deffunc H₁( Element of REAL n, Element of REAL n) -> Element of REAL = In ((Sum (mlt ($1,$2))),REAL);
consider f being Function of [:(REAL n),(REAL n):],REAL such that
A1: for x, y being Element of REAL n holds f . (x,y) = H₁(x,y) from BINOP_1:sch 4();
take f ; :: thesis: for x, y being Element of REAL n holds f . (x,y) = Sum (mlt (x,y))
let x, y be Element of REAL n; :: thesis: f . (x,y) = Sum (mlt (x,y))
f . (x,y) = H₁(x,y) by A1;
hence f . (x,y) = Sum (mlt (x,y)) ; :: thesis: verum