for F being Function
for i1, i2, xi1 being set
for Ai2 being Subset of (F . i2) st product F <> {} & xi1 in F . i1 & i1 in dom F & i2 in dom F & Ai2 <> F . i2 holds
( (proj (F,i1)) " {xi1} c= (proj (F,i2)) " Ai2 iff ( i1 = i2 & xi1 in Ai2 ) )