Who Cites totalorder?
totalorder	Def totalorder(E)(tr) == p,q:Label. agree_on_common(|MS(E)|;map(msg(E);tr delivered at p);map(msg(E);tr delivered at q))
	Thm* E:EventStruct. totalorder(E) TraceProperty(E)
deliveries_at	Def tr delivered at p == filter(e.is-send(E)(e)loc(E)(e) = p;tr)
	Thm* E:EventStruct, p:Label, tr:|E| List. tr delivered at p |E| List
event_msg	Def msg(E) == 1of(2of(2of(E)))
	Thm* E:EventStruct. msg(E) |E||MS(E)|
map	Def map(f;as) == Case of as; nil nil ; a.as' [(f(a)) / map(f;as')] (recursive)
	Thm* A,B:Type, f:(AB), l:A List. map(f;l) B List
	Thm* A,B:Type, f:(AB), l:A List. map(f;l) B List
event_msg_str	Def MS(E) == 1of(2of(E))
	Thm* E:EventStruct. MS(E) MessageStruct
carrier	Def |S| == 1of(S)
	Thm* S:Structure. |S| Type
agree_on_common	Def agree_on_common(T;as;bs) == Case of as nil True a.as' Case of bs nil True b.bs' (a bs) & agree_on_common(T;as';bs) (b as) & agree_on_common(T;as;bs') a = b T & agree_on_common(T;as';bs') (recursive)
	Thm* T:Type, as,bs:T List. agree_on_common(T;as;bs) Prop
lbl	Def Label == {p:Pattern| ground_ptn(p) }
	Thm* Label Type
event_loc	Def loc(E) == 1of(2of(2of(2of(E))))
	Thm* E:EventStruct. loc(E) |E|Label
eq_lbl	Def l1 = l2 == Case(l1) Case ptn_atom(x) = > Case(l2) Case ptn_atom(y) = > x=yAtom Default = > false Case ptn_int(x) = > Case(l2) Case ptn_int(y) = > x=y Default = > false Case ptn_var(x) = > Case(l2) Case ptn_var(y) = > x=yAtom Default = > false Case ptn_pr( < x, y > ) = > Case(l2) Case ptn_pr( < u, v > ) = > x = uy = v Default = > false Default = > false (recursive)
	Thm* l1,l2:Pattern. l1 = l2
event_is_snd	Def is-send(E) == 1of(2of(2of(2of(2of(E)))))
	Thm* E:EventStruct. is-send(E) |E|
l_member	Def (x l) == i:. i < ||l|| & x = l[i] T
	Thm* T:Type, x:T, l:T List. (x l) Prop
select	Def l[i] == hd(nth_tl(i;l))
	Thm* A:Type, l:A List, n:. 0n n < ||l|| l[n] A
nth_tl	Def nth_tl(n;as) == if n0 as else nth_tl(n-1;tl(as)) fi (recursive)
	Thm* A:Type, as:A List, i:. nth_tl(i;as) A List
le_int	Def ij == j < i
	Thm* i,j:. (ij)
bnot	Def b == if b false else true fi
	Thm* b:. b
ground_ptn	Def ground_ptn(p) == Case(p) Case ptn_var(v) = > false Case ptn_pr( < x, y > ) = > ground_ptn(x)ground_ptn(y) Default = > true (recursive)
	Thm* p:Pattern. ground_ptn(p)
band	Def pq == if p q else false fi
	Thm* p,q:. (pq)
filter	Def filter(P;l) == reduce(a,v. if P(a) [a / v] else v fi;nil;l)
	Thm* T:Type, P:(T), l:T List. filter(P;l) T List
pi2	Def 2of(t) == t.2
	Thm* A:Type, B:(AType), p:(a:AB(a)). 2of(p) B(1of(p))
pi1	Def 1of(t) == t.1
	Thm* A:Type, B:(AType), p:(a:AB(a)). 1of(p) A
nat	Def == {i:| 0i }
	Thm* Type
le	Def AB == B < A
	Thm* i,j:. (ij) Prop
not	Def A == A False
	Thm* A:Prop. (A) Prop
assert	Def b == if b True else False fi
	Thm* b:. b Prop
ptn	Def Pattern == rec(T.ptn_con(T))
	Thm* Pattern Type
case_default	Def Default = > body(value,value) == body
case_lbl_pair	Def Case ptn_pr( < x, y > ) = > body(x;y) cont(x1,z) == InjCase(x1; _. cont(z,z); x2. InjCase(x2; _. cont(z,z); x2@0. InjCase(x2@0; _. cont(z,z); x2@1. x2@1/x3,x2@2. body(x3;x2@2))))
case	Def Case(value) body == body(value,value)
eq_atom	Def x=yAtom == if x=yAtomtrue; false fi
	Thm* x,y:Atom. x=yAtom
case_ptn_var	Def Case ptn_var(x) = > body(x) cont(x1,z) == (x1.inr(x2) = > (x1.inr(x2) = > (x1.inl(x2) = > body(hd([x2 / tl(x1)])) cont(hd(x1),z))([x2 / tl(x1)]) cont (hd(x1) ,z)) ([x2 / tl(x1)]) cont (hd(x1) ,z)) ([x1])
eq_int	Def i=j == if i=j true ; false fi
	Thm* i,j:. (i=j)
case_ptn_int	Def Case ptn_int(x) = > body(x) cont(x1,z) == (x1.inr(x2) = > (x1.inl(x2) = > body(hd([x2 / tl(x1)])) cont(hd(x1),z))([x2 / tl(x1)]) cont (hd(x1) ,z)) ([x1])
case_ptn_atom	Def Case ptn_atom(x) = > body(x) cont(x1,z) == InjCase(x1; x2. body(x2); _. cont(z,z))
reduce	Def reduce(f;k;as) == Case of as; nil k ; a.as' f(a,reduce(f;k;as')) (recursive)
	Thm* A,B:Type, f:(ABB), k:B, as:A List. reduce(f;k;as) B
length	Def ||as|| == Case of as; nil 0 ; a.as' ||as'||+1 (recursive)
	Thm* A:Type, l:A List. ||l||
	Thm* ||nil||
ptn_con	Def ptn_con(T) == Atom++Atom+(TT)
	Thm* T:Type. ptn_con(T) Type
hd	Def hd(l) == Case of l; nil "?" ; h.t h
	Thm* A:Type, l:A List. ||l||1 hd(l) A
	Thm* A:Type, l:A List. hd(l) A
tl	Def tl(l) == Case of l; nil nil ; h.t t
	Thm* A:Type, l:A List. tl(l) A List
case_inl	Def inl(x) = > body(x) cont(value,contvalue) == InjCase(value; x. body(x); _. cont(contvalue,contvalue))
case_inr	Def inr(x) = > body(x) cont(value,contvalue) == InjCase(value; _. cont(contvalue,contvalue); x. body(x))
lt_int	Def i < j == if i < j true ; false fi
	Thm* i,j:. (i < j)

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