{ 
[A:
']. [dfp1,dfp2:DataflowProgram(A)]. [B:Type].
[G:bag(df-program-type(dfp1)) 
bag(df-program-type(dfp2)) bag(B)]
(parallel-df-prog2(B;G;dfp1;dfp2) 
DataflowProgram(A))
supposing valueall-type(B) }
{ Proof }
Definitions occuring in Statement :
parallel-df-prog2: parallel-df-prog2(B;G;dfp1;dfp2),
df-program-type: df-program-type(dfp),
dataflow-program: DataflowProgram(A),
uimplies: b supposing a,
uall: [x:A]. B[x],
member: t T,
function: x:A B[x],
universe: Type,
bag: bag(T),
valueall-type: valueall-type(T)
Definitions :
implies: P 
Q,
axiom: Ax,
parallel-df-prog2: parallel-df-prog2(B;G;dfp1;dfp2),
df-program-type: df-program-type(dfp),
bag: bag(T),
all: x:A. B[x],
function: x:A B[x],
isect: 
x:A. B[x],
uall: [x:A]. B[x],
uimplies: b supposing a,
valueall-type: valueall-type(T),
equal: s = t,
dataflow-program: DataflowProgram(A),
universe: Type,
member: t T,
bool: 
,
natural_number: $n,
atom: Atom$n,
int: 
,
atom: Atom,
rec: rec(x.A[x]),
quotient: x,y:A//B[x; y],
tunion: 
x:A.B[x],
b-union: A B,
list: type List,
so_apply: x[s],
or: P 
Q,
guard: {T},
l_member: (x l),
true: True,
prop: 
,
so_lambda: 
x.t[x],
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),
assert: 
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,
squash: 
T,
sq_stable: SqStable(P),
fpf: a:A fp-> B[a],
strong-subtype: strong-subtype(A;B),
le: A B,
ge: i 
j ,
not: 
A,
less_than: a < b,
and: P 
Q,
uiff: uiff(P;Q),
subtype_rel: A r B,
it: 
,
inr: inr x ,
empty-bag: {},
apply: f a,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
spread: spread def,
evalall: evalall(t),
lambda: x.A[x],
inl: inl x ,
unit: Unit,
union: left + right,
pair: <a, b>,
set: {x:A| B[x]} ,
product: x:A 
B[x]
Lemmas :
unit_wf,
empty-bag_wf,
it_wf,
evalall_wf,
member_wf,
subtype_rel_wf,
sq_stable__all,
squash_wf,
sq_stable__equal,
sq_stable__valueall-type,
product-valueall-type,
union-valueall-type,
equal-valueall-type,
bag-valueall-type,
dataflow-program_wf,
valueall-type_wf,
df-program-type_wf,
bag_wf
\mforall{}[A:\mBbbU{}']. \mforall{}[dfp1,dfp2:DataflowProgram(A)]. \mforall{}[B:Type].
\mforall{}[G:bag(df-program-type(dfp1)) {}\mrightarrow{} bag(df-program-type(dfp2)) {}\mrightarrow{} bag(B)]
(parallel-df-prog2(B;G;dfp1;dfp2) \mmember{} DataflowProgram(A))
supposing valueall-type(B)
Date html generated:
2011_08_16-AM-09_42_34
Last ObjectModification:
2011_06_18-AM-08_33_24
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