Nuprl Lemma : fix_wf_dataflow_w_state
∀[A,B,S:Type]. ∀[s0:S]. ∀[F:Top ⟶ Top ⟶ Top ⋂ ⋂P:Type. ((S ⟶ P) ⟶ S ⟶ A ⟶ (P × B))]. (fix(F) s0 ∈ dataflow(A;B))
Proof
Definitions occuring in Statement :
dataflow: dataflow(A;B),
isect2: T1 ⋂ T2,
uall: ∀[x:A]. B[x],
top: Top,
member: t ∈ T,
apply: f a,
fix: fix(F),
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],
member: t ∈ T,
dataflow: dataflow(A;B),
so_lambda: λ2x.t[x],
so_apply: x[s]
Latex:
\mforall{}[A,B,S:Type]. \mforall{}[s0:S]. \mforall{}[F:Top {}\mrightarrow{} Top {}\mrightarrow{} Top \mcap{} \mcap{}P:Type. ((S {}\mrightarrow{} P) {}\mrightarrow{} S {}\mrightarrow{} A {}\mrightarrow{} (P \mtimes{} B))].
(fix(F) s0 \mmember{} dataflow(A;B))
Date html generated:
2016_05_17-AM-10_19_36
Last ObjectModification:
2015_12_29-PM-05_30_19
Theory : process-model
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