Who Cites rel eq?
rel_eq	Def rel_eq(a;b) == eq_relname(a.name;b.name)termlist_eq(a.args;b.args)
	Thm* a,b:rel(). rel_eq(a;b)
rel_args	Def t.args == 2of(t)
	Thm* t:rel(). t.args Term List
termlist_eq	Def termlist_eq(a;b) == Case of a; nil Case of b; nil true ; x.xs false ; x.xs Case of b; nil false ; x'.xs' term_eq(x;x')termlist_eq(xs;xs') (recursive)
	Thm* a,b:Term List. termlist_eq(a;b)
rel_name	Def t.name == 1of(t)
	Thm* t:rel(). t.name relname()
eq_relname	Def eq_relname(a;b) == Case(a) Case eq(x) = > Case(b) Case eq(x') = > st_eq(x;x') Case x' = > false Default = > false Case x = > Case(b) Case eq(x') = > false Case x' = > x = x' Default = > false Default = > false
	Thm* a,b:relname(). eq_relname(a;b)
term_eq	Def term_eq(a;b) == Case(a) Case x;y = > Case(b) Case x';y' = > term_eq(x;x')term_eq(y;y') Case tree_leaf(x) = > false Default = > True Case tree_leaf(x) = > Case(b) Case x';y' = > false Case tree_leaf(x') = > (x=x') Default = > True Default = > True (recursive)
	Thm* a,b:Term. term_eq(a;b)
st_eq	Def st_eq(s1;s2) == Case(s1) Case a;b = > Case(s2) Case a';b' = > st_eq(a;a')st_eq(b;b') Default = > false Case tree_leaf(x) = > Case(s2) Case a';b' = > false Case tree_leaf(y) = > InjCase(x; x'. InjCase(y; y'. x' = y'; b. false); a. InjCase(y; y'. false; b. true)) Default = > false Default = > false (recursive)
	Thm* s1,s2:SimpleType. st_eq(s1;s2)
ts_eq	Def (a=b) == ts_case(a)var(v)= > ts_case(b)var(v')= > v = v'var'(x)= > falseopr(x)= > falsefvar(x)= > falsetrace(x)= > falseend_ts_case var'(p)= > ts_case(b)var(x)= > falsevar'(p')= > p = p'opr(x)= > falsefvar(x)= > falsetrace(x)= > falseend_ts_case opr(op)= > ts_case(b)var(x)= > falsevar'(x)= > falseopr(op')= > op = op'fvar(x)= > falsetrace(x)= > falseend_ts_case fvar(f)= > ts_case(b)var(x)= > falsevar'(x)= > falseopr(x)= > falsefvar(f')= > f = f'trace(x)= > falseend_ts_case trace(P)= > ts_case(b)var(x)= > falsevar'(x)= > falseopr(x)= > falsefvar(x)= > falsetrace(P')= > P = P'end_ts_case end_ts_case
	Thm* a,b:ts(). (a=b)
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
band	Def pq == if p q else false fi
	Thm* p,q:. (pq)
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
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
case_default	Def Default = > body(value,value) == body
case_relname_other	Def Case x = > body(x) cont(x1,z) == (x1.inr(x2) = > body(hd([x2 / tl(x1)])) cont(hd(x1),z))([x1])
case_relname_eq	Def Case eq(x) = > body(x) cont(x1,z) == InjCase(x1; x2. body(x2); _. cont(z,z))
case	Def Case(value) body == body(value,value)
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))
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))))
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))
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])
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_inr	Def inr(x) = > body(x) cont(value,contvalue) == InjCase(value; _. cont(contvalue,contvalue); x. body(x))
case_inl	Def inl(x) = > body(x) cont(value,contvalue) == InjCase(value; x. body(x); _. cont(contvalue,contvalue))
case_ts_var	Def Case ts_var(x) = > body(x) cont(x1,z) == InjCase(x1; x2. body(x2); _. cont(z,z))

Syntax:

rel_eq(a;b)

has structure:

rel_eq(a; b)

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