set IT = INTERSECTION 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 /\ B1;
set UAB = A2 /\ B2;
INTERSECTION A,B = Inter (A1 /\ B1),(A2 /\ B2) by LemmaA, A1, A2;
hence INTERSECTION A,B is IntervalSet of U ; :: thesis: verum