let I be set ; :: thesis: for X, Y being ManySortedSet of I holds X (\) Y c= X
let X, Y be ManySortedSet of I; :: thesis: X (\) Y c= X

now :: thesis: for i being object st i in I holds
(X (\) Y) . i c= X . i

let i be object ; :: thesis: ( i in I implies (X (\) Y) . i c= X . i )
assume A1: i in I ; :: thesis: (X (\) Y) . i c= X . i
(X . i) \ (Y . i) c= X . i ;
hence (X (\) Y) . i c= X . i by A1, Def6; :: thesis: verum

end;

hence X (\) Y c= X ; :: thesis: verum