Who Cites pred?
pred	Def Fmla == Collection(rel())
	Thm* Fmla{i} Type{i'}
col	Def Collection(T) == TProp
	Thm* T:Type{i'}. Collection{i}(T) Type{i'}
dec	Def dec() == LabelSimpleType
	Thm* dec() Type
decl	Def Decl == LabelType
	Thm* Decl{i} Type{i'}
sig	Def sig() == (LabelSimpleType)(Label(SimpleType List))
	Thm* sig() Type
sig_mng	Def [[s]] rho == < op.[[s.fun(op)]] rho,R.[[s.rel(R)]] rho >
	Thm* s:sig(), rho:Decl{i}. sig_mng{i:l}(s; rho) Decl{i}Decl{i'}
rel	Def rel() == relname()(Term List)
	Thm* rel() Type
relname	Def relname() == SimpleType+Label
	Thm* relname() Type
st	Def SimpleType == Tree(Label+Unit)
	Thm* SimpleType Type
subtype	Def S T == x:S. x T
term	Def Term == Tree(ts())
	Thm* Term Type
ts	Def ts() == Label+Label+Label+Label+Label
	Thm* ts() Type
lbl	Def Label == {p:Pattern| ground_ptn(p) }
	Thm* Label Type
sig_rel	Def t.rel == 2of(t)
	Thm* t:sig(). t.rel Label(SimpleType List)
st_list_mng	Def [[l]] rho == reduce(s,m. [[s]] rhom;Prop;l)
	Thm* l:SimpleType List, rho:Decl{i}. [[l]] rho{i} Type{i'}
sig_fun	Def t.fun == 1of(t)
	Thm* t:sig(). t.fun LabelSimpleType
st_mng	Def [[s]] rho == t_iterate(st_lift(rho);x,y. xy;s)
	Thm* rho:Decl, s:SimpleType. [[s]] rho Type
tree	Def Tree(E) == rec(T.tree_con(E;T))
	Thm* E:Type. Tree(E) Type
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)
assert	Def b == if b True else False fi
	Thm* b:. b Prop
ptn	Def Pattern == rec(T.ptn_con(T))
	Thm* Pattern Type
pi2	Def 2of(t) == t.2
	Thm* A:Type, B:(AType), p:(a:AB(a)). 2of(p) B(1of(p))
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
pi1	Def 1of(t) == t.1
	Thm* A:Type, B:(AType), p:(a:AB(a)). 1of(p) A
st_lift	Def st_lift(rho)(x) == InjCase(x; x'. rho(x'); a. Top)
	Thm* rho:(LabelType). st_lift(rho) (Label+Unit)Type
t_iterate	Def t_iterate(l;n;t) == Case(t) Case x;y = > n(t_iterate(l;n;x),t_iterate(l;n;y)) Case tree_leaf(x) = > l(x) Default = > True (recursive)
	Thm* E,A:Type, l:(EA), n:(AAA), t:Tree(E). t_iterate(l;n;t) A
tree_con	Def tree_con(E;T) == E+(TT)
	Thm* E,T:Type. tree_con(E;T) Type
case_default	Def Default = > body(value,value) == body
band	Def pq == if p q else false fi
	Thm* p,q:. (pq)
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_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])
case	Def Case(value) body == body(value,value)
ptn_con	Def ptn_con(T) == Atom++Atom+(TT)
	Thm* T:Type. ptn_con(T) Type
top	Def Top == Void given Void
	Thm* Top Type
case_tree_leaf	Def Case tree_leaf(x) = > body(x) cont(x1,z) == InjCase(x1; x2. body(x2); _. cont(z,z))
case_node	Def Case x;y = > body(x;y) cont(x1,z) == InjCase(x1; _. cont(z,z); x2. x2/x3,x2@0. body(x3;x2@0))
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))

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