for A being Subset of (TOP-REAL 3)
for B being non empty convex Subset of (TOP-REAL 2)
for r being Real
for x being Element of (TOP-REAL 3) st A = { x where x is Element of (TOP-REAL 3) : ( |[(x `1),(x `2)]| in B & x `3 = r ) } holds
( not A is empty & A is convex )