let r, x0, x1, x2, x3 be Real; :: thesis: for f being Function of REAL,REAL holds [!(r (#) f),x0,x1,x2,x3!] = r * [!f,x0,x1,x2,x3!]
let f be Function of REAL,REAL; :: thesis: [!(r (#) f),x0,x1,x2,x3!] = r * [!f,x0,x1,x2,x3!]
[!(r (#) f),x0,x1,x2,x3!] = ((r * [!f,x0,x1,x2!]) - [!(r (#) f),x1,x2,x3!]) / (x0 - x3) by Th5
.= ((r * [!f,x0,x1,x2!]) - (r * [!f,x1,x2,x3!])) / (x0 - x3) by Th5
.= (r * ([!f,x0,x1,x2!] - [!f,x1,x2,x3!])) / (x0 - x3) ;
hence [!(r (#) f),x0,x1,x2,x3!] = r * [!f,x0,x1,x2,x3!] by XCMPLX_1:74; :: thesis: verum