reserve x, y, z, w for Real;
reserve n for Element of NAT;

theorem Th3:
  sech x <= 1 & 0 < sech x & sech 0 = 1
proof
A1: 2/2 >= 2/(exp_R(x)+exp_R(-x)) by Lm9,XREAL_1:183;
  0 < cosh.x by SIN_COS2:15;
  then 0 < cosh x by SIN_COS2:def 4;
  then
A2: 0 < 1/cosh(x) by XREAL_1:139;
  sech 0 = 1/1 by Lm1,SIN_COS5:def 2
    .= 1;
  hence thesis by A2,A1,SIN_COS5:36,def 2;
end;
