Nuprl Lemma : rec-bind-nxt_wf
∀[A,B,C:Type]. ∀[X:C ─→ hdataflow(A;B)]. ∀[Y:C ─→ hdataflow(A;C)]. ∀[p:bag(hdataflow(A;B)) × bag(hdataflow(A;C))].
∀[a:A].
(rec-bind-nxt(X;Y;p;a) ∈ bag(hdataflow(A;B)) × bag(hdataflow(A;C)) × bag(B)) supposing
(valueall-type(B) and
valueall-type(C))
Proof
Definitions occuring in Statement :
rec-bind-nxt: rec-bind-nxt(X;Y;p;a),
hdataflow: hdataflow(A;B),
valueall-type: valueall-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ─→ B[x],
product: x:A × B[x],
universe: Type,
bag: bag(T)
Lemmas :
valueall-type-has-valueall,
bag-valueall-type,
product-valueall-type,
hdataflow-valueall-type,
evalall-reduce,
bag-map_wf,
bag-append_wf,
bag-combine_wf,
valueall-type_wf,
bag_wf,
hdataflow_wf,
bag-mapfilter_wf,
hdf-running_wf,
assert_wf,
bag-filter_wf,
subtype_rel_bag
\mforall{}[A,B,C:Type]. \mforall{}[X:C {}\mrightarrow{} hdataflow(A;B)]. \mforall{}[Y:C {}\mrightarrow{} hdataflow(A;C)].
\mforall{}[p:bag(hdataflow(A;B)) \mtimes{} bag(hdataflow(A;C))]. \mforall{}[a:A].
(rec-bind-nxt(X;Y;p;a) \mmember{} bag(hdataflow(A;B)) \mtimes{} bag(hdataflow(A;C)) \mtimes{} bag(B)) supposing
(valueall-type(B) and
valueall-type(C))
Date html generated:
2015_07_17-AM-08_08_00
Last ObjectModification:
2015_01_27-PM-00_06_23
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