Nuprl Lemma : recprocess_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]))]. ∀[ext:⋂T:Type
(E[T]
⟶ M[T]
⟶ T
⟶ E[T])].
(recprocess(s0;s,m.next[s;m];e,m,p.ext[e;m;p]) ∈ 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 :
recprocess: recprocess(s0;s,m.next[s; m];e,m,p.ext[e; m; p]),
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;s3],
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,
recprocess: recprocess(s0;s,m.next[s; m];e,m,p.ext[e; m; p]),
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,
so_apply: x[s1;s2;s3],
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]))].
\mforall{}[ext:\mcap{}T:Type. (E[T] {}\mrightarrow{} M[T] {}\mrightarrow{} T {}\mrightarrow{} E[T])].
(recprocess(s0;s,m.next[s;m];e,m,p.ext[e;m;p]) \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_46
Last ObjectModification:
2015_12_29-AM-09_36_35
Theory : event-ordering
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