
theorem Th87:
for X be non empty set, F be Field_Subset of X, K be Subset-Family of X
 st K is MonotoneClass of X & F c= K
  holds sigma F = monotoneclass F & sigma F c= K
proof
   let X be non empty set, F be Field_Subset of X, K be Subset-Family of X;
   assume that
A1: K is MonotoneClass of X and
A2: F c= K;
   thus sigma F = monotoneclass F by PROB_3:73;
   hence sigma F c= K by A1,A2,PROB_3:def 11;
end;
