Nuprl Lemma : hdf-compose1-ap
∀[A,B,C:Type]. ∀[X:hdataflow(A;B)]. ∀[f:B ─→ C]. ∀[a:A].
f o X(a) ~ <f o (fst(X(a))), bag-map(f;snd(X(a)))> supposing valueall-type(C)
Proof
Definitions occuring in Statement :
hdf-compose1: f o X,
hdf-ap: X(a),
hdataflow: hdataflow(A;B),
valueall-type: valueall-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
pi1: fst(t),
pi2: snd(t),
function: x:A ─→ B[x],
pair: <a, b>,
universe: Type,
sqequal: s ~ t,
bag-map: bag-map(f;bs)
Lemmas :
hdf-halted_wf,
bool_wf,
eqtt_to_assert,
hdf_ap_halt_lemma,
hdataflow-ext,
bag_wf,
unit_wf2,
hdf_halted_inl_red_lemma,
false_wf,
hdf_halted_halt_red_lemma,
bag_map_empty_lemma,
true_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
hdf-ap-inl,
hdf-ap-run,
valueall-type-has-valueall,
bag-valueall-type,
bag-map_wf,
evalall-reduce,
not_wf,
valueall-type_wf,
hdataflow_wf
\mforall{}[A,B,C:Type]. \mforall{}[X:hdataflow(A;B)]. \mforall{}[f:B {}\mrightarrow{} C]. \mforall{}[a:A].
f o X(a) \msim{} <f o (fst(X(a))), bag-map(f;snd(X(a)))> supposing valueall-type(C)
Date html generated:
2015_07_17-AM-08_05_26
Last ObjectModification:
2015_01_27-PM-00_16_35
Home
Index