
theorem Th42:
  for L being non empty RelStr, Y being Subset of L, x being
  Element of L holds {x} "/\" Y = {x "/\" y where y is Element of L: y in Y}
proof
  let L be non empty RelStr, Y be Subset of L, x be Element of L;
  thus {x} "/\" Y c= {x "/\" y where y is Element of L: y in Y}
  proof
    let q be object;
    assume q in {x} "/\" Y;
    then consider s, t being Element of L such that
A1: q = s "/\" t and
A2: s in {x} and
A3: t in Y;
    s = x by A2,TARSKI:def 1;
    hence thesis by A1,A3;
  end;
  let q be object;
  assume q in {x "/\" y where y is Element of L: y in Y};
  then
A4: ex y being Element of L st q = x "/\" y & y in Y;
  x in {x} by TARSKI:def 1;
  hence thesis by A4;
end;
