defpred S_{1}[ object ] means ex W being strict Subspace of V st

( W = $1 & dim W = n );

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 W being strict Subspace of V st

( W = x & dim W = n ) ) ) & ( for x being object holds

( x in b_{2} iff ex W being strict Subspace of V st

( W = x & dim W = n ) ) ) holds

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

( W = $1 & dim W = n );

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

( W = x & dim W = n ) ) ) & ( for x being object holds

( x in b

( W = x & dim W = n ) ) ) holds

b