theorem :: DIOPHAN1:17

for n being Nat
for r being Real st r is irrational & n > 0 holds
|.(r - (((c_n r) . n) / ((c_d r) . n))).| + |.(r - (((c_n r) . (n + 1)) / ((c_d r) . (n + 1)))).| = |.((((c_n r) . n) / ((c_d r) . n)) - (((c_n r) . (n + 1)) / ((c_d r) . (n + 1)))).|