{ 
prg:eclass-program{i:l}(Message). S:LimitedType. P:S 
.
f:Id eclass-program-type(prg) {v:S| 
P[v]} . g:eclass-program-type(prg\000C)
(Id List). h:Name.
assuming(env,r.reliable-env(env; r))
mk-init-sys(prop-rule-realizer(eclass-program-flows(prg);S;f;g;h)) |=
es.defined-class(prg) 
f
baseclass(h; S; v.P[v])@g }
{ Proof }
Definitions occuring in Statement :
prop-rule-realizer: prop-rule-realizer(pr;T;f;g;hdr),
std-l2m: std-l2m(),
std-n2m: std-n2m(),
strong-realizes: strong-realizes,
mk-init-sys: mk-init-sys(Cs),
Message: Message,
reliable-env: reliable-env(env; r),
defined-class: defined-class(prg),
eclass-program-flows: eclass-program-flows(p),
eclass-program-type: eclass-program-type(prg),
eclass-program: eclass-program{i:l}(Info),
es-propagation-rule: A f B@g,
Id: Id,
name: Name,
assert: b,
bool: ,
so_apply: x[s],
all: x:A. B[x],
set: {x:A| B[x]} ,
function: x:A B[x],
list: type List,
limited-type: LimitedType
Definitions :
RepUR: Error :RepUR,
Repeat: Error :Repeat,
AssertBY: Error :AssertBY,
member: t 
T,
Complete: Error :Complete,
universe: Type,
Try: Error :Try,
CollapseTHENA: Error :CollapseTHENA,
eclass: EClass(A[eo; e]),
Message: Message,
Auto: Error :Auto,
D: Error :D,
CollapseTHEN: Error :CollapseTHEN,
MaAuto: Error :MaAuto,
so_lambda: 
x.t[x],
strong-realizes: strong-realizes,
function: x:A B[x],
all: x:A. B[x],
product: x:A 
B[x],
eclass-program: eclass-program{i:l}(Info),
equal: s = t,
isect: 
x:A. B[x],
uall: [x:A]. B[x],
so_lambda: x y.t[x; y],
std-l2m: std-l2m(),
std-n2m: std-n2m(),
mk-init-sys: mk-init-sys(Cs),
prop-rule-realizer: prop-rule-realizer(pr;T;f;g;hdr),
eclass-program-flows: eclass-program-flows(p),
pair: <a, b>,
eclass-program-type: eclass-program-type(prg),
name: Name,
list: type List,
Id: Id,
limited-type: LimitedType,
fpf: a:A fp-> B[a],
set: {x:A| B[x]} ,
dataflow-program: DataflowProgram(A),
bool: ,
df-program-type: df-program-type(dfp),
union: left + right,
top: Top,
intensional-universe: IType,
exists: 
x:A. B[x],
subtype_rel: A 
r B,
uimplies: b supposing a,
es-E-interface: E(X),
subtype: S T,
defined-class: defined-class(prg),
assert: b,
fpf-join: f 
g,
fpf-single: x : v,
so_apply: x[s],
apply: f a,
prop: 
,
system-strongly-realizes: system-strongly-realizes,
reliable-env: reliable-env(env; r),
implies: P Q,
system-realizes: system-realizes,
sub-system: sub-system(P.M[P];S1;S2),
InitialSystem: InitialSystem(P.M[P]),
mData: mData,
lambda: x.A[x],
System: System(P.M[P]),
std-initial: std-initial(S),
uiff: uiff(P;Q),
and: P 
Q,
less_than: a < b,
not: 
A,
ge: i 
j ,
le: A 
B,
strong-subtype: strong-subtype(A;B),
ldag: LabeledDAG(T),
event-ordering+: EO+(Info),
es-E: E,
event_ordering: EO,
dataflow-set-class: dataflow-set-class(x.P[x]),
df-program-meaning: df-program-meaning(dfp),
fpf-cap: f(x)?z,
id-deq: IdDeq,
null-df-program: null-df-program(B),
dataflow: dataflow(A;B),
corec: corec(T.F[T]),
atom: Atom$n,
deq: EqDecider(T),
class-program: ClassProgram(T),
ma-state: State(ds),
