theorem Th38:
  a in X implies a [= "\/"(X,C) & "/\"(X,C) [= a
proof
  assume
A1: a in X;
  X is_less_than "\/"(X,C) by Def21;
  hence a [= "\/"(X,C) by A1;
  {b: b is_less_than X} is_less_than a
  proof
    let c;
    assume c in {b: b is_less_than X};
    then ex b st c = b & b is_less_than X;
    hence c [= a by A1;
  end;
  hence thesis by Def21;
end;
