set IT = DIFFERENCE (A,B);
consider A1, A2 being Subset of U such that
A1:
( A1 c= A2 & A = Inter (A1,A2) )
by Th11;
consider B1, B2 being Subset of U such that
A2:
( B1 c= B2 & B = Inter (B1,B2) )
by Th11;
set LAB = A1 \ B2;
set UAB = A2 \ B1;
DIFFERENCE (A,B) = Inter ((A1 \ B2),(A2 \ B1))
by Th39, A1, A2;
hence
DIFFERENCE (A,B) is IntervalSet of U
; verum