fpf-sub: f g,
true: True,
bag: bag(T),
b-union: A 
B,
pi1: fst(t),
spread: spread def,
isect2: T1 T2,
fset: FSet{T},
record: record(x.T[x]),
record+: record+,
labeled-graph: LabeledGraph(T),
iff: P 
Q,
or: P 
Q,
rev_implies: P Q,
tag-by: zT,
sq_stable: SqStable(P),
squash: 
T,
ext-eq: A 
B,
ParallelOp: Error :ParallelOp,
tactic: Error :tactic,
Unfold: Error :Unfold,
ORELSE: Error :ORELSE,
RepeatFor: Error :RepeatFor,
THENM: Error :THENM,
parameter: parm{i},
Component: Component,
nat: 
,
pCom: pCom(P.M[P]),
EnvType: EnvType,
RunType: RunType,
pEnvType: pEnvType(T.M[T]),
pRunType: pRunType(T.M[T]),
InitSys: InitSys,
unit: Unit,
l_all: (xL.P[x]),
es-loc: loc(e),
lg-all: xG.P[x],
Proc-out-at: Proc-out-at(es;P;e),
pi2: snd(t),
atom: Atom,
com-kind: com-kind(c),
token: "$token",
es-causl: (e < e'),
es-info: info(e),
comm-msg: comm-msg(c),
inl: inl x ,
ProcOut: ProcOut,
l_member: (x l),
dep-isect: Error :dep-isect,
ifthenelse: if b then t else f fi ,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
let: let,
eq_atom: eq_atom$n(x;y),
eq_atom: x =a y,
record-select: r.x,
subsys: S1 S2,
component: component(P.M[P]),
ProcOut-all: ProcOut-all(G;p.P[p]),
Proc: Proc,
Process: Process(P.M[P]),
pMsg: pMsg(P.M[P]),
process: process(P.M[P];P.E[P]),
Com: Com(P.M[P]),
es-propagation-rule: A f B@g,
baseclass: BaseClass(h;T),
es-base-E: es-base-E(es),
sq_type: SQType(T),
l_exists: (xL. P[x]),
l_disjoint: l_disjoint(T;l1;l2),
Sys: Sys,
lg-contains: g1 g2,
pInTransit: pInTransit(P.M[P]),
sublist: L1 L2,
int_seg: {i..j
},
natural_number: $n,
lg-size: lg-size(g),
int: 
,
lg-label: lg-label(g;x),
minus: -n,
lelt: i j < k,
false: False,
void: Void,
in-eclass: e 
X,
length: ||as||,
select: l[i],
eclass-val: X(e),
btrue: tt,
guard: {T},
modulus-of-ccontinuity: modulus-of-ccontinuity(omega;I;f),
partitions: partitions(I;p),
i-member: r I,
rleq: x y,
rnonneg: rnonneg(r),
req: x = y,
is_accum_splitting: is_accum_splitting(T;A;L;LL;L2;f;g;x),
is_list_splitting: is_list_splitting(T;L;LL;L2;f),
so_apply: x[s1;s2],
SplitOn: Error :SplitOn,
deq-member: deq-member(eq;x;L),
can-apply: can-apply(f;x),
dataflow-history-val: dataflow-history-val(es;e;x.P[x]),
fpf-dom: x dom(f),
fpf_ap_pair: fpf_ap_pair{fpf_ap_pair_compseq_tag_def:o}(x; eq; f; d),
bnot: 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),
bfalse: ff,
le_int: i z j,
lt_int: i <z j,
do-apply: do-apply(f;x),
outl: outl(x),
last: last(L),
data-stream: data-stream(P;L),
map: map(f;as),
es-le-before: loc(e),
dataflow-to-Process: dataflow-to-Process,
prop-rule-realizer-out: prop-rule-realizer-out(T;x;f;g;hdr),
cand: A c B,
suptype: suptype(S; T),
isl: isl(x),
valueall-type: valueall-type(T),
value-type: value-type(T),
no_repeats: no_repeats(T;l),
prime_ideal_p: IsPrimeIdeal(R;P),
integ_dom_p: IsIntegDom(r),
grp_leq: a b,
monoid_hom_p: IsMonHom{M1,M2}(f),
group_p: IsGroup(T;op;id;inv),
monoid_p: IsMonoid(T;op;id),
monot: monot(T;x,y.R[x; y];f),
cancel: Cancel(T;S;op),
