Nuprl Lemma : parallel-bind-program-eq-gen
∀[Info,B1,B2,C:Type]. ∀[X1:Id ─→ hdataflow(Info;B1)]. ∀[X2:Id ─→ hdataflow(Info;B2)].
∀[Y1:B1 ─→ Id ─→ hdataflow(Info;C)]. ∀[Y2:B2 ─→ Id ─→ hdataflow(Info;C)].
(X1 >>= Y1 || X2 >>= Y2
= X1 + X2 >>= λb.case b of inl(b1) => Y1 b1 | inr(b2) => Y2 b2
∈ (Id ─→ hdataflow(Info;C))) supposing
(valueall-type(C) and
valueall-type(B1) and
valueall-type(B2))
Proof
Definitions occuring in Statement :
eclass-disju-program: xpr + ypr,
parallel-class-program: X || Y,
bind-class-program: xpr >>= ypr,
Id: Id,
valueall-type: valueall-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
apply: f a,
lambda: λx.A[x],
function: x:A ─→ B[x],
decide: case b of inl(x) => s[x] | inr(y) => t[y],
universe: Type,
equal: s = t ∈ T,
hdataflow: hdataflow(A;B)
Lemmas :
local-class-equality,
bind-class_wf,
eclass-disju_wf,
hdataflow-class_wf,
parallel-class-program_wf,
bind-class-program_wf,
pi2_wf,
hdataflow_wf,
bag_wf,
hdf-ap_wf,
iterate-hdataflow_wf,
es-loc_wf,
event-ordering+_subtype,
map_wf,
es-E_wf,
es-info_wf,
es-before_wf,
event-ordering+_wf,
all_wf,
equal_wf,
class-ap_wf,
sq_exists_subtype_rel,
Id_wf,
parallel-class_wf,
squash_wf,
true_wf,
eclass_wf,
eclass-disju-bind-left,
iff_weakening_equal,
eclass-disju-program_wf,
list_wf,
valueall-type_wf,
bool_wf,
hdf-halted_wf,
hdf-parallel_wf,
hdf-bind_wf,
hdf-parallel-bind-halt-eq-gen,
hdf-union_wf,
lifting-apply-decide,
hdf-union-eq-disju
Latex:
\mforall{}[Info,B1,B2,C:Type]. \mforall{}[X1:Id {}\mrightarrow{} hdataflow(Info;B1)]. \mforall{}[X2:Id {}\mrightarrow{} hdataflow(Info;B2)].
\mforall{}[Y1:B1 {}\mrightarrow{} Id {}\mrightarrow{} hdataflow(Info;C)]. \mforall{}[Y2:B2 {}\mrightarrow{} Id {}\mrightarrow{} hdataflow(Info;C)].
(X1 >>= Y1 || X2 >>= Y2 = X1 + X2 >>= \mlambda{}b.case b of inl(b1) => Y1 b1 | inr(b2) => Y2 b2) supposing
(valueall-type(C) and
valueall-type(B1) and
valueall-type(B2))
Date html generated:
2015_07_22-PM-00_05_55
Last ObjectModification:
2015_02_04-PM-05_10_43
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