 reserve n,i,k,m for Nat;
 reserve p for Prime;

theorem LogExp:
  for x being Real holds
    ln.(exp_R.x) = x
  proof
    let x be Real;
A1: exp_R.x in right_open_halfline 0 by XXREAL_1:235,SIN_COS:54;
    log (number_e, exp_R.x) = x by TAYLOR_1:13;
    hence thesis by A1,TAYLOR_1:def 3,def 2;
  end;
