deffunc H₁( Element of Funcs (A,COMPLEX), Element of Funcs (A,COMPLEX)) -> Element of Funcs (A,COMPLEX) = multcomplex .: ($1,$2);
consider F being BinOp of (Funcs (A,COMPLEX)) such that
A1: for x, y being Element of Funcs (A,COMPLEX) holds F . (x,y) = H₁(x,y) from BINOP_1:sch 4();
take F ; :: thesis: for f, g being Element of Funcs (A,COMPLEX) holds F . (f,g) = multcomplex .: (f,g)
let f, g be Element of Funcs (A,COMPLEX); :: thesis: F . (f,g) = multcomplex .: (f,g)
thus F . (f,g) = multcomplex .: (f,g) by A1; :: thesis: verum