theorem Th6: :: SEQ_4:6

for g1, g2 being Real
for X being real-membered set st ( for r being Real st r in X holds
r <= g1 ) & ( for s being Real st 0 < s holds
ex r being Real st
( r in X & g1 - s < r ) ) & ( for r being Real st r in X holds
r <= g2 ) & ( for s being Real st 0 < s holds
ex r being Real st
( r in X & g2 - s < r ) ) holds
g1 = g2