theorem Th14: :: MESFUN18:14

for n being non zero Nat
for f being PartFunc of [:(CarProduct ((Seg n) --> RNS_Real)),RNS_Real:],RNS_Real
for g being PartFunc of [:(CarProduct ((Seg n) --> REAL)),REAL:],REAL
for p being Element of CarProduct ((Seg n) --> REAL) st f is_continuous_on dom f & f = g holds
ProjPMap1 (g,p) is continuous