set IT = DIFFERENCE A,B;
consider A1, A2 being Subset of U such that
A1:
( A1 c= A2 & A = Inter A1,A2 )
by U2;
consider B1, B2 being Subset of U such that
A2:
( B1 c= B2 & B = Inter B1,B2 )
by U2;
set LAB = A1 \ B2;
set UAB = A2 \ B1;
DIFFERENCE A,B = Inter (A1 \ B2),(A2 \ B1)
by LemmaC, A1, A2;
hence
DIFFERENCE A,B is IntervalSet of U
; verum