:: deftheorem Def4 defines middle_sum INTEGR15:def 4 :

for A being non empty closed_interval Subset of REAL

for f being Function of A,REAL

for T being DivSequence of A

for S being middle_volume_Sequence of f,T

for b_{5} being Real_Sequence holds

( b_{5} = middle_sum (f,S) iff for i being Element of NAT holds b_{5} . i = middle_sum (f,(S . i)) );

for A being non empty closed_interval Subset of REAL

for f being Function of A,REAL

for T being DivSequence of A

for S being middle_volume_Sequence of f,T

for b

( b