reserve i, x, I for set,
  A, M for ManySortedSet of I,
  f for Function,
  F for ManySortedFunction of I;

theorem Th1:
  for X being non empty set for x, y being set st x c= y holds { t
  where t is Element of X : y c= t } c= { z where z is Element of X : x c= z }
proof
  let X be non empty set, x, y be set such that
A1: x c= y;
  let a be object;
   reconsider aa=a as set by TARSKI:1;
  assume a in { t where t is Element of X : y c= t };
  then
A2: ex b be Element of X st b = a & y c= b;
  then x c= aa by A1;
  hence thesis by A2;
end;
