
theorem
  for D being non empty set, S being non empty Subset of D, f1,f2 being
  BinOp of D, g1,g2 being BinOp of S st g1 = f1||S & g2 = f2||S holds f1
  is_distributive_wrt f2 implies g1 is_distributive_wrt g2
proof
  let D be non empty set, S be non empty Subset of D, f1,f2 be BinOp of D;
  let g1,g2 be BinOp of S;
  assume g1 = f1||S & g2 = f2||S & f1 is_left_distributive_wrt f2 & f1
  is_right_distributive_wrt f2;
  hence g1 is_left_distributive_wrt g2 & g1 is_right_distributive_wrt g2 by Th3
;
end;
