for A1, A2 being non empty set
for B1, B2 being set st A1 c= A2 & B1 c= B2 holds
ex F being Function of (thin_cylinders (A1,B1)),(thin_cylinders (A2,B2)) st
for x being set st x in thin_cylinders (A1,B1) holds
ex Bo being Subset of B1 ex yo1 being Function of Bo,A1 ex yo2 being Function of Bo,A2 st
( Bo is finite & yo1 = yo2 & x = cylinder0 (A1,B1,Bo,yo1) & F . x = cylinder0 (A2,B2,Bo,yo2) )