Some definitions of interest.
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'}
ESAxioms	Def ESAxioms{i:l} Def ESAxioms(E; Def ESAxioms(T; Def ESAxioms(M; Def ESAxioms(loc; Def ESAxioms(kind; Def ESAxioms(val; Def ESAxioms(when; Def ESAxioms(after; Def ESAxioms(sends; Def ESAxioms(sender; Def ESAxioms(index; Def ESAxioms(first; Def ESAxioms(pred; Def ESAxioms(causl) Def == (e,e':E. loc(e) = loc(e')  Id  causl(e,e')  e = e'  causl(e',e)) Def == & (e:E. (first(e))  (e':E. loc(e') = loc(e)  Id  causl(e',e))) Def == & (e:E.  Def == & ((first(e)) Def == & ( Def == & (loc(pred(e)) = loc(e)  Id & causl(pred(e),e) Def == & (& (e':E.  Def == & (& (loc(e') = loc(e)  Id  (causl(pred(e),e') & causl(e',e)))) Def == & (e:E.  Def == & ((first(e))  (x:Id. when(x,e) = after(x,pred(e))  T(loc(e),x))) Def == & (Trans e,e':E. causl(e,e')) Def == & SWellFounded(causl(e,e')) Def == & (e:E.  Def == & (isrcv(kind(e)) Def == & ( Def == & ((sends(lnk(kind(e)),sender(e)))[(index(e))] Def == & (= Def == & (msg(lnk(kind(e));tag(kind(e));val(e)) Def == & ( Msg(M)) Def == & (e:E. isrcv(kind(e))  causl(sender(e),e)) Def == & (e,e':E. Def == & (causl(e,e') Def == & ( Def == & ((first(e')) & causl(e,pred(e'))  e = pred(e') Def == & ( isrcv(kind(e')) & causl(e,sender(e'))  e = sender(e')) Def == & (e:E. isrcv(kind(e))  loc(e) = destination(lnk(kind(e)))) Def == & (e:E, l:IdLnk. Def == & (loc(e) = source(l)  sends(l,e) = nil  Msg_sub(l; M) List) Def == & (e,e':E. Def == & (isrcv(kind(e)) Def == & ( Def == & (isrcv(kind(e')) Def == & ( Def == & (lnk(kind(e)) = lnk(kind(e')) Def == & ( Def == & ((causl(e,e') Def == & (( Def == & ((causl(sender(e),sender(e')) Def == & (( sender(e) = sender(e')  E & index(e)<index(e'))) Def == & (e:E, l:IdLnk, n:||sends(l,e)||. Def == & (e':E.  Def == & (isrcv(kind(e')) & lnk(kind(e')) = l & sender(e') = e & index(e') = n)
	Thm* E:Type{i}, T,V:(IdIdType{i}), M:(IdLnkIdType{i}), loc:(EId), Thm* kind:(EKnd), val:(e:Eeventtype(kind;loc;V;M;e)), Thm* when,after:(x:Ide:ET(loc(e),x)), Thm* sends:(l:IdLnkE(Msg_sub(l; M) List)), Thm* sender:({e:E| isrcv(kind(e)) }E), Thm* index:(e:{e:E| isrcv(kind(e)) }||sends(lnk(kind(e)),sender(e))||), Thm* first:(E), pred:({e':E| first(e') }E), causl:(EEProp{i}). Thm* ESAxioms{i:l} Thm* ESAxioms(E; Thm* ESAxioms(T; Thm* ESAxioms(M; Thm* ESAxioms(loc; Thm* ESAxioms(kind; Thm* ESAxioms(val; Thm* ESAxioms(when; Thm* ESAxioms(after; Thm* ESAxioms(sends; Thm* ESAxioms(sender; Thm* ESAxioms(index; Thm* ESAxioms(first; Thm* ESAxioms(pred; Thm* ESAxioms(causl) Thm*  Prop{i'}
