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
Definitions unfolded in proof :
rec-dataflow-state: rec-dataflow-state(s0;s,m.next[s; m];L),
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
or: P ∨ Q,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
cons: [a / b],
colength: colength(L),
guard: {T},
decidable: Dec(P),
nil: [],
it: ⋅,
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_type: SQType(T),
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
pi1: fst(t)
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:
2016_05_17-AM-10_20_48
Last ObjectModification:
2016_01_18-AM-00_20_35
Theory : process-model
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