Nuprl Lemma : parallel-bind-program-eq
∀[Info,B,C:Type]. ∀[X1,X2:Id ─→ hdataflow(Info;B)]. ∀[X:B ─→ Id ─→ hdataflow(Info;C)].
(X1 >>= X || X2 >>= X = X1 || X2 >>= X ∈ (Id ─→ hdataflow(Info;C))) supposing (valueall-type(C) and valueall-type(B))
Proof
Definitions occuring in Statement :
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],
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T,
hdataflow: hdataflow(A;B)
Lemmas :
local-class-equality,
bind-class_wf,
parallel-class_wf,
hdataflow-class_wf,
sq_exists_subtype_rel,
Id_wf,
hdataflow_wf,
all_wf,
es-E_wf,
event-ordering+_subtype,
equal_wf,
bag_wf,
class-ap_wf,
hdf-ap_wf,
iterate-hdataflow_wf,
es-loc_wf,
map_wf,
es-info_wf,
es-before_wf,
squash_wf,
true_wf,
eclass_wf,
event-ordering+_wf,
parallel-class-bind-left,
iff_weakening_equal,
bind-class-program_wf,
parallel-class-program_wf,
hdf-parallel-bind-halt-eq,
list_wf,
valueall-type_wf,
pi2_wf
Latex:
\mforall{}[Info,B,C:Type]. \mforall{}[X1,X2:Id {}\mrightarrow{} hdataflow(Info;B)]. \mforall{}[X:B {}\mrightarrow{} Id {}\mrightarrow{} hdataflow(Info;C)].
(X1 >>= X || X2 >>= X = X1 || X2 >>= X) supposing (valueall-type(C) and valueall-type(B))
Date html generated:
2015_07_22-PM-00_05_53
Last ObjectModification:
2015_02_04-PM-05_10_38
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