Nuprl Lemma : hdf-halted-compose2
∀[A,B,C:Type]. ∀[X1:hdataflow(A;B ─→ bag(C))]. ∀[X2:hdataflow(A;B)].
uiff(↑hdf-halted(X1 o X2);↑(hdf-halted(X1) ∨bhdf-halted(X2))) supposing valueall-type(C)
Proof
Definitions occuring in Statement :
hdf-compose2: X o Y,
hdf-halted: hdf-halted(P),
hdataflow: hdataflow(A;B),
bor: p ∨bq,
valueall-type: valueall-type(T),
assert: ↑b,
uiff: uiff(P;Q),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
function: x:A ─→ B[x],
universe: Type,
bag: bag(T)
Lemmas :
assert_of_bor,
hdf-halted_wf,
bag_wf,
assert_witness,
bor_wf,
assert_wf,
hdf-compose2_wf,
valueall-type_wf,
hdataflow_wf,
bnot_wf,
not_wf,
or_wf,
bool_cases,
subtype_base_sq,
bool_wf,
bool_subtype_base,
eqtt_to_assert,
eqff_to_assert,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot,
hdf_halted_halt_red_lemma,
equal_wf,
bool_cases_sqequal,
assert-bnot,
hdf_halted_run_red_lemma
\mforall{}[A,B,C:Type]. \mforall{}[X1:hdataflow(A;B {}\mrightarrow{} bag(C))]. \mforall{}[X2:hdataflow(A;B)].
uiff(\muparrow{}hdf-halted(X1 o X2);\muparrow{}(hdf-halted(X1) \mvee{}\msubb{}hdf-halted(X2))) supposing valueall-type(C)
Date html generated:
2015_07_17-AM-08_05_34
Last ObjectModification:
2015_01_27-PM-00_16_13
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