for n being Nat st n >0 holds for a, b being Element of Segm n holds ( ( a + b < n implies (addint n). (a,b) = a + b ) & ( (addint n). (a,b) = a + b implies a + b < n ) & ( a + b >= n implies (addint n). (a,b) =(a + b)- n ) & ( (addint n). (a,b) =(a + b)- n implies a + b >= n ) )