theorem Th40:
for x be Point of product G,a be Real
 holds proj(i).(a*x) = a*(proj(i).x)
proof
   let x be Point of product G,a  be Real;
   reconsider a as Real;
   reconsider v=a*x as Element of product carr G by Th10;
   reconsider s=x as Element of product carr G by Th10;
   proj(i).(a*x)= v.i & proj(i).x = s.i by Def3;
   hence thesis by Th13;
end;
