deffunc H₁( Real) -> Element of REAL = ((exp_R . $1) - (exp_R . (- $1))) / ((exp_R . $1) + (exp_R . (- $1)));
consider f being Function of REAL ,REAL such that
A1: for d being Element of REAL holds f . d = H₁(d) from FUNCT_2:sch 4();
take f ; :: thesis: for d being real number holds f . d = ((exp_R . d) - (exp_R . (- d))) / ((exp_R . d) + (exp_R . (- d)))
let d be real number ; :: thesis: f . d = ((exp_R . d) - (exp_R . (- d))) / ((exp_R . d) + (exp_R . (- d)))
d is Real by XREAL_0:def 1;
hence f . d = ((exp_R . d) - (exp_R . (- d))) / ((exp_R . d) + (exp_R . (- d))) by A1; :: thesis: verum