Nuprl Lemma : iterate-hdf-bind-simple
∀[A,B,C:Type]. ∀[X:hdataflow(A;B)]. ∀[Y:B ─→ hdataflow(A;C)].
∀[L:A List]. ∀[a:A]. ((snd(X >>= Y*(L)(a))) = (snd(simple-hdf-bind(X;Y)*(L)(a))) ∈ bag(C)) supposing valueall-type(C)
Proof
Definitions occuring in Statement :
simple-hdf-bind: simple-hdf-bind(X;Y),
hdf-bind: X >>= Y,
iterate-hdataflow: P*(inputs),
hdf-ap: X(a),
hdataflow: hdataflow(A;B),
list: T List,
valueall-type: valueall-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
pi2: snd(t),
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T,
bag: bag(T)
Lemmas :
list_induction,
all_wf,
bag_wf,
hdataflow_wf,
bag-filter_wf,
bnot_wf,
hdf-halted_wf,
subtype_rel_bag,
assert_wf,
hdf-ap_wf,
iterate-hdataflow_wf,
mk-hdf_wf,
bag-null_wf,
bool_wf,
eqtt_to_assert,
assert-bag-null,
bind-nxt_wf,
bfalse_wf,
simple-bind-nxt_wf,
list_wf,
iter_hdf_nil_lemma,
equal_wf,
iter_hdf_cons_lemma,
valueall-type_wf,
empty-bag_wf,
bag_filter_empty_lemma,
pi2_wf,
band_commutes,
iff_weakening_equal,
equal-wf-T-base,
bor_wf,
or_wf,
not_wf,
iff_transitivity,
iff_weakening_uiff,
assert_of_band,
bnot_thru_band,
eqff_to_assert,
assert_of_bor,
assert_of_bnot,
hdataflow-ext,
unit_wf2,
false_wf,
true_wf,
bag_map_empty_lemma,
valueall-type-has-valueall,
bag-valueall-type,
product-valueall-type,
hdataflow-valueall-type,
bag-map_wf,
bag-append_wf,
evalall-reduce,
bag-combine_wf,
bag-map-append,
top_wf,
bag-append-empty,
bag-subtype-list,
bag-filter-split,
equal-empty-bag,
equal-wf-base-T,
bag-combine-map,
bag-combine-empty-right,
squash_wf,
set-valueall-type,
bag-combine-append-left,
subtype_rel_dep_function,
subtype_rel_self,
set_wf,
empty_bag_append_lemma,
decidable__cand,
decidable__assert,
iterate-hdf-halt,
subtype_rel_list,
subtype_base_sq,
unit_subtype_base,
equal-unit,
it_wf,
hdf-halt_wf,
hdf_ap_halt_lemma,
bag-map-map,
pi1_wf_top,
cons_wf,
bag-filter-wf3,
bag-filter-append,
assert_elim,
not_assert_elim,
btrue_neq_bfalse,
empty-bag-iff-no-member
\mforall{}[A,B,C:Type]. \mforall{}[X:hdataflow(A;B)]. \mforall{}[Y:B {}\mrightarrow{} hdataflow(A;C)].
\mforall{}[L:A List]. \mforall{}[a:A]. ((snd(X >>= Y*(L)(a))) = (snd(simple-hdf-bind(X;Y)*(L)(a))))
supposing valueall-type(C)
Date html generated:
2015_07_17-AM-08_07_52
Last ObjectModification:
2015_02_03-PM-09_48_46
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