let X, Y be RealNormSpace; :: thesis: for f, h being Point of
for a being Real holds
( h = a * f iff for x being VECTOR of holds h . x = a * (f . x) )
let f, h be Point of ; :: thesis: for a being Real holds
( h = a * f iff for x being VECTOR of holds h . x = a * (f . x) )
let a be Real; :: thesis: ( h = a * f iff for x being VECTOR of holds h . x = a * (f . x) )
reconsider f1 = f as VECTOR of ;
reconsider h1 = h as VECTOR of ;
( h = a * f iff h1 = a * f1 ) ;
hence ( h = a * f iff for x being VECTOR of holds h . x = a * (f . x) ) by Th30; :: thesis: verum