theorem
  f=h & x=z & f is_partial_differentiable_in x,i,j implies
  partdiff(f,x,i,j).<*1*> = <*partdiff(h,z,i,j)*>
proof
  assume that
A1: f=h and
A2: x=z and
A3: f is_partial_differentiable_in x,i,j;
A4: Proj(i,m).x=<*proj(i,m).z*> by A2,Def4;
A5: Proj(j,n)*f*reproj(i,x) is_differentiable_in Proj(i,m).x by A3;
  Proj(j,n)*f*reproj(i,x) =<>*(proj(j,n)*h*reproj(i,z)) by A1,A2,Th22;
  hence thesis by A4,A5,Th10;
end;
