[x],
isect: 
x:A. B[x],
subtype_rel: A r B,
es-first: first(e),
assert: 
b,
fpf-dom: x dom(f),
fpf_ap_compose: fpf_ap_compose{fpf_ap_compose_compseq_tag_def:o}(x; eq; f; g),
fpf_dom_compose: fpf_dom_compose{fpf_dom_compose_compseq_tag_def:o}(f; g; x; eq),
iter_df_nil: iter_df_nil{iter_df_nil_compseq_tag_def:o}(P),
es-info: info(e),
es-loc: loc(e),
iterate-dataflow: P*(inputs),
dataflow-ap: df(a),
pi2: snd(t),
firstn: firstn(n;as),
nil: [],
cons: [car / cdr],
list: type List,
sqequal: s ~ t,
last: last(L),
tl: tl(l),
hd: hd(l),
es-le-before: loc(e),
dataflow-history-val: dataflow-history-val(es;e;x.P[x]),
empty-bag: {},
bfalse: ff,
btrue: tt,
eq_bool: p =b q,
lt_int: i <z j,
le_int: i z j,
eq_int: (i =
j),
null: null(as),
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),
deq-member: deq-member(eq;x;L),
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,
bnot: b,
unit: Unit,
es-local-pred: last(P),
bool: 
,
atom: Atom$n,
atom: Atom,
rec: rec(x.A[x]),
tunion: 
x:A.B[x],
b-union: A B,
is_list_splitting: is_list_splitting(T;L;LL;L2;f),
is_accum_splitting: is_accum_splitting(T;A;L;LL;L2;f;g;x),
bag-member: bag-member(T;x;bs),
req: x = y,
rnonneg: rnonneg(r),
rleq: x y,
i-member: r I,
partitions: partitions(I;p),
modulus-of-ccontinuity: modulus-of-ccontinuity(omega;I;f),
fpf-sub: f g,
classrel: v X(e),
sq_stable: SqStable(P),
quotient: x,y:A//B[x; y],
rec-dataflow: rec-dataflow(s0;s,m.next[s; m]),
inl: inl x ,
it: 
,
inr: inr x ,
bag-size: bag-size(bs),
isl: isl(x),
evalall: evalall(t),
let: let,
rec_dataflow_ap: rec_dataflow_ap_compseq_tag_def,
fpf-ap: f(x),
MaAuto: Error :MaAuto,
Auto: Error :Auto,
CollapseTHEN: Error :CollapseTHEN,
CollapseTHENA: Error :CollapseTHENA,
RepUR: Error :RepUR,
D: Error :D,
RepeatFor: Error :RepeatFor,
sq_type: SQType(T),
tag-by: zT,
rev_implies: P 
Q,
iff: P Q,
record: record(x.T[x]),
fset: FSet{T},
isect2: T1 T2,
stream: stream(A),
deq: EqDecider(T),
ma-state: State(ds),
es-base-E: es-base-E(es),
token: "$token",
guard: {T},
class-program: ClassProgram(T),
es-E-interface: E(X),
corec: corec(T.F[T]),
compose: f o g,
fpf_ap_pair: fpf_ap_pair{fpf_ap_pair_compseq_tag_def:o}(x; eq; f; d),
eqof: eqof(d),
fpf-domain: fpf-domain(f),
es-p-le: e p e',
es-p-locl: e p< e',
causal-predecessor: causal-predecessor(es;p),
es-pred: pred(e),
map: map(f;as),
data-stream: data-stream(P;L),
append: as @ bs,
label: ...$L... t,
es-before: before(e),
listp: A List
,
combination: Combination(n;T),
rev_uimplies: rev_uimplies(P;Q),
upto: upto(n),
length: ||as||,
delay-dataflow: delay-dataflow(P),
Knd: Knd,
rcv: rcv(l,tg),
locl: locl(a),
refl: Refl(T;x,y.E[x; y]),
sym: Sym(T;x,y.E[x; y]),
trans: Trans(T;x,y.E[x; y]),
equiv_rel: EquivRel(T;x,y.E[x; y]),
es-interface-prior-vals: X(e),
filter: filter(P;l),
permutation: permutation(T;L1;L2),
intensional-universe: IType,
so_apply: x[s],
primrec: primrec(n;b;c),
