reserve f for PartFunc of REAL-NS 1,REAL-NS 1;
reserve g for PartFunc of REAL,REAL;
reserve x for Point of REAL-NS 1;
reserve y for Real;

theorem Th10:
  f=<>*g & x=<*y*> & f is_differentiable_in x implies diff(f,x).<*
  1*>=<*diff(g,y)*>
proof
  assume that
A1: f=<>*g and
A2: x=<*y*> and
A3: f is_differentiable_in x;
  g is_differentiable_in y by A1,A2,A3,Th7;
  hence thesis by A1,A2,Th8;
end;
