Who Cites rel addprime?
rel_addprime	Def (r)' == mk_rel(r.name, map(t.(t)';r.args))
	Thm* r:rel(). (r)' rel()
addprime	Def (t)' == term_iterate(x.x';x.x';op.op;f.f;P.trace(P);a,b. a b;t)
	Thm* t:Term. (t)' Term
rel_free_vars	Def rel_free_vars(r) == reduce(t,vs. term_free_vars(t) @ vs;nil;r.args)
	Thm* r:rel(). rel_free_vars(r) Label List
term_free_vars	Def term_free_vars(t) == term_iterate(f.nil;f.nil;f.nil;v.[v];P.nil;x,y. x @ y;t)
	Thm* t:Term. term_free_vars(t) Label List
append	Def as @ bs == Case of as; nil bs ; a.as' [a / (as' @ bs)] (recursive)
	Thm* T:Type, as,bs:T List. (as @ bs) T List
rel	Def rel() == relname()(Term List)
	Thm* rel() Type
term	Def Term == Tree(ts())
	Thm* Term Type
relname	Def relname() == SimpleType+Label
	Thm* relname() Type
ts	Def ts() == Label+Label+Label+Label+Label
	Thm* ts() Type
st	Def SimpleType == Tree(Label+Unit)
	Thm* SimpleType Type
lbl	Def Label == {p:Pattern| ground_ptn(p) }
	Thm* Label Type
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
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
rel_args	Def t.args == 2of(t)
	Thm* t:rel(). t.args Term List
tapp	Def t1 t2 == tree_node( < t1, t2 > )
	Thm* t1,t2:Term. t1 t2 Term
ttrace	Def trace(l) == tree_leaf(ts_trace(l))
	Thm* l:Label. trace(l) Term
tfvar	Def l == tree_leaf(ts_fvar(l))
	Thm* l:Label. l Term
topr	Def f == tree_leaf(ts_op(f))
	Thm* f:Label. f Term
tpvar	Def l' == tree_leaf(ts_pvar(l))
	Thm* l:Label. l' Term
term_iterate	Def term_iterate(v;p;op;f;tr;a;t) == t_iterate(x.ts_case(x)var(a)= > v(a)var'(b)= > p(b)opr(c)= > op(c)fvar(d)= > f(d)trace(P)= > tr(P)end_ts_case ;a;t)
	Thm* A:Type, v,op,f,p,tr:(LabelA), a:(AAA), t:Term. term_iterate(v;p;op;f;tr;a;t) A
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
rel_name	Def t.name == 1of(t)
	Thm* t:rel(). t.name relname()
mk_rel	Def mk_rel(name, args) == < name,args >
	Thm* name:relname(), args:Term List. mk_rel(name, args) rel()
pi2	Def 2of(t) == t.2
	Thm* A:Type, B:(AType), p:(a:AB(a)). 2of(p) B(1of(p))
node	Def tree_node( < x, y > ) == tree_node( < x,y > )
	Thm* E:Type, x,y:Tree(E). tree_node( < x, y > ) Tree(E)
ts_trace	Def ts_trace(x) == inr(inr(inr(inr(x))))
	Thm* x:Label. ts_trace(x) ts()
tree_leaf	Def tree_leaf(x) == inl(x)
	Thm* E,T:Type, x:E. tree_leaf(x) tree_con(E;T)
	Thm* E:Type, x:E. tree_leaf(x) Tree(E)
ts_fvar	Def ts_fvar(x) == inr(inr(inr(inl(x))))
	Thm* x:Label. ts_fvar(x) ts()
ts_op	Def ts_op(x) == inr(inr(inl(x)))
	Thm* x:Label. ts_op(x) ts()
ts_pvar	Def ts_pvar(x) == inr(inl(x))
	Thm* x:Label. ts_pvar(x) ts()
ts_case	Def ts_case(x)var(a)= > v(a)var'(b)= > p(b)opr(f)= > op(f)fvar(x)= > f(x)trace(P)= > t(P)end_ts_case == Case(x) Case ts_var(a) = > v(a) Case ts_pvar(b) = > p(b) Case ts_op(f) = > op(f) Case ts_fvar(x) = > f(x) Case ts_trace(P) = > t(P) Default = >
	Thm* A:Type, v,op,f,p,t:(LabelA), x:ts(). ts_case(x)var(a)= > v(a)var'(b)= > p(b)opr(f)= > op(f)fvar(y)= > f(y)trace(P)= > t(P)end_ts_case A
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
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
tree	Def Tree(E) == rec(T.tree_con(E;T))
	Thm* E:Type. Tree(E) Type
pi1	Def 1of(t) == t.1
	Thm* A:Type, B:(AType), p:(a:AB(a)). 1of(p) A
tree_node	Def tree_node(x) == inr(x)
	Thm* E,T:Type, x:(TT). tree_node(x) tree_con(E;T)
	Thm* E:Type, x,y:Tree(E). tree_node( < x,y > ) Tree(E)
case_ts_trace	Def Case ts_trace(x) = > body(x) cont(x1,z) == (x1.inr(x2) = > (x1.inr(x2) = > (x1.inr(x2) = > (x1.inr(x2) = > body(hd([x2 / tl(x1)])) cont(hd(x1),z))([x2 / tl(x1)]) cont(hd(x1),z))([x2 / tl(x1)]) cont(hd(x1),z))([x2 / tl(x1)]) cont(hd(x1),z))([x1])
case_ts_fvar	Def Case ts_fvar(x) = > body(x) cont(x1,z) == (x1.inr(x2) = > (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))([x2 / tl(x1)]) cont(hd(x1),z))([x1])
case_ts_op	Def Case ts_op(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_ts_pvar	Def Case ts_pvar(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_ts_var	Def Case ts_var(x) = > body(x) cont(x1,z) == InjCase(x1; x2. body(x2); _. cont(z,z))
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))
tree_con	Def tree_con(E;T) == E+(TT)
	Thm* E,T:Type. tree_con(E;T) Type

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