let r, x0, x1, x2 be Real; for f being Function of REAL,REAL holds [!(r (#) f),x0,x1,x2!] = r * [!f,x0,x1,x2!]
let f be Function of REAL,REAL; [!(r (#) f),x0,x1,x2!] = r * [!f,x0,x1,x2!]
[!(r (#) f),x0,x1,x2!] =
((r * [!f,x0,x1!]) - [!(r (#) f),x1,x2!]) / (x0 - x2)
by DIFF_1:31
.=
((r * [!f,x0,x1!]) - (r * [!f,x1,x2!])) / (x0 - x2)
by DIFF_1:31
.=
(r * ([!f,x0,x1!] - [!f,x1,x2!])) / (x0 - x2)
;
hence
[!(r (#) f),x0,x1,x2!] = r * [!f,x0,x1,x2!]
by XCMPLX_1:74; verum