reserve x,y,c for set;

theorem
  for S being non empty ManySortedSign st S = BitSubtracterWithBorrowStr
  (x, y, c ) holds x in the carrier of S & y in the carrier of S & c in the
  carrier of S
proof
  set S1 = 2GatesCircStr(x,y,c, 'xor');
  let S be non empty ManySortedSign;
A1: x in the carrier of S1 & y in the carrier of S1 by FACIRC_1:60;
A2: c in the carrier of S1 by FACIRC_1:60;
  assume S = BitSubtracterWithBorrowStr(x,y,c);
  hence thesis by A1,A2,FACIRC_1:20;
end;
