theorem :: CKSPACE1:20

for m being non zero Element of NAT
for k being Element of NAT
for X being non empty open Subset of (REAL m)
for F, G, H being VECTOR of (R_Algebra_of_Ck_Functions (k,X))
for f, g, h being PartFunc of (REAL m),REAL st f = F & g = G & h = H holds
( H = F + G iff for x being Element of X holds h . x = (f . x) + (g . x) )