let r, x0, x1, x2 be Real; :: thesis: 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; :: thesis: [!(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; :: thesis: verum