let a be Complex; :: thesis: for X being non empty compact TopSpace
for f, g being Function of the carrier of X,COMPLEX
for F, G being Point of (C_Normed_Algebra_of_ContinuousFunctions X) st f = F & g = G holds
( G = a * F iff for x being Element of X holds g . x = a * (f . x) )
let X be non empty compact TopSpace; :: thesis: for f, g being Function of the carrier of X,COMPLEX
for F, G being Point of (C_Normed_Algebra_of_ContinuousFunctions X) st f = F & g = G holds
( G = a * F iff for x being Element of X holds g . x = a * (f . x) )
let f, g be Function of the carrier of X,COMPLEX; :: thesis: for F, G being Point of (C_Normed_Algebra_of_ContinuousFunctions X) st f = F & g = G holds
( G = a * F iff for x being Element of X holds g . x = a * (f . x) )
let F, G be Point of (C_Normed_Algebra_of_ContinuousFunctions X); :: thesis: ( f = F & g = G implies ( G = a * F iff for x being Element of X holds g . x = a * (f . x) ) )
reconsider f1 = F, g1 = G as VECTOR of (C_Algebra_of_ContinuousFunctions X) ;
( G = a * F iff g1 = a * f1 ) ;
hence ( f = F & g = G implies ( G = a * F iff for x being Element of X holds g . x = a * (f . x) ) ) by Th11; :: thesis: verum