for M being non limit_cardinal Aleph
for I being Ideal of M st I is_complete_with M & Frechet_Ideal M c= I holds
ex S being Subset-Family of M st
( card S = M & ( for X1 being set st X1 in S holds
not X1 in I ) & ( for X1, X2 being set st X1 in S & X2 in S & X1 <> X2 holds
X1 misses X2 ) )