
theorem SetFor10:
  for x1,x2,x3,x4,x5,x6,x7,x8,x9,x10 being object holds
    {x1,x2,x3,x4,x5,x6,x7,x8,x9,x10} =
       {x1,x2,x3,x4,x5} \/ {x6,x7,x8,x9,x10}
  proof
    let x1,x2,x3,x4,x5,x6,x7,x8,x9,x10 be object;
    thus {x1,x2,x3,x4,x5,x6,x7,x8,x9,x10} c=
       {x1,x2,x3,x4,x5} \/ {x6,x7,x8,x9,x10}
    proof
      let x be object;
      assume x in {x1,x2,x3,x4,x5,x6,x7,x8,x9,x10}; then
      x = x1 or x = x2 or x = x3 or x = x4 or x = x5 or
        x = x6 or x = x7 or x = x8 or x = x9 or x = x10
          by ENUMSET1:def 8; then
      x in {x1,x2,x3,x4,x5} or
        x in {x6,x7,x8,x9,x10} by ENUMSET1:def 3;
      hence thesis by XBOOLE_0:def 3;
    end;
    let x be object;
    assume x in {x1,x2,x3,x4,x5} \/ {x6,x7,x8,x9,x10}; then
    per cases by XBOOLE_0:def 3;
    suppose x in {x1,x2,x3,x4,x5}; then
      x = x1 or x = x2 or x = x3 or x = x4 or x = x5 by ENUMSET1:def 3;
      hence thesis by ENUMSET1:def 8;
    end;
    suppose x in {x6,x7,x8,x9,x10}; then
      x = x6 or x = x7 or x = x8 or x = x9 or x = x10 by ENUMSET1:def 3;
      hence thesis by ENUMSET1:def 8;
    end;
  end;