data_stream_nil: data_stream_nil{data_stream_nil_compseq_tag_def:o}(P),
iter_df_cons: iter_df_cons{iter_df_cons_compseq_tag_def:o}(as; a; P),
buffer-dataflow: buffer-dataflow(s;x.P[x]),
seq-dataflow: seq-dataflow(P;Q),
bag_size_empty: bag_size_empty{bag_size_empty_compseq_tag_def:o}
Lemmas :
bfalse_wf,
bool_subtype_base,
last-map,
data-stream-null-df-program,
null-map,
es-le-before-not-null,
not_assert_elim,
seq-dataflow_wf,
buffer-dataflow_wf,
pi1_wf,
iterate-dataflow-append,
last-lemma-sq,
dataflow-ap_wf,
pi2_wf,
firstn_wf,
assert_of_null,
not_functionality_wrt_uiff,
data-stream-cons,
last_append,
data-stream-append,
iterate-dataflow_wf,
assert_of_lt_int,
assert_functionality_wrt_uiff,
bnot_of_lt_int,
assert_of_le_int,
le_int_wf,
intensional-universe_wf,
permutation_wf,
list-subtype,
corec_wf,
null-data-stream,
quotient_wf,
equiv_rel_wf,
trans_wf,
sym_wf,
refl_wf,
delay-dataflow_wf,
subtype_rel_list,
length-data-stream,
null_wf3,
delay-df-program-meaning,
length_wf1,
append_wf,
map_length,
non_neg_length,
length_append,
length_cons,
es-before_wf,
length_nil,
length_wf_nat,
pos_length2,
non_null_iff_length,
es-before_wf3,
es-locl_wf,
length-map,
map_append_sq,
es-le-before_wf2,
es-le_wf,
es-le-before-pred,
last_wf,
data-stream_wf,
es-loc-pred,
atom2_subtype_base,
es-le-before_wf,
map_wf,
es-pred-causl,
es-pred_wf,
l_member_wf,
fpf-domain_wf,
false_wf,
member-fpf-dom,
iff_transitivity,
iff_weakening_uiff,
assert-deq-member,
not_functionality_wrt_iff,
deq-member_wf,
delay-df-program_wf,
dataflow-set-class_wf,
primed-class-pred,
fpf-cap_wf,
df-program-meaning_wf,
dataflow_wf,
null-df-program_wf,
dataflow_subtype,
sq_stable__subtype_rel,
true_wf,
squash_wf,
es-base-E_wf,
subtype_rel_bag,
subtype_base_sq,
unit_wf,
empty-bag_wf,
bag-size_wf,
lt_int_wf,
ifthenelse_wf,
it_wf,
eq_int_wf,
isl_wf,
band_wf,
evalall-reduce,
es-info_wf,
fpf-ap_wf,
sq_stable__valueall-type,
product-valueall-type,
union-valueall-type,
equal-valueall-type,
bag-valueall-type,
top_wf,
fpf_wf,
es-loc_wf,
id-deq_wf,
fpf-dom_wf,
assert_wf,
not_wf,
bnot_wf,
bool_wf,
assert_of_bnot,
eqff_to_assert,
uiff_transitivity,
eqtt_to_assert,
first0,
last-data-stream,
fpf-trivial-subtype-top,
df-program-type_wf,
subtype_rel_wf,
eclass_wf,
delay-program_wf,
defined-class_wf,
es-interface-top,
eclass-program-type_wf,
member_wf,
event-ordering+_wf,
event-ordering+_inc,
es-E_wf,
valueall-type_wf,
eclass-ext,
primed-class_wf,
eclass-program_wf,
subtype_rel_self,
bag_wf,
dataflow-program_wf,
Id_wf,
es-causl-swellfnd,
nat_wf,
nat_properties,
ge_wf,
le_wf,
es-causl_wf,
decidable__assert,
es-first_wf
\mforall{}[Info:Type]. \mforall{}[P:eclass-program\{i:l\}(Info)].
(defined-class(delay-program(P)) = Prior(defined-class(P)))
Date html generated:
2011_08_16-PM-06_28_11
Last ObjectModification:
2011_06_20-AM-01_53_38
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