{ 
[A:Type]. [p,q:DataflowProgram(A)].
df-program-meaning(p) = df-program-meaning(q)
supposing (df-program-type(p) = df-program-type(q))
(
R:df-program-statetype(p)? 
df-program-statetype(q)? 
df-prog-equiv(A;p;q;s1,s2.R[s1;s2])) }
{ Proof }
Definitions occuring in Statement :
df-prog-equiv: df-prog-equiv(A;p;q;s1,s2.R[s1; s2]),
df-program-meaning: df-program-meaning(dfp),
df-program-statetype: df-program-statetype(dfp),
df-program-type: df-program-type(dfp),
dataflow-program: DataflowProgram(A),
dataflow: dataflow(A;B),
uimplies: b supposing a,
uall: [x:A]. B[x],
prop: ,
so_apply: x[s1;s2],
exists: x:A. B[x],
and: P Q,
unit: Unit,
function: x:A B[x],
union: left + right,
universe: Type,
equal: s = t,
bag: bag(T)
Definitions :
tactic: Error :tactic,
RepeatFor: Error :RepeatFor,
RepUR: Error :RepUR,
bag: bag(T),
union: left + right,
unit: Unit,
so_lambda: 
x y.t[x; y],
decide: case b of inl(x) => s[x] | inr(y) => t[y],
apply: f a,
pair: <a, b>,
empty-bag: {},
inl: inl x ,
MaAuto: Error :MaAuto,
CollapseTHENA: Error :CollapseTHENA,
Repeat: Error :Repeat,
CollapseTHEN: Error :CollapseTHEN,
D: Error :D,
Auto: Error :Auto,
member: t 
T,
and: P Q,
isect: 
x:A. B[x],
prop: ,
universe: Type,
equal: s = t,
df-program-statetype: df-program-statetype(dfp),
function: x:A B[x],
so_apply: x[s1;s2],
df-prog-equiv: df-prog-equiv(A;p;q;s1,s2.R[s1; s2]),
product: x:A 
B[x],
exists: x:A. B[x],
uimplies: b supposing a,
dataflow-program: DataflowProgram(A),
uall: [x:A]. B[x],
dataflow: dataflow(A;B),
df-program-type: df-program-type(dfp),
df-program-meaning: df-program-meaning(dfp),
axiom: Ax,
all: x:A. B[x],
subtype_rel: A 
r B,
uiff: uiff(P;Q),
less_than: a < b,
not: 
A,
ge: i 
j ,
le: A 
B,
strong-subtype: strong-subtype(A;B),
fpf: a:A fp-> B[a],
limited-type: LimitedType,
lambda: x.A[x],
squash: 
T,
true: True,
so_lambda: x.t[x],
assert: 
b,
l_member: (x l),
list: type List,
guard: {T},
or: P 
Q,
implies: P 
Q,
so_apply: x[s],
rationals: 
,
Id: Id,
IdLnk: IdLnk,
Knd: Knd,
cand: A c B,
bool: 
,
spread: spread def,
set: {x:A| B[x]} ,
df-program-in-state-ap': df-program-in-state-ap'(dfp;s;m),
df-program-state: df-program-state(dfp),
df-program-in-state-ap: df-program-in-state-ap(dfp;s;m),
pi2: snd(t),
ifthenelse: if b then t else f fi ,
isl: isl(x),
outl: outl(x),
valueall-type: valueall-type(T),
inr: inr x ,
subtype: S T,
quotient: x,y:A//B[x; y],
sq_stable: SqStable(P),
fpf-sub: f g,
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,
bag-member: bag-member(T;x;bs),
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),
b-union: A 
B,
tunion: x:A.B[x],
rec: rec(x.A[x]),
atom: Atom,
int: 
,
atom: Atom$n,
natural_number: $n,
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],
iff: P 
Q,
decidable: Dec(P),
l_disjoint: l_disjoint(T;l1;l2),
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),
infix_ap: x f y,
l_all: (xL.P[x]),
l_exists: (xL. P[x]),
prime: prime(a),
reducible: reducible(a),
cmp-le: cmp-le(cmp;x;y),
l_contains: A B,
grp_lt: a < b,
set_lt: a <p b,
set_leq: a b,
assoced: a ~ b,
divides: b | a,
false: False,
pi1: fst(t),
rel_plus: R
,
rel_exp: R^n,
llex: llex(A;a,b.<[a; b])
Lemmas :
sq_stable__equal,
sq_stable__all,
pi2_wf,
sq_stable_from_decidable,
equal-valueall-type,
union-valueall-type,
sq_stable__valueall-type,
valueall-type_wf,
member_wf,
empty-bag_wf,
rec-dataflow-equal,
uall_wf,
squash_wf,
true_wf,
df-program-type_wf,
bag_wf,
dataflow_wf,
df-program-meaning_wf,
dataflow-program_wf,
df-prog-equiv_wf,
unit_wf,
df-program-statetype_wf
\mforall{}[A:Type]. \mforall{}[p,q:DataflowProgram(A)].
df-program-meaning(p) = df-program-meaning(q)
supposing (df-program-type(p) = df-program-type(q))
\mwedge{} (\mexists{}R:df-program-statetype(p)? {}\mrightarrow{} df-program-statetype(q)? {}\mrightarrow{} \mBbbP{}
df-prog-equiv(A;p;q;s1,s2.R[s1;s2]))
Date html generated:
2011_08_16-AM-09_36_49
Last ObjectModification:
2011_06_17-PM-01_34_29
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