let x0, x1, x2 be Real; :: thesis: for f1, f2 being Function of REAL,REAL holds [!(f1 + f2),x0,x1,x2!] = [!f1,x0,x1,x2!] + [!f2,x0,x1,x2!]
let f1, f2 be Function of REAL,REAL; :: thesis: [!(f1 + f2),x0,x1,x2!] = [!f1,x0,x1,x2!] + [!f2,x0,x1,x2!]
[!(f1 + f2),x0,x1,x2!] = (([!f1,x0,x1!] + [!f2,x0,x1!]) - [!(f1 + f2),x1,x2!]) / (x0 - x2) by DIFF_1:32
.= (([!f1,x0,x1!] + [!f2,x0,x1!]) - ([!f1,x1,x2!] + [!f2,x1,x2!])) / (x0 - x2) by DIFF_1:32
.= (([!f1,x0,x1!] - [!f1,x1,x2!]) + ([!f2,x0,x1!] - [!f2,x1,x2!])) / (x0 - x2) ;
hence [!(f1 + f2),x0,x1,x2!] = [!f1,x0,x1,x2!] + [!f2,x0,x1,x2!] by XCMPLX_1:62; :: thesis: verum