theorem
  B <> {} & (for x st x in B holds f.x [= g.x) implies FinMeet(B,f) [=
  FinMeet(B,g)
proof
  assume that
A1: B <> {} and
A2: for x st x in B holds f.x [= g.x;
  now
    let x;
    assume
A3: x in B;
    then f.x [= g.x by A2;
    hence FinMeet(B,f) [= g.x by A3,Th41;
  end;
  hence thesis by A1,Th46;
end;
