Nuprl Lemma : hdf-parallel-halted
∀[A,B:Type].
∀[inputs:A List]. ∀[X,Y:hdataflow(A;B)].
hdf-halted(X || Y*(inputs)) = hdf-halted(X*(inputs)) ∧b hdf-halted(Y*(inputs))
supposing valueall-type(B)
Proof
Definitions occuring in Statement :
hdf-parallel: X || Y,
iterate-hdataflow: P*(inputs),
hdf-halted: hdf-halted(P),
hdataflow: hdataflow(A;B),
list: T List,
band: p ∧b q,
valueall-type: valueall-type(T),
bool: 𝔹,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Lemmas :
list_induction,
uall_wf,
hdataflow_wf,
equal_wf,
bool_wf,
hdf-halted_wf,
iterate-hdataflow_wf,
hdf-parallel_wf,
eqtt_to_assert,
iter_hdf_nil_lemma,
hdf_halted_halt_red_lemma,
btrue_wf,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
hdf_halted_run_red_lemma,
bfalse_wf,
iter_hdf_cons_lemma,
list_wf,
valueall-type_wf,
hdf-ap_wf,
bag_wf,
iff_weakening_equal,
squash_wf,
true_wf,
pi1_wf_top,
top_wf,
hdf-parallel-ap,
subtype_rel_product,
subtype_top
\mforall{}[A,B:Type].
\mforall{}[inputs:A List]. \mforall{}[X,Y:hdataflow(A;B)].
hdf-halted(X || Y*(inputs)) = hdf-halted(X*(inputs)) \mwedge{}\msubb{} hdf-halted(Y*(inputs))
supposing valueall-type(B)
Date html generated:
2015_07_17-AM-08_06_23
Last ObjectModification:
2015_02_03-PM-09_47_21
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