
theorem
  for V being non empty RLSStruct, M,N being Subset of V st M is cone &
  N is cone holds M /\ N is cone
proof
  let V be non empty RLSStruct;
  let M,N be Subset of V;
  assume that
A1: M is cone and
A2: N is cone;
  let r be Real;
  let v be VECTOR of V;
  assume that
A3: r > 0 and
A4: v in M /\ N;
  v in N by A4,XBOOLE_0:def 4;
  then
A5: r*v in N by A2,A3;
  v in M by A4,XBOOLE_0:def 4;
  then r*v in M by A1,A3;
  hence thesis by A5,XBOOLE_0:def 4;
end;
