Nuprl Lemma : hdf-parallel-bind-halt-eq
∀[A,B,C:Type]. ∀[X1,X2:hdataflow(A;B)]. ∀[X:B ─→ hdataflow(A;C)].
(∀inputs:A List. hdf-halted(X1 >>= X || X2 >>= X*(inputs)) = hdf-halted(X1 || X2 >>= X*(inputs))) supposing
(valueall-type(C) and
valueall-type(B))
Proof
Definitions occuring in Statement :
list: T List,
valueall-type: valueall-type(T),
bool: 𝔹,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T,
hdf-bind: X >>= Y,
hdf-parallel: X || Y,
iterate-hdataflow: P*(inputs),
hdf-halted: hdf-halted(P),
hdataflow: hdataflow(A;B)
Lemmas :
empty-bag_wf,
hdataflow_wf,
bag_wf,
equal-wf-T-base,
and_wf,
equal_wf,
hdf-bind-gen_wf,
empty_bag_append_lemma,
hdf-parallel_wf,
bag-append_wf,
list_induction,
all_wf,
bool_wf,
hdf-halted_wf,
iterate-hdataflow_wf,
list_wf,
iter_hdf_nil_lemma,
iter_hdf_cons_lemma,
eqtt_to_assert,
assert-bag-null,
hdf_halted_halt_red_lemma,
bag_map_empty_lemma,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
hdf_halted_run_red_lemma,
bag-append-eq-empty,
btrue_wf,
ppcc-problem,
iff_imp_equal_bool,
true_wf,
false_wf,
iff_weakening_equal,
bfalse_wf,
hdf_ap_halt_lemma,
assert_of_band,
assert_wf,
iterate-hdf-halt,
subtype_rel_list,
top_wf,
assert_functionality_wrt_uiff,
bag-null_wf,
hdf-bind-gen-halted,
hdf-halted-is-halt,
equal-wf-base-T,
hdf-ap_wf,
hdf-parallel-halt,
hdf-halt_wf,
iff_transitivity,
iff_weakening_uiff,
hdf-bind-gen-halt-left,
hdf-ap-run,
valueall-type-has-valueall,
bag-valueall-type,
evalall-reduce,
bnot_wf,
hdf-bind-gen-ap,
squash_wf,
pi1_wf_top,
valueall-type_wf,
hdf-parallel-ap,
subtype_rel_product,
subtype_top,
bag-filter_wf,
bag-map_wf,
pi2_wf,
subtype_rel_bag,
bag-combine_wf,
bag-filter-append,
bag-map-append,
bag-append-assoc-comm,
bag-append-assoc
Latex:
\mforall{}[A,B,C:Type]. \mforall{}[X1,X2:hdataflow(A;B)]. \mforall{}[X:B {}\mrightarrow{} hdataflow(A;C)].
(\mforall{}inputs:A List
hdf-halted(X1 >>= X || X2 >>= X*(inputs)) = hdf-halted(X1 || X2 >>= X*(inputs))) supposing
(valueall-type(C) and
valueall-type(B))
Date html generated:
2015_07_22-PM-00_05_50
Last ObjectModification:
2015_02_04-PM-05_23_44
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