fun_thru_2op: FunThru2op(A;B;opa;opb;f),
fun_thru_1op: fun_thru_1op(A;B;opa;opb;f),
dist_1op_2op_lr: Dist1op2opLR(A;1op;2op),
action_p: IsAction(A;x;e;S;f),
bilinear_p: IsBilinear(A;B;C;+a;+b;+c;f),
bilinear: BiLinear(T;pl;tm),
inverse: Inverse(T;op;id;inv),
comm: Comm(T;op),
assoc: Assoc(T;op),
ident: Ident(T;op;id),
coprime: CoPrime(a,b),
uconnex: uconnex(T; x,y.R[x; y]),
connex: Connex(T;x,y.R[x; y]),
uanti_sym: UniformlyAntiSym(T;x,y.R[x; y]),
anti_sym: AntiSym(T;x,y.R[x; y]),
utrans: UniformlyTrans(T;x,y.E[x; y]),
trans: Trans(T;x,y.E[x; y]),
usym: UniformlySym(T;x,y.E[x; y]),
sym: Sym(T;x,y.E[x; y]),
urefl: UniformlyRefl(T;x,y.E[x; y]),
refl: Refl(T;x,y.E[x; y]),
eqfun_p: IsEqFun(T;eq),
inject: Inj(A;B;f),
inv_funs: InvFuns(A;B;f;g),
uni_sat: a = !x:T. Q[x],
decidable: Dec(P),
infix_ap: x f y,
lg-edge: lg-edge(g;a;b),
path-goes-thru: x-f*-y thru i,
cut-order: a (X;f) b,
collect-event: collect-event(es;X;n;v.num[v];L.P[L];e),
same-thread: same-thread(es;p;e;e'),
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'),
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,
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),
prime: prime(a),
reducible: reducible(a),
l_contains: A B,
grp_lt: a < b,
set_lt: a <p b,
set_leq: a b,
assoced: a ~ b,
divides: b | a,
nil: [],
remove-repeats: remove-repeats(eq;L),
hd: hd(l),
cons: [car / cdr],
listp: A List
,
combination: Combination(n;T),
less: if (a) < (b) then c else d,
eq_str: Error :eq_str,
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,
null: null(as),
eq_int: (i =
j),
sqequal: s ~ t,
es-before: before(e),
add: n + m,
is-dag: is-dag(g),
locl: locl(a),
Knd: Knd,
rcv: rcv(l,tg),
primrec: primrec(n;b;c),
tl: tl(l),
MaAuto: Error :MaAuto,
make-lg: make-lg(L),
compose: f o g,
filter: filter(P;l),
limited-type-level: limited-type-level{i:l}(n;T),
es-init: es-init(es;e),
ldst: destination(l),
lsrc: source(l),
es-first: first(e),
causal-predecessor: causal-predecessor(es;p),
es-p-locl: e p< e',
es-p-le: e p e',
grp_car: |g|,
real: 
,
tagged-tag: x.tag,
tagged-val: x.val,
inr: inr x ,
it: 
,
decide_bfalse: decide_bfalse{decide_bfalse_compseq_tag_def:o}(v11.g[v11]; v21.f[v21]),
BHyp: Error :BHyp,
rationals: 
,
Subst': Error :Subst',
label: ...$L... t,
spreadn: spread3,
name_eq: name_eq(x;y),
eq_bool: p =b q,
upto: upto(n),
ExRepD: Error :ExRepD,
rev_uimplies: rev_uimplies(P;Q),
append: as @ bs,
IdLnk: IdLnk,
HypSubst: Error :HypSubst
Lemmas :
member_upto,
rev_implies_wf,
iff_wf,
nat_properties,
uiff_inversion,
pi2_wf,
outl_wf,
union_subtype_base,
unit_subtype_base,
upto_wf,
btrue_wf,
intensional-universe_wf2,
btrue_neq_bfalse,
eq_type_wf,
name_eq_wf,
assert-name_eq,
uiff_transitivity,
not_functionality_wrt_uiff,
assert-eq_type,
isl_wf,
subtype_rel_set,
es-interface-subtype_rel,
eclass_wf2,
select_member,
int_seg_properties,
select_wf,
bfalse_wf,
es-le-before-not-null,
null-map,
data-stream-null-df-program,
event_ordering_wf,
es-le-before_wf2,
es-le_wf,
lg-all_wf_dag,
select-map,
