theorem Th41:
  a in X & a is_less_than X implies "/\"(X,C) = a
proof
  assume that
A1: a in X and
A2: a is_less_than X;
A3: "/\"(X,C) [= a by A1,Th38;
  a [= "/\"(X,C) by A2,Th39;
  hence thesis by A3,LATTICES:8;
end;
