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'}
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-locl	Def (e <loc e') == loc(e) = loc(e')  Id & (e < e')
ma-state	Def State(ds) == x:Idds(x)?Top
Id	Def Id == Atom
	Thm* Id  Type
d-single-pre	Def @i (with ds: ds action a:T precondition a(v) is P s v)(j) Def == if eqof(IdDeq)(j,i) (with ds: ds action a:T precondition a(v) is P s v) Def == else  fi
es-E	Def E == 1of(es)
es-after	Def (x after e) Def == 1of(2of(2of(2of(2of(2of(2of(2of(2of(2of(2of(es)))))))))))(x,e)
es-valtype	Def valtype(e) == if isrcv(e) rcvtype(e) else acttype(e) fi
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-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
id-deq	Def IdDeq == product-deq(Atom;;AtomDeq;NatDeq)
locl	Def locl(a) == inr(a)
	Thm* a:Id. locl(a)  Knd
not	Def A == A  False
	Thm* A:Prop. (A)  Prop
top	Def Top == Void given Void
	Thm* Top  Type

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