:: deftheorem defines is_continuous_on PDIFF_7:def 7 :
for m, n being non zero Nat
for f being PartFunc of (REAL m),(REAL n)
for X being set holds
( f is_continuous_on X iff ( X c= dom f & ( for x0 being Element of REAL m st x0 in X holds
f | X is_continuous_in x0 ) ) );