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'}
Knd	Def Knd == (IdLnkId)+Id
	Thm* Knd  Type
Msg_sub	Def Msg_sub(l; M) == {m:Msg(M)| haslink(l; m) }
	Thm* M:(IdLnkIdType), l:IdLnk. Msg_sub(l; M)  Type
es-Msgl	Def (Msg on l) == {m:Msg| haslink(l; m) }
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
haslink	Def haslink(l; m) == mlnk(m) = l
	Thm* M:(IdLnkIdType), l:IdLnk, m:Msg(M). haslink(l; m)  Prop
IdLnk	Def IdLnk == IdId
	Thm* IdLnk  Type
es-locl	Def (e <loc e') == loc(e) = loc(e')  Id & (e < e')
Id	Def Id == Atom
	Thm* Id  Type
deq	Def EqDecider(T) == eq:TTx,y:T. x = y  (eq(x,y))
	Thm* T:Type. EqDecider(T)  Type
assert	Def b == if b True else False fi
	Thm* b:. b  Prop
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-causl	Def (e < e') Def == 1of(2of(2of(2of(2of(2of(2of(2of(2of(2of(2of(2of(2of(2of(2of(2of(2of( Def == 1of(es))))))))))))))))) Def == (e Def == ,e')
es-first	Def first(e) Def == 1of(2of(2of(2of(2of(2of(2of(2of(2of(2of(2of(2of(2of(2of(2of( Def == 1of(es))))))))))))))) Def == (e)
es-index	Def index(e) Def == 1of(2of(2of(2of(2of(2of(2of(2of(2of(2of(2of(2of(2of(2of(es)))))))))))))) Def == (e)
es-isrcv	Def isrcv(e) == isrcv(kind(e))
es-lnk	Def lnk(e) == lnk(kind(e))
es-loc	Def loc(e) == 1of(2of(2of(2of(2of(2of(2of(es)))))))(e)
es-pred	Def pred(e) Def == 1of(2of(2of(2of(2of(2of(2of(2of(2of(2of(2of(2of(2of(2of(2of(2of( Def == 1of(es)))))))))))))))) Def == (e)
es-sender	Def sender(e) Def == 1of(2of(2of(2of(2of(2of(2of(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-tag	Def tag(e) == tag(kind(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)
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
iff	Def P  Q == (P  Q) & (P  Q)
	Thm* A,B:Prop. (A  B)  Prop
int_seg	Def {i..j} == {k:| i  k < j }
	Thm* m,n:. {m..n}  Type
isrcv	Def isrcv(k) == isl(k)
	Thm* k:Knd. isrcv(k)
ldst	Def destination(l) == 1of(2of(l))
	Thm* l:IdLnk. destination(l)  Id
length	Def ||as|| == Case of as; nil  0 ; a.as'  ||as'||+1  (recursive)
	Thm* A:Type, l:A List. ||l||
	Thm* ||nil||
lnk	Def lnk(k) == 1of(outl(k))
	Thm* k:Knd. isrcv(k)  lnk(k)  IdLnk
lsrc	Def source(l) == 1of(l)
	Thm* l:IdLnk. source(l)  Id
strongwellfounded	Def SWellFounded(R(x;y)) == f:(T). x,y:T. R(x;y)  f(x)<f(y)
	Thm* T:Type, R:(TTType). SWellFounded(R(x,y))  Prop
not	Def A == A  False
	Thm* A:Prop. (A)  Prop
select	Def l[i] == hd(nth_tl(i;l))
	Thm* A:Type, l:A List, n:. 0n  n<||l||  l[n]  A
tagof	Def tag(k) == 2of(outl(k))
	Thm* k:Knd. isrcv(k)  tag(k)  Id
top	Def Top == Void given Void
	Thm* Top  Type
trans	Def Trans x,y:T. E(x;y) == a,b,c:T. E(a;b)  E(b;c)  E(a;c)
	Thm* T:Type, E:(TTProp). (Trans x,y:T. E(x,y))  Prop

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