|  | Who Cites dec  mng? | 
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| dec_mng | Def [[d]] rho == Case(d) Case x : s = >   x:[[s]] rho | 
 | |  | Thm*  rho:Decl, d:dec(). [[d]] rho  Decl | 
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| st_mng | Def [[s]] rho == t_iterate(st_lift(rho);  x,y. x   y;s) | 
 | |  | Thm*  rho:Decl, s:SimpleType. [[s]] rho  Type | 
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| dbase | Def  x:y(a) == if a =  x  y else Top fi | 
 | |  | Thm*  x:Label, y:Type.  x:y  Decl | 
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| case_mk_dec | Def Case lbl : typ = >  body(lbl;typ)(x,z) == x/x2,x1. body(x2;x1) | 
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| 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:(E   A), n:(A   A   A), t:Tree(E). t_iterate(l;n;t)  A | 
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| 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    | 
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| case | Def Case(value) body == body(value,value) | 
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| st_lift | Def st_lift(rho)(x) == InjCase(x; x'. rho(x'); a. Top) | 
 | |  | Thm*  rho:(Label   Type). st_lift(rho)  (Label+Unit)   Type | 
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| top | Def Top == Void given Void | 
 | |  | Thm* Top  Type | 
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| case_default | Def Default = >  body(value,value) == body | 
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| case_tree_leaf | Def Case tree_leaf(x) = >  body(x) cont(x1,z) == InjCase(x1; x2. body(x2); _. cont(z,z)) | 
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| 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)) | 
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| band | Def p   q == if p  q else false  fi | 
 | |  | Thm*  p,q:  . (p   q)    | 
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| 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)))) | 
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| eq_atom | Def x=  y  Atom == if x=y  Atom  true  ; false  fi | 
 | |  | Thm*  x,y:Atom. x=  y  Atom    | 
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| 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]) | 
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| eq_int | Def i=  j == if i=j  true  ; false  fi | 
 | |  | Thm*  i,j:  . (i=  j)    | 
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| 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]) | 
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| case_ptn_atom | Def Case ptn_atom(x) = >  body(x) cont(x1,z) == InjCase(x1; x2. body(x2); _. cont(z,z)) | 
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| 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 | 
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| tl | Def tl(l) == Case of l; nil  nil ; h.t  t | 
 | |  | Thm*  A:Type, l:A List. tl(l)  A List | 
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| case_inl | Def inl(x) = >  body(x) cont(value,contvalue) == InjCase(value; x. body(x); _. cont(contvalue,contvalue)) | 
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| case_inr | Def inr(x) = >  body(x) cont(value,contvalue) == InjCase(value; _. cont(contvalue,contvalue); x. body(x)) |