theorem Th22: :: FUNCSDOM:22

for x1, x2 being set
for A being non empty set st A = {x1,x2} & x1 <> x2 holds
ex f, g being Element of Funcs (A,REAL) st
( ( for a, b being Real st (RealFuncAdd A) . (((RealFuncExtMult A) . [a,f]),((RealFuncExtMult A) . [b,g])) = RealFuncZero A holds
( a = 0 & b = 0 ) ) & ( for h being Element of Funcs (A,REAL) ex a, b being Real st h = (RealFuncAdd A) . (((RealFuncExtMult A) . [a,f]),((RealFuncExtMult A) . [b,g])) ) )