thus ( X misses Y implies for e being ExtReal holds
( not e in X or not e in Y ) ) by XBOOLE_0:3; :: thesis: ( ( for e being ExtReal holds
( not e in X or not e in Y ) ) implies X misses Y )
assume A1: for e being ExtReal holds
( not e in X or not e in Y ) ; :: thesis: X misses Y
assume X meets Y ; :: thesis: contradiction
then ex x being object st
( x in X & x in Y ) by XBOOLE_0:3;
hence contradiction by A1; :: thesis: verum