
theorem Th37:
  for x,b being non pair set holds the carrier of BitCompStr(x,b)
  = {x,b} \/ {[<*x,b*>,xor2a],[<*x,b*>,and2a]}
proof
  let x,b be non pair set;
  set p = <*x,b*>;
  set S1 = CompStr(x,b);
  set S2 = IncrementStr(x,b);
  the carrier of S1 = {x,b} \/ {[p,xor2a]} & the carrier of S2 = {x,b} \/
  {[p, and2a]} by Th27,Th31;
  then
  the carrier of BitCompStr(x,b) = ({x,b} \/ {[p,xor2a]}) \/ ({x,b} \/ {[p
  ,and2a]}) by CIRCCOMB:def 2
    .= {x,b} \/ ({x,b} \/ {[p,xor2a]}) \/ {[p,and2a]} by XBOOLE_1:4
    .= ({x,b} \/ {x,b}) \/ {[p,xor2a]} \/ {[p,and2a]} by XBOOLE_1:4
    .= {x,b} \/ ({[p,xor2a]} \/ {[p,and2a]}) by XBOOLE_1:4
    .= {x,b} \/ {[p,xor2a],[p,and2a]} by ENUMSET1:1;
  hence thesis;
end;
