Nuprl Lemma : glues-via-flow-lemma1
∀[Info:Type]
∀es:EO+(Info)
∀[A:Type]
∀Sys,In,Out:EClass(A). ∀f:E(Sys) ⟶ E(Sys).
((∀x:E(Sys). f x c≤ x)
⇒ (global-order-preserving(es;Sys;f)
⇒ (Bij(E(Out);E(In);λe.f**(e)) ⇒ λe.f**(e) glues In ──λe.In(e)⟶ Out) supposing
((∀e1,e2:E(Out). (loc(e1) = loc(e2) ∈ Id)) and
(∀e:E(Out). (Out(e) = Sys(e) ∈ A)) and
(∀e:E(In). (Sys(e) = In(e) ∈ A)) and
(∀e:E(Sys). (Sys(e) = Sys(f e) ∈ A)) and
(∀e:E(Sys). (↑e ∈b In ⇐⇒ (f e) = e ∈ E)))) supposing
((E(Out) ⊆r E(Sys)) and
(E(In) ⊆r E(Sys))))
Proof
Definitions occuring in Statement :
glues: g glues Ia ──f⟶ Ib,
global-order-preserving: global-order-preserving(es;X;f),
es-E-interface: E(X),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-fix: f**(e),
es-causle: e c≤ e',
es-loc: loc(e),
es-E: E,
Id: Id,
biject: Bij(A;B;f),
assert: ↑b,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
apply: f a,
lambda: λx.A[x],
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
uimplies: b supposing a,
member: t ∈ T,
subtype_rel: A ⊆r B,
iff: P ⇐⇒ Q,
and: P ∧ Q,
es-E-interface: E(X),
prop: ℙ,
rev_implies: P ⇐ Q,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
top: Top,
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_type: SQType(T),
guard: {T},
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True,
strong-interface-fifo: strong-interface-fifo(es;X;f),
squash: ↓T
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info)
\mforall{}[A:Type]
\mforall{}Sys,In,Out:EClass(A). \mforall{}f:E(Sys) {}\mrightarrow{} E(Sys).
((\mforall{}x:E(Sys). f x c\mleq{} x)
{}\mRightarrow{} (global-order-preserving(es;Sys;f)
{}\mRightarrow{} (Bij(E(Out);E(In);\mlambda{}e.f**(e)) {}\mRightarrow{} \mlambda{}e.f**(e) glues In {}{}\mlambda{}e.In(e){}\mrightarrow{} Out) supposing
((\mforall{}e1,e2:E(Out). (loc(e1) = loc(e2))) and
(\mforall{}e:E(Out). (Out(e) = Sys(e))) and
(\mforall{}e:E(In). (Sys(e) = In(e))) and
(\mforall{}e:E(Sys). (Sys(e) = Sys(f e))) and
(\mforall{}e:E(Sys). (\muparrow{}e \mmember{}\msubb{} In \mLeftarrow{}{}\mRightarrow{} (f e) = e)))) supposing
((E(Out) \msubseteq{}r E(Sys)) and
(E(In) \msubseteq{}r E(Sys))))
Date html generated:
2016_05_17-AM-08_14_45
Last ObjectModification:
2016_01_17-PM-02_47_51
Theory : event-ordering
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