let F, G be Function of V1,V2; ( ( for v being Element of V1 holds F . v = a * (f . v) ) & ( for v being Element of V1 holds G . v = a * (f . v) ) implies F = G )
assume that
A2:
for v being Element of V1 holds F . v = a * (f . v)
and
A3:
for v being Element of V1 holds G . v = a * (f . v)
; F = G
hence
F = G
by FUNCT_2:63; verum