theorem Th42: :: SEQFUNC:43

for D being non empty set
for H being Functional_Sequence of D,REAL
for X being set holds
( H is_unif_conv_on X iff ( X common_on_dom H & H is_point_conv_on X & ( for r being Real st 0 < r holds
ex k being Nat st
for n being Nat
for x being Element of D st n >= k & x in X holds
|.(((H . n) . x) - ((lim (H,X)) . x)).| < r ) ) )