theorem
for G be RealNormSpace-Sequence,
     F be RealNormSpace,
     i be Element of dom G,
     x be Point of product G,
     xi be Point of G.i,
     f be PartFunc of product G,F,
     g be PartFunc of G.i,F
      st proj(i).x=xi & g=f*reproj(i,x)
 holds
    diff(g,xi) = partdiff(f,x,i)
proof
   let G be RealNormSpace-Sequence,
       F be RealNormSpace,
       i be Element of dom G,
       x be Point of product G,
       xi be Point of G.i,
       f be PartFunc of product G,F,
       g be PartFunc of G.i,F;
   i=In(i,dom G) by SUBSET_1:def 8;
   hence thesis;
end;