le_wf,
length-map,
atom2_subtype_base,
es-causl_irreflexivity,
es-loc-pred,
intensional-universe_subtype_base,
limited-type-level_wf,
atom_subtype_base,
product_subtype_base,
list_subtype_base,
set_subtype_base,
isect_subtype_base,
primrec_wf,
map-map,
member_null,
pos_length2,
null-data-stream,
subtype_rel_list,
listp_properties,
last-map,
guard_wf,
last_wf,
map_wf,
data-stream_wf,
datastream-dataflow-to-Process,
length_wf_nat,
es-before_wf,
non_neg_length,
es-before_wf2,
length-append,
assert_of_lt_int,
length_wf1,
lt_int_wf,
es-le-before_wf,
map_wf_listp,
listp_wf,
l_member-set,
Process_wf,
member_map,
list-subtype,
sq_stable_from_decidable,
dataflow-to-Process_wf,
prop-rule-realizer-out_wf,
Com_wf,
bnot_wf,
deq-member_wf,
assert-deq-member,
not_functionality_wrt_iff,
assert_of_bnot,
iff_weakening_uiff,
iff_transitivity,
eqff_to_assert,
eqtt_to_assert,
bool_cases,
eclass-val_wf,
squash_wf,
in-eclass_wf,
assert_elim,
bool_subtype_base,
true_wf,
ifthenelse_wf,
false_wf,
es-interface-val_wf,
es-is-interface_wf,
sq_stable__assert,
es-interface-subtype_rel2,
ldag_wf,
nat_wf,
lg-size_wf,
lg-label_wf_dag,
int_seg_wf,
Sys_wf,
InitSys_wf,
subsys_weakening,
sublist_wf,
component_wf,
lg-contains_wf,
pInTransit_wf,
subsys_wf,
not_wf,
l_disjoint_wf,
l_exists_wf,
es-E-interface_wf,
subtype_base_sq,
es-base-E_wf,
es-interface-top,
es-propagation-rule_wf,
baseclass_wf,
Proc_wf,
pMsg_wf,
comm-msg_wf,
es-info_wf,
com-kind_wf,
es-causl_wf,
ProcOut-all_wf,
components-realize2,
pCom_wf,
strong-realizes_functionality,
reliable-env_wf2,
RunType_wf,
EnvType_wf,
unit_wf,
l_all_wf,
l_all_wf2,
es-loc_wf,
pi1_wf_top,
Proc-out-at_wf,
Component_wf,
l_member_wf,
ext-eq_weakening,
subtype_rel_weakening,
ext-eq_inversion,
sq_stable__subtype_rel,
subtype_rel_self,
dataflow_subtype,
null-df-program_wf,
id-deq_wf,
top_wf,
dataflow_wf,
df-program-type_wf,
df-program-meaning_wf,
fpf-cap_wf,
dataflow-program_wf,
dataflow-set-class_wf,
event-ordering+_inc,
es-E_wf,
event-ordering+_wf,
eclass_wf,
std-initial_wf,
System_wf,
mData_wf,
InitialSystem_wf,
sub-system_wf,
system-realizes_wf,
system-strongly-realizes_wf,
reliable-env_wf,
eclass-program_wf,
Message_wf,
limited-type_wf,
subtype_rel_wf,
member_wf,
intensional-universe_wf,
bool_wf,
assert_wf,
name_wf,
Id_wf,
std-l2m_wf,
std-n2m_wf,
prop-rule-realizer_wf,
mk-init-sys_wf,
strong-realizes_wf
\mforall{}prg:eclass-program\{i:l\}(Message). \mforall{}S:LimitedType. \mforall{}P:S {}\mrightarrow{} \mBbbB{}. \mforall{}f:Id
{}\mrightarrow{} eclass-program-type(prg)
{}\mrightarrow{} \{v:S| \muparrow{}P[v]\} .
\mforall{}g:eclass-program-type(prg) {}\mrightarrow{} (Id List). \mforall{}h:Name.
assuming(env,r.reliable-env(env; r))
mk-init-sys(prop-rule-realizer(eclass-program-flows(prg);S;f;g;h)) |=
es.defined-class(prg) {}f\mRightarrow{} baseclass(h; S; v.P[v])@g
Date html generated:
2011_08_17-PM-04_21_19
Last ObjectModification:
2011_01_13-PM-08_33_26
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