
theorem
  for x,y be Element of BOOLEAN*
  st x in rng Nat2BL & y in rng Nat2BL
  holds x+y =y+x
  proof
    let x,y be Element of BOOLEAN*;
    assume AS:x in rng Nat2BL & y in rng Nat2BL; then
    consider n be Element of NAT such that
    A1: x =Nat2BL.n by FUNCT_2:113;
    consider m be Element of NAT such that
    A2: y =Nat2BL.m by AS,FUNCT_2:113;
    thus x+y = Nat2BL.(n+m) by A1,A2,LM100
    .=y+x by A1,A2,LM100;
  end;
