theorem Th76:
  A c= B implies union A c= union B
proof
  assume
A1: A c= B;
  let x;
  assume x in union A;
  then consider Y such that
A2: x in Y and
A3: Y in A by TARSKI:def 4;
  Y in B by A1,A3;
  hence thesis by A2,TARSKI:def 4;
end;
