deffunc H₁( Real, Real) -> Element of REAL = In (|.($1 - $2).|,REAL);
consider F being Function of [:REAL,REAL:],REAL such that
A1: for x, y being Element of REAL holds F . (x,y) = H₁(x,y) from BINOP_1:sch 4();
take F ; :: thesis: for x, y being Real holds F . (x,y) = |.(x - y).|
let x, y be Real; :: thesis: F . (x,y) = |.(x - y).|
reconsider x = x, y = y as Element of REAL by XREAL_0:def 1;
F . (x,y) = H₁(x,y) by A1;
hence F . (x,y) = |.(x - y).| ; :: thesis: verum