Nuprl Lemma : hdf-bind-gen-compose1-left
∀[A,B,C,U:Type]. ∀[f:B ─→ C]. ∀[X:hdataflow(A;B)]. ∀[Y:C ─→ hdataflow(A;U)]. ∀[hdfs:bag(hdataflow(A;U))].
(f o X (hdfs) >>= Y = X (hdfs) >>= Y o f ∈ hdataflow(A;U)) supposing (valueall-type(C) and valueall-type(U))
Proof
Definitions occuring in Statement :
hdf-bind-gen: X (hdfs) >>= Y,
hdf-compose1: f o X,
hdataflow: hdataflow(A;B),
compose: f o g,
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,
bag: bag(T)
Lemmas :
hdataflow-equal,
hdf-bind-gen_wf,
hdf-compose1_wf,
compose_wf,
list_wf,
valueall-type_wf,
bag_wf,
hdataflow_wf,
list_induction,
all_wf,
equal_wf,
bool_wf,
hdf-halted_wf,
iterate-hdataflow_wf,
iter_hdf_nil_lemma,
iter_hdf_cons_lemma,
eqtt_to_assert,
hdf_halted_halt_red_lemma,
bag-null_wf,
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,
hdf-compose1-ap,
bag-map-map,
hdf-bind-gen-ap,
hdf-out_wf,
hdf_out_halt_red_lemma,
hdf_ap_halt_lemma,
bag_map_empty_lemma,
hdataflow-ext,
unit_wf2,
hdf_halted_inl_red_lemma,
false_wf,
bag-map_wf,
hdf-ap_wf,
bag-append_wf,
empty-bag_wf,
true_wf,
valueall-type-has-valueall,
bag-valueall-type,
product-valueall-type,
hdataflow-valueall-type,
bag-filter-wf3,
bnot_wf,
bag-combine_wf,
hdf-ap-inl,
hdf-ap-run,
evalall-reduce,
not_wf,
hdf-out-run,
bag-filter_wf,
subtype_rel_bag,
assert_wf
\mforall{}[A,B,C,U:Type]. \mforall{}[f:B {}\mrightarrow{} C]. \mforall{}[X:hdataflow(A;B)]. \mforall{}[Y:C {}\mrightarrow{} hdataflow(A;U)].
\mforall{}[hdfs:bag(hdataflow(A;U))].
(f o X (hdfs) >>= Y = X (hdfs) >>= Y o f) supposing (valueall-type(C) and valueall-type(U))
Date html generated:
2015_07_17-AM-08_07_14
Last ObjectModification:
2015_01_27-PM-00_07_28
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