Nuprl Lemma : hdf-bind-gen-halted
∀[A,B,C:Type]. ∀[X:hdataflow(A;B)]. ∀[Y:B ─→ hdataflow(A;C)]. ∀[hdfs:bag(hdataflow(A;C))].
hdf-halted(X (hdfs) >>= Y) = hdf-halted(X) ∧b bag-null(hdfs) supposing valueall-type(C)
Proof
Definitions occuring in Statement :
hdf-bind-gen: X (hdfs) >>= Y,
hdf-halted: hdf-halted(P),
hdataflow: hdataflow(A;B),
band: p ∧b q,
valueall-type: valueall-type(T),
bool: 𝔹,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T,
bag-null: bag-null(bs),
bag: bag(T)
Lemmas :
bool_wf,
eqtt_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bag-null,
hdataflow_wf,
hdf_halted_halt_red_lemma,
btrue_wf,
eqff_to_assert,
assert-bnot,
iff_transitivity,
assert_wf,
hdf-halted_wf,
bag-null_wf,
equal-wf-T-base,
iff_weakening_uiff,
assert_of_band,
hdf_halted_run_red_lemma,
bfalse_wf,
valueall-type_wf,
bag_wf
\mforall{}[A,B,C:Type]. \mforall{}[X:hdataflow(A;B)]. \mforall{}[Y:B {}\mrightarrow{} hdataflow(A;C)]. \mforall{}[hdfs:bag(hdataflow(A;C))].
hdf-halted(X (hdfs) >>= Y) = hdf-halted(X) \mwedge{}\msubb{} bag-null(hdfs) supposing valueall-type(C)
Date html generated:
2015_07_17-AM-08_06_58
Last ObjectModification:
2015_01_27-PM-00_06_48
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