theorem Th30:
  f=F & g=G implies ( G = a*F iff for x be Element of X holds g.x = a*f.x )
proof
  reconsider f1=F, g1=G as VECTOR of R_Algebra_of_BoundedFunctions X;
A1: G=a*F iff g1=a*f1;
  assume f=F & g=G;
  hence thesis by A1,Th13;
end;
