reserve N,M,K for ExtNat;
reserve X for ext-natural-membered set;

theorem
  for F, X being set st X in F & X is ext-natural-membered
  holds meet F is ext-natural-membered
proof
  let F, X be set;
  assume A1: X in F & X is ext-natural-membered;
  let x be object;
  assume x in meet F;
  then x in X by A1, SETFAM_1:def 1;
  hence thesis by A1;
end;
