let I be set ; :: thesis: for X, Y being ManySortedSet of I holds X /\ Y misses X \+\ Y
let X, Y be ManySortedSet of I; :: thesis: X /\ Y misses X \+\ Y

now

let i be set ; :: thesis: ( i in I implies (X /\ Y) . i misses (X \+\ Y) . i )
assume i in I ; :: thesis: (X /\ Y) . i misses (X \+\ Y) . i
then ( (X /\ Y) . i = (X . i) /\ (Y . i) & (X \+\ Y) . i = (X . i) \+\ (Y . i) ) by Def8, Th4;
hence (X /\ Y) . i misses (X \+\ Y) . i by XBOOLE_1:103; :: thesis: verum

end;

hence X /\ Y misses X \+\ Y by Def11; :: thesis: verum