Some definitions of interest.
d-es	Def es is an event system of D Def == w:World, p:FairFifo. PossibleWorld(D;w) & es = ES(w)  ES
d-realizes	Def D  Def realizes es.P(es) Def == D':Dsys.  Def == D  D'  (w:World, p:FairFifo. PossibleWorld(D';w)  P(ES(w)))
d-realizes2	Def D realizes2 es.P(es) == w:World, p:FairFifo. PossibleWorld(D;w)  P(ES(w))
dsys	Def Dsys == IdMsgA
	Thm* Dsys  Type{i'}
ma-valtype	Def ma-valtype(da; k) == da(k)?Top
Kind-deq	Def KindDeq == union-deq(IdLnkId;Id;product-deq(IdLnk;Id;IdLnkDeq;IdDeq);IdDeq)
event_system	Def ES Def == E:Type Def == EqDecider(E)(T:IdIdType Def == EqDecider(E)(V:IdIdType Def == EqDecider(E)(M:IdLnkIdType Def == EqDecider(E)(Top(loc:EId Def == EqDecider(E)(Top(kind:EKnd Def == EqDecider(E)(Top(val:(e:Eeventtype(kind;loc;V;M;e)) Def == EqDecider(E)(Top(when:(x:Ide:ET(loc(e),x)) Def == EqDecider(E)(Top(after:(x:Ide:ET(loc(e),x)) Def == EqDecider(E)(Top(sends:(l:IdLnkE(Msg_sub(l; M) List)) Def == EqDecider(E)(Top(sender:{e:E| isrcv(kind(e)) }E Def == EqDecider(E)(Top(index:(e:{e:E| isrcv(kind(e)) }||sends Def == EqDecider(E)(Top(index:(e:{e:E| isrcv(kind(e)) }||(lnk(kind(e)) Def == EqDecider(E)(Top(index:(e:{e:E| isrcv(kind(e)) }||,sender(e))||) Def == EqDecider(E)(Top(first:E Def == EqDecider(E)(Top(pred:{e':E| (first(e')) }E Def == EqDecider(E)(Top(causl:EEProp Def == EqDecider(E)(Top(ESAxioms{i:l} Def == EqDecider(E)(Top(ESAxioms(E; Def == EqDecider(E)(Top(ESAxioms(T; Def == EqDecider(E)(Top(ESAxioms(M; Def == EqDecider(E)(Top(ESAxioms(loc; Def == EqDecider(E)(Top(ESAxioms(kind; Def == EqDecider(E)(Top(ESAxioms(val; Def == EqDecider(E)(Top(ESAxioms(when; Def == EqDecider(E)(Top(ESAxioms(after; Def == EqDecider(E)(Top(ESAxioms(sends; Def == EqDecider(E)(Top(ESAxioms(sender; Def == EqDecider(E)(Top(ESAxioms(index; Def == EqDecider(E)(Top(ESAxioms(first; Def == EqDecider(E)(Top(ESAxioms(pred; Def == EqDecider(E)(Top(ESAxioms(causl) Def == EqDecider(E)(Top(Top))
	Thm* ES  Type{i'}
Knd	Def Knd == (IdLnkId)+Id
	Thm* Knd  Type
es-Msg	Def Msg == Msg(1of(2of(2of(2of(2of(es))))))
Msg	Def Msg(M) == l:IdLnkt:IdM(l,t)
	Thm* M:(IdLnkIdType). Msg(M)  Type
IdLnk	Def IdLnk == IdId
	Thm* IdLnk  Type
ma-state	Def State(ds) == x:Idds(x)?Top
Id	Def Id == Atom
	Thm* Id  Type
d-single-sends	Def d-single-sends(i; ds; da; k; l; f)(j) Def == if eqof(IdDeq)(j,i) ma-single-sends(ds; da; k; l; f) else  fi
id-deq	Def IdDeq == product-deq(Atom;;AtomDeq;NatDeq)
assert	Def b == if b True else False fi
	Thm* b:. b  Prop
es-E	Def E == 1of(es)
es-valtype	Def valtype(e) == if isrcv(e) rcvtype(e) else acttype(e) fi
es-isrcv	Def isrcv(e) == isrcv(kind(e))
es-lnk	Def lnk(e) == lnk(kind(e))
es-kind	Def kind(e) == 1of(2of(2of(2of(2of(2of(2of(2of(es))))))))(e)
es-loc	Def loc(e) == 1of(2of(2of(2of(2of(2of(2of(es)))))))(e)
es-sends	Def sends(l;e) Def == 1of(2of(2of(2of(2of(2of(2of(2of(2of(2of(2of(2of(es))))))))))))(l,e)
es-val	Def val(e) == 1of(2of(2of(2of(2of(2of(2of(2of(2of(es)))))))))(e)
es-vartype	Def vartype(i;x) == 1of(2of(2of(es)))(i,x)
es-when	Def (x when e) == 1of(2of(2of(2of(2of(2of(2of(2of(2of(2of(es))))))))))(x,e)
fpf	Def a:A fp-> B(a) == d:A Lista:{a:A| (a  d) }B(a)
	Thm* A:Type, B:(AType). a:A fp-> B(a)  Type
fpf-cap	Def f(x)?z == if x  dom(f) f(x) else z fi
lsrc	Def source(l) == 1of(l)
	Thm* l:IdLnk. source(l)  Id
mlnk	Def mlnk(m) == 1of(m)
	Thm* M:(IdLnkIdType), m:Msg(M). mlnk(m)  IdLnk
	Thm* the_es:ES, m:Msg. mlnk(m)  IdLnk
rcv	Def rcv(l; tg) == inl(<l,tg>)
	Thm* l:IdLnk, tg:Id. rcv(l; tg)  Knd
tagged-messages	Def tagged-messages(l;s;v;L) == map(x.<l,x>;tagged-list-messages(s;v;L))
top	Def Top == Void given Void
	Thm* Top  Type

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