defpred S_{1}[ object ] means ex B being MSSubset of U0 st

( B in SubSort A & $1 = B . s );

for X1, X2 being set st ( for x being object holds

( x in X1 iff S_{1}[x] ) ) & ( for x being object holds

( x in X2 iff S_{1}[x] ) ) holds

X1 = X2 from XBOOLE_0:sch 3();

hence for b_{1}, b_{2} being set st ( for x being object holds

( x in b_{1} iff ex B being MSSubset of U0 st

( B in SubSort A & x = B . s ) ) ) & ( for x being object holds

( x in b_{2} iff ex B being MSSubset of U0 st

( B in SubSort A & x = B . s ) ) ) holds

b_{1} = b_{2}
; :: thesis: verum

( B in SubSort A & $1 = B . s );

for X1, X2 being set st ( for x being object holds

( x in X1 iff S

( x in X2 iff S

X1 = X2 from XBOOLE_0:sch 3();

hence for b

( x in b

( B in SubSort A & x = B . s ) ) ) & ( for x being object holds

( x in b

( B in SubSort A & x = B . s ) ) ) holds

b