Nuprl Lemma : rec-dataflow_wf2
∀[S,A,B:Type ⟶ Type].
(let Proc = corec(P.A[P] ⟶ (P × B[P])) in
∀s0:S[Proc]. ∀next:⋂T:{T:Type| Proc ⊆r T} . (S[A[T] ⟶ (T × B[T])] ⟶ A[T] ⟶ (S[T] × B[T])).
(rec-dataflow(s0;s,m.next[s;m]) ∈ Proc)) supposing
(Continuous+(T.B[T]) and
Continuous+(T.A[T]) and
Continuous+(T.S[T]))
Proof
Definitions occuring in Statement :
rec-dataflow: rec-dataflow(s0;s,m.next[s; m]),
corec: corec(T.F[T]),
strong-type-continuous: Continuous+(T.F[T]),
let: let,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
so_apply: x[s1;s2],
so_apply: x[s],
all: ∀x:A. B[x],
member: t ∈ T,
set: {x:A| B[x]} ,
isect: ⋂x:A. B[x],
function: x:A ⟶ B[x],
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
strong-type-continuous: Continuous+(T.F[T]),
ext-eq: A ≡ B,
and: P ∧ Q,
subtype_rel: A ⊆r B,
let: let,
all: ∀x:A. B[x],
rec-dataflow: rec-dataflow(s0;s,m.next[s; m]),
so_lambda: λ2x.t[x],
so_apply: x[s],
isect2: T1 ⋂ T2,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
top: Top,
bfalse: ff,
so_apply: x[s1;s2],
implies: P ⇒ Q,
prop: ℙ
Latex:
\mforall{}[S,A,B:Type {}\mrightarrow{} Type].
(let Proc = corec(P.A[P] {}\mrightarrow{} (P \mtimes{} B[P])) in
\mforall{}s0:S[Proc]. \mforall{}next:\mcap{}T:\{T:Type| Proc \msubseteq{}r T\} . (S[A[T] {}\mrightarrow{} (T \mtimes{} B[T])] {}\mrightarrow{} A[T] {}\mrightarrow{} (S[T] \mtimes{} B[T])).
(rec-dataflow(s0;s,m.next[s;m]) \mmember{} Proc)) supposing
(Continuous+(T.B[T]) and
Continuous+(T.A[T]) and
Continuous+(T.S[T]))
Date html generated:
2016_05_17-AM-10_19_57
Last ObjectModification:
2015_12_29-PM-05_30_08
Theory : process-model
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