reserve f,f1,f2,g for PartFunc of REAL,REAL;
reserve A for non empty closed_interval Subset of REAL;
reserve p,r,x,x0 for Real;
reserve n for Element of NAT;
reserve Z for open Subset of REAL;

theorem Th25:
  -cos is_differentiable_in x & diff(-cos,x) = sin.x
proof
A1: cos is_differentiable_in x by SIN_COS:63;
  then diff(-cos,x) = -diff(cos,x) by Th22
    .= - -sin.x by SIN_COS:63;
  hence thesis by A1,Th22;
end;
