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Specification remtau
enrich
   option, 
   stream
with
   functions 
       . ! : ('a → Option('e)) → Stream('a) → Stream('e);
       . ! : ('a → Option('e)) → List('a) → List('e);
       . + . : Option('e) × Stream('e) → Stream('e);
   
   variables 
       α : Stream('a);
       β : Stream('e);
       al : List('a);
       el : List('e);
       a : 'a;
       e : 'e;
       af : Nat → 'a;
       ef : Nat → 'e;
       m : Nat;
       n : Nat;
       oe : Option('e);
       ext : 'a → Option('e);
   
   
   axioms 
      addopt: oe + β = (oe = None ⊃ [];⌜oe.get '⌝ ) + β;
      used for: s, ls;
      
      remtau-empty: ext !([]) = [];
      used for: s, ls;
      
      remtau-cons: ext !(⌜a '⌝  + α) = ext(a) + ext !(α);
      used for: s, ls;
      
      remtau-alltau: (∀ n. ⌜n⌝  < # α → ext(α[n]) = None) → ext !(α) = [];
      
      finremtau-def: ext !(⌜al⌝ ) = ⌜ext !(al)⌝ ;
      used for: s, ls;
   
   
end enrich