theorem :: MESFUN7C:17

for X being non empty set
for S being SigmaField of X
for f being with_the_same_dom Functional_Sequence of X,REAL
for F being SetSequence of S
for r being Real st ( for n being Nat holds F . n = (dom (f . 0)) /\ (great_eq_dom ((f . n),r)) ) holds
meet (rng F) = (dom (f . 0)) /\ (great_eq_dom ((inf f),r))