for n being Element of NAT
for A being non empty closed_interval Subset of REAL
for f being Function of A,(REAL n)
for g being Function of A,(REAL-NS n)
for T being DivSequence of A
for S being middle_volume_Sequence of f,T
for U being middle_volume_Sequence of g,T st f = g & S = U holds
middle_sum (f,S) = middle_sum (g,U)