Nuprl Lemma : hdf-halted-compose2-iterate
∀[A,B,C:Type]. ∀[inputs:A List]. ∀[X1:hdataflow(A;B ─→ bag(C))]. ∀[X2:hdataflow(A;B)].
hdf-halted(X1 o X2*(inputs)) = hdf-halted(X1*(inputs)) ∨bhdf-halted(X2*(inputs)) supposing valueall-type(C)
Proof
Definitions occuring in Statement :
hdf-compose2: X o Y,
iterate-hdataflow: P*(inputs),
hdf-halted: hdf-halted(P),
hdataflow: hdataflow(A;B),
list: T List,
bor: p ∨bq,
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: bag(T)
Lemmas :
list_induction,
uall_wf,
hdataflow_wf,
bag_wf,
isect_wf,
valueall-type_wf,
equal_wf,
bool_wf,
hdf-halted_wf,
iterate-hdataflow_wf,
hdf-compose2_wf,
bor_wf,
iter_hdf_nil_lemma,
iff_imp_equal_bool,
assert_wf,
hdf-halted-compose2,
iff_wf,
iter_hdf_cons_lemma,
list_wf,
iff_weakening_equal,
squash_wf,
true_wf,
pi1_wf_top,
top_wf,
hdf-compose2-ap,
subtype_rel_product,
subtype_top
\mforall{}[A,B,C:Type]. \mforall{}[inputs:A List]. \mforall{}[X1:hdataflow(A;B {}\mrightarrow{} bag(C))]. \mforall{}[X2:hdataflow(A;B)].
hdf-halted(X1 o X2*(inputs)) = hdf-halted(X1*(inputs)) \mvee{}\msubb{}hdf-halted(X2*(inputs))
supposing valueall-type(C)
Date html generated:
2015_07_17-AM-08_05_34
Last ObjectModification:
2015_02_03-PM-09_46_26
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