
theorem Th36:
  for x,b being non pair set holds x in the carrier of BitCompStr(
x,b) & b in the carrier of BitCompStr(x,b) & [<*x,b*>,xor2a] in the carrier of
  BitCompStr(x,b) & [<*x,b*>,and2a] in the carrier of BitCompStr(x,b)
proof
  let x,b be non pair set;
  set p = <*x,b*>;
  set S1 = CompStr(x,b);
  set S2 = IncrementStr(x,b);
A1: [p,xor2a] in the carrier of S1 & [p,and2a] in the carrier of S2 by
FACIRC_1:43;
  x in the carrier of S1 & b in the carrier of S1 by FACIRC_1:43;
  hence thesis by A1,FACIRC_1:20;
end;
