reserve X for BCK-algebra;
reserve x,y for Element of X;
reserve IT for non empty Subset of X;

theorem Th2:
  for X being BCK-algebra holds for x,y being Element of X holds x\
  (x\y) <= y & x\(x\y) <= x
proof
  let X be BCK-algebra;
  let x,y be Element of X;
A1: 0.X\(x\y) = (x\y)` .= 0.X by BCIALG_1:def 8;
  ((x\(x\y))\(0.X\(x\y)))\(x\0.X)=0.X by BCIALG_1:def 3;
  then ((x\(x\y))\0.X)\x = 0.X by A1,BCIALG_1:2;
  then (x\(x\y))\y = 0.X & (x\(x\y))\x = 0.X by BCIALG_1:1,2;
  hence thesis;
end;
