let x1, x2, x3, x4, x5, x6 be set ; :: thesis: {x1,x2,x3,x4,x5,x6} = {x1,x3,x6} \/ {x2,x4,x5}
thus {x1,x2,x3,x4,x5,x6} c= {x1,x3,x6} \/ {x2,x4,x5} :: according to XBOOLE_0:def 10 :: thesis: {x1,x3,x6} \/ {x2,x4,x5} c= {x1,x2,x3,x4,x5,x6}

proof

let x be object ; :: according to TARSKI:def 3 :: thesis: ( not x in {x1,x2,x3,x4,x5,x6} or x in {x1,x3,x6} \/ {x2,x4,x5} )
assume x in {x1,x2,x3,x4,x5,x6} ; :: thesis: x in {x1,x3,x6} \/ {x2,x4,x5}
then ( x = x1 or x = x2 or x = x3 or x = x4 or x = x5 or x = x6 ) by ENUMSET1:def 4;
then ( x in {x1,x3,x6} or x in {x2,x4,x5} ) by ENUMSET1:def 1;
hence x in {x1,x3,x6} \/ {x2,x4,x5} by XBOOLE_0:def 3; :: thesis: verum

end;

let x be object ; :: according to TARSKI:def 3 :: thesis: ( not x in {x1,x3,x6} \/ {x2,x4,x5} or x in {x1,x2,x3,x4,x5,x6} )
assume x in {x1,x3,x6} \/ {x2,x4,x5} ; :: thesis: x in {x1,x2,x3,x4,x5,x6}
then ( x in {x1,x3,x6} or x in {x2,x4,x5} ) by XBOOLE_0:def 3;
then ( x = x1 or x = x3 or x = x6 or x = x2 or x = x4 or x = x5 ) by ENUMSET1:def 1;
hence x in {x1,x2,x3,x4,x5,x6} by ENUMSET1:def 4; :: thesis: verum