Nuprl Lemma : iterate-rec-dataflow
∀[S,A,B:Type]. ∀[next:S ─→ A ─→ (S × B)]. ∀[L:A List]. ∀[s0:S].
(rec-dataflow(s0;s,m.next[s;m])*(L) ~ rec-dataflow(rec-dataflow-state(s0;s,m.next[s;m];L);s,m.next[s;m]))
Proof
Definitions occuring in Statement :
iterate-dataflow: P*(inputs),
rec-dataflow-state: rec-dataflow-state(s0;s,m.next[s; m];L),
rec-dataflow: rec-dataflow(s0;s,m.next[s; m]),
list: T List,
uall: ∀[x:A]. B[x],
so_apply: x[s1;s2],
function: x:A ─→ B[x],
product: x:A × B[x],
universe: Type,
sqequal: s ~ t
Lemmas :
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
equal-wf-T-base,
colength_wf_list,
list-cases,
iter_df_nil_lemma,
list_accum_nil_lemma,
product_subtype_list,
spread_cons_lemma,
sq_stable__le,
le_antisymmetry_iff,
add_functionality_wrt_le,
add-associates,
add-zero,
zero-add,
le-add-cancel,
nat_wf,
decidable__le,
false_wf,
not-le-2,
condition-implies-le,
minus-add,
minus-one-mul,
add-commutes,
le_wf,
subtract_wf,
not-ge-2,
less-iff-le,
minus-minus,
add-swap,
subtype_base_sq,
set_subtype_base,
int_subtype_base,
iter_df_cons_lemma,
rec_dataflow_ap_lemma,
list_accum_cons_lemma,
list_wf
Latex:
\mforall{}[S,A,B:Type]. \mforall{}[next:S {}\mrightarrow{} A {}\mrightarrow{} (S \mtimes{} B)]. \mforall{}[L:A List]. \mforall{}[s0:S].
(rec-dataflow(s0;s,m.next[s;m])*(L) \msim{} rec-dataflow(rec-dataflow-state(s0;s,m.next[s;m];L);
s,m.next[s;m]))
Date html generated:
2015_07_23-AM-11_05_53
Last ObjectModification:
2015_01_28-PM-11_35_28
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