
theorem
  for K being add-associative right_zeroed right_complementable
     left-distributive non empty doubleLoopStr
  for a,b,c be Element of K holds (a - b)*c = a*c - b*c
proof
  let K be add-associative right_zeroed right_complementable left-distributive
  non empty doubleLoopStr;
  let y,z,x be Element of K;
  thus (y-z)*x = y*x+(-z)*x by Def3
    .= y*x -z*x by Th5;
end;
