Nuprl Lemma : hdf-bind-gen-left-halt
∀[A,B,C:Type]. ∀[Y:B ─→ hdataflow(A;C)]. ∀[hdfs:bag(hdataflow(A;C))].
hdf-halt() (hdfs) >>= Y = hdf-halt() (hdfs) >>= λx.hdf-return({x}) ∈ hdataflow(A;C) supposing valueall-type(C)
Proof
Definitions occuring in Statement :
hdf-bind-gen: X (hdfs) >>= Y,
hdf-return: hdf-return(x),
hdf-halt: hdf-halt(),
hdataflow: hdataflow(A;B),
valueall-type: valueall-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
lambda: λx.A[x],
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T,
single-bag: {x},
bag: bag(T)
Lemmas :
list_induction,
all_wf,
hdataflow_wf,
bag_wf,
equal_wf,
bool_wf,
hdf-halted_wf,
iterate-hdataflow_wf,
hdf-bind-gen_wf,
hdf-halt_wf,
hdf-return_wf,
single-bag_wf,
list_wf,
iter_hdf_nil_lemma,
iter_hdf_cons_lemma,
hdf_halted_halt_red_lemma,
hdf_ap_halt_lemma,
bag_map_empty_lemma,
bag-null_wf,
eqtt_to_assert,
assert-bag-null,
btrue_wf,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
equal-wf-T-base,
hdf_halted_run_red_lemma,
bfalse_wf,
bag-filter_wf,
bnot_wf,
bag-map_wf,
hdf-ap_wf,
bag-append_wf,
empty-bag_wf,
subtype_rel_bag,
assert_wf,
hdf-bind-gen-ap,
and_wf,
squash_wf,
true_wf,
hdf-out_wf,
hdf_out_halt_red_lemma,
valueall-type-has-valueall,
bag-valueall-type,
product-valueall-type,
hdataflow-valueall-type,
bag-combine_wf,
hdf-out-run,
evalall-reduce
\mforall{}[A,B,C:Type]. \mforall{}[Y:B {}\mrightarrow{} hdataflow(A;C)]. \mforall{}[hdfs:bag(hdataflow(A;C))].
hdf-halt() (hdfs) >>= Y = hdf-halt() (hdfs) >>= \mlambda{}x.hdf-return(\{x\}) supposing valueall-type(C)
Date html generated:
2015_07_17-AM-08_07_10
Last ObjectModification:
2015_01_27-PM-00_07_31
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