Nuprl Lemma : rec-process_wf
∀[S,M,E:Type ⟶ Type].
  (∀[s0:S[process(P.M[P];P.E[P])]]. ∀[next:⋂T:{T:Type| process(P.M[P];P.E[P]) ⊆r T} 
                                             (S[M[T] ⟶ (T × E[T])] ⟶ M[T] ⟶ (S[T] × E[T]))].
     (RecProcess(s0;s,m.next[s;m]) ∈ process(P.M[P];P.E[P]))) supposing 
     (Continuous+(T.E[T]) and 
     Continuous+(T.M[T]) and 
     Continuous+(T.S[T]))
Proof
Definitions occuring in Statement : 
rec-process: RecProcess(s0;s,m.next[s; m])
, 
process: process(P.M[P];P.E[P])
, 
strong-type-continuous: Continuous+(T.F[T])
, 
uimplies: b supposing a
, 
subtype_rel: A ⊆r B
, 
uall: ∀[x:A]. B[x]
, 
so_apply: x[s1;s2]
, 
so_apply: x[s]
, 
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]
, 
member: t ∈ T
, 
uimplies: b supposing a
, 
rec-process: RecProcess(s0;s,m.next[s; m])
, 
process: process(P.M[P];P.E[P])
, 
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]
, 
subtype_rel: A ⊆r B
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
prop: ℙ
Latex:
\mforall{}[S,M,E:Type  {}\mrightarrow{}  Type].
    (\mforall{}[s0:S[process(P.M[P];P.E[P])]].  \mforall{}[next:\mcap{}T:\{T:Type|  process(P.M[P];P.E[P])  \msubseteq{}r  T\} 
                                                                                          (S[M[T]  {}\mrightarrow{}  (T  \mtimes{}  E[T])]  {}\mrightarrow{}  M[T]  {}\mrightarrow{}  (S[T]  \mtimes{}  E[T]))].
          (RecProcess(s0;s,m.next[s;m])  \mmember{}  process(P.M[P];P.E[P])))  supposing 
          (Continuous+(T.E[T])  and 
          Continuous+(T.M[T])  and 
          Continuous+(T.S[T]))
Date html generated:
2016_05_16-AM-11_43_33
Last ObjectModification:
2015_12_29-AM-09_35_48
Theory : event-ordering
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