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

theorem Th1:
  tanh x = sinh(x)/cosh(x) & tanh 0 = 0
proof
A1: tanh 0 = tanh.0 by SIN_COS2:def 6
    .= sinh.0/cosh.0 by SIN_COS2:17
    .= 0 by SIN_COS2:16;
  tanh(x) = tanh.x by SIN_COS2:def 6
    .= sinh.x/cosh.x by SIN_COS2:17
    .= sinh(x)/cosh.x by SIN_COS2:def 2
    .= sinh(x)/cosh(x) by SIN_COS2:def 4;
  hence thesis by A1;
end;
