for seq, seq1 being Real_Sequence holds
( ( seq is increasing & seq1 is constant implies seq + seq1 is increasing ) & ( seq is decreasing & seq1 is constant implies seq + seq1 is decreasing ) & ( seq is non-decreasing & seq1 is constant implies seq + seq1 is non-decreasing ) & ( seq is non-increasing & seq1 is constant implies seq + seq1 is non-increasing ) )