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
Lemmas :
assert_wf,
in-eclass_wf,
assert_witness,
es-E_wf,
event-ordering+_subtype,
all_wf,
equal_wf,
Id_wf,
es-loc_wf,
eclass-val_wf,
assert_elim,
subtype_base_sq,
bool_wf,
bool_subtype_base,
es-E-interface-property,
iff_wf,
global-order-preserving_wf,
subtype_rel_wf,
es-E-interface_wf,
es-interface-subtype_rel2,
top_wf,
es-causle_wf,
eclass_wf,
event-ordering+_wf,
es-fix_wf2,
es-fix_property,
es-fix-order-preserving,
strong-interface-fifo-order-preserving,
biject_wf,
glues-iff,
es-fix-causle,
fun-connected-induction,
squash_wf,
subtype_top,
event-ordering+_cumulative2,
iff_weakening_equal,
fun-connected_wf,
not_wf,
true_wf
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:
2015_07_21-PM-04_24_33
Last ObjectModification:
2015_02_04-PM-06_01_44
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