eventtype	Def eventtype(k;loc;V;M;e) == kindcase(k(e);a.V(loc(e),a);l,t.M(l,t))
	Thm* E:Type, V:(IdIdType), M:(IdLnkIdType), loc:(EId), k:(EKnd), Thm* e:E. eventtype(k;loc;V;M;e)  Type
fair-fifo	Def FairFifo Def == (i:Id, t:, l:IdLnk. source(l) = i  onlnk(l;m(i;t)) = nil  Msg List) Def == & (i:Id, t:. Def == & (isnull(a(i;t)) Def == & ( Def == & ((x:Id. s(i;t+1).x = s(i;t).x  vartype(i;x)) Def == & (& m(i;t) = nil  Msg List) Def == & (i:Id, t:, l:IdLnk. Def == & (isrcv(l;a(i;t)) Def == & ( Def == & (destination(l) = i Def == & (& ||queue(l;t)||1 & hd(queue(l;t)) = msg(a(i;t))  Msg) Def == & (l:IdLnk, t:. Def == & (t':.  Def == & (tt' & isrcv(l;a(destination(l);t'))  queue(l;t') = nil  Msg List)
w-es	Def ES(the_w;p) Def == <E Def == ,product-deq(Id;;IdDeq;NatDeq) Def == ,(i,x. vartype(i;x)) Def == ,(i,a. V(i;locl(a))) Def == ,the_w.M Def == , Def == ,(e.loc(e)) Def == ,(e.kind(e)) Def == ,(e.val(e)) Def == ,(x,e. (x when e)) Def == ,(x,e. (x after e)) Def == ,(l,e. sends(l;e)) Def == ,(e.sender(e)) Def == ,(e.index(e)) Def == ,(e.first(e)) Def == ,(e.pred(e)) Def == ,(e,e'. e <c e') Def == ,world_DASH_event_DASH_system{1:l, i:l}(the_w,p) Def == ,>
locl	Def locl(a) == inr(a)
	Thm* a:Id. locl(a)  Knd
w-causl	Def e <c e' == e e,e'. e <loc e'  isrcv(kind(e')) & e = sender(e')  E^+ e'
w-E	Def E == {p:(Id)| isnull(a(1of(p);2of(p))) }
w-M	Def w.M == 1of(2of(2of(w)))
w-V	Def V(i;k) == kindcase(k;a.1of(2of(w))(i,a);l,tg.1of(2of(2of(w)))(l,tg))
w-after	Def (x after e) == s(1of(e);2of(e)+1).x
w-index	Def index(e) Def == ||rcvs(lnk(kind(e));time(e))||-||snds(lnk(kind(e));time(sender(e)))||
w-sender	Def sender(e) == <source(lnk(kind(e))),mu(t.match(lnk(kind(e));t;time(e)))>
w-ekind	Def kind(e) == kind(act(e))
w-eval	Def val(e) == val(act(e))
w-first	Def first(e) Def == if time(e)=0 true Def == i; isnull(a(loc(e);time(e)-1)) first(<loc(e),time(e)-1>) Def == else false fi Def (recursive)
w-pred	Def pred(e) Def == if isnull(a(loc(e);time(e)-1)) pred(<loc(e),time(e)-1>) Def == else <loc(e),time(e)-1> fi Def (recursive)
w-sends	Def sends(l;e) == onlnk(l;m(loc(e);time(e)))
w-loc	Def loc(e) == 1of(e)
w-vartype	Def vartype(i;x) == w.T(i,x)
w-when	Def (x when e) == s(1of(e);2of(e)).x
world	Def World Def == T:IdIdType Def == TA:IdIdType Def == M:IdLnkIdType Def == (i:Id(x:IdT(i,x)))(i:Idaction(w-action-dec(TA;M;i))) Def == (i:Id({m:Msg(M)| source(mlnk(m)) = i } List))Top
	Thm* World  Type{i'}

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