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

theorem
  (tanh(y)+tanh(z))/(tanh(y)-tanh(z)) = sinh(y+z)/sinh(y-z)
proof
A1: cosh(y) <> 0 & cosh(z) <> 0 by Lm1;
  (tanh(y)+tanh(z))/(tanh(y)-tanh(z)) = sinh(y+z)/(cosh(y)*cosh(z))/(tanh(
  y)-tanh(z)) by Lm11
    .= sinh(y+z)/(cosh(y)*cosh(z))/(sinh(y-z)/(cosh(y)*cosh(z))) by Lm11
    .= sinh(y+z)/sinh(y-z) by A1,XCMPLX_1:6,55;
  hence thesis;
end;
