|  | Who Cites lbls  member? | 
|  | 
| lbls_member | Def x  ls == reduce(  a,b. x =  a   b;false  ;ls) | 
 | |  | Thm*  x:Label, ls:Label List. x  ls    | 
|  | 
| eq_lbl | Def l1 =  l2
 == Case(l1)
 Case ptn_atom(x) = > 
 Case(l2)
 Case ptn_atom(y) = > 
 x=  y  Atom
 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=  y  Atom
 Default = >  false  Case ptn_pr( < x, y > ) = > 
 Case(l2)
 Case ptn_pr( < u, v > ) = > 
 x =  u   y =  v
 Default = >  false  Default = >  false  (recursive) | 
 | |  | Thm*  l1,l2:Pattern. l1 =  l2    | 
|  | 
| bor | Def p   q == if p  true  else q fi | 
 | |  | Thm*  p,q:  . (p   q)    | 
|  | 
| 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:(A   B   B), k:B, as:A List. reduce(f;k;as)  B | 
|  | 
| case_default | Def Default = >  body(value,value) == body | 
|  | 
| band | Def p   q == if p  q else false  fi | 
 | |  | Thm*  p,q:  . (p   q)    | 
|  | 
| 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=  y  Atom == if x=y  Atom  true  ; false  fi | 
 | |  | Thm*  x,y:Atom. x=  y  Atom    | 
|  | 
| 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)) | 
|  | 
| 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)) |