{ 
[A:Type]. [dfp:DataflowProgram(A)]. [s:df-program-statetype(dfp)?]. [m:A].
(df-program-in-state-ap'(dfp;s;m)
df-program-statetype(dfp)? 
bag(df-program-type(dfp))) }
{ Proof }
Definitions occuring in Statement :
df-program-in-state-ap': df-program-in-state-ap'(dfp;s;m),
df-program-statetype: df-program-statetype(dfp),
df-program-type: df-program-type(dfp),
dataflow-program: DataflowProgram(A),
uall: [x:A]. B[x],
unit: Unit,
member: t T,
product: x:A B[x],
union: left + right,
universe: Type,
bag: bag(T)
Definitions :
equal: s = t,
member: t T,
df-program-in-state-ap': df-program-in-state-ap'(dfp;s;m),
df-program-type: df-program-type(dfp),
bag: bag(T),
unit: Unit,
df-program-statetype: df-program-statetype(dfp),
union: left + right,
product: x:A B[x],
axiom: Ax,
isect: 
x:A. B[x],
uall: [x:A]. B[x],
dataflow-program: DataflowProgram(A),
universe: Type,
all: x:A. B[x],
function: x:A 
B[x],
bool: 
,
implies: P 
Q,
int: 
,
bnot: 
b,
assert: 
b,
isl: isl(x),
bor: p 
q,
band: p 
q,
bimplies: p q,
eq_lnk: a = b,
eq_id: a = b,
name_eq: name_eq(x;y),
deq-all-disjoint: deq-all-disjoint(eq;ass;bs),
deq-disjoint: deq-disjoint(eq;as;bs),
deq-member: deq-member(eq;x;L),
q_le: q_le(r;s),
q_less: q_less(r;s),
qeq: qeq(r;s),
eq_atom: eq_atom$n(x;y),
not: A,
eq_type: eq_type(T;T'),
bag-null: bag-null(bs),
b-exists: (
i<n.P[i])_b,
bl-exists: (xL.P[x])_b,
bl-all: (xL.P[x])_b,
dcdr-to-bool: [d],
infix_ap: x f y,
apply: f a,
grp_blt: a < b,
set_blt: a < b,
null: null(as),
eq_atom: x =a y,
eq_int: (i =
j),
le_int: i 
z j,
lt_int: i <z j,
eq_bool: p =b q,
uiff: uiff(P;Q),
and: P Q,
uimplies: b supposing a,
btrue: tt,
bfalse: ff,
ifthenelse: if b then t else f fi ,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
df-program-in-state-ap: df-program-in-state-ap(dfp;s;m),
outl: outl(x),
prop: 
,
pair: <a, b>,
limited-type: LimitedType,
false: False,
void: Void,
empty-bag: {}
Lemmas :
df-program-type_wf,
empty-bag_wf,
assert_wf,
not_wf,
bnot_wf,
bool_wf,
unit_wf,
df-program-statetype_wf,
outl_wf,
df-program-in-state-ap_wf,
isl_wf,
assert_of_bnot,
eqff_to_assert,
uiff_transitivity,
eqtt_to_assert,
dataflow-program_wf
\mforall{}[A:Type]. \mforall{}[dfp:DataflowProgram(A)]. \mforall{}[s:df-program-statetype(dfp)?]. \mforall{}[m:A].
(df-program-in-state-ap'(dfp;s;m) \mmember{} df-program-statetype(dfp)? \mtimes{} bag(df-program-type(dfp)))
Date html generated:
2011_08_16-AM-09_36_19
Last ObjectModification:
2011_06_17-PM-01_08_16
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