
theorem
for X be non empty set, F be Field_Subset of X, L be SetSequence of X
 st rng L is MonotoneClass of X & F c= rng L
 holds sigma F = monotoneclass F & sigma F c= rng L
proof
   let X be non empty set, F be Field_Subset of X, L be SetSequence of X;
   assume
A1: rng L is MonotoneClass of X & F c= rng L;
   thus sigma F = monotoneclass F by PROB_3:73;
   hence sigma F c= rng L by A1,PROB_3:def 11;
end;
