let r, x0, x1, x2, x3, x4 be Real; :: thesis: for f being Function of REAL,REAL holds [!(r (#) f),x0,x1,x2,x3,x4!] = r * [!f,x0,x1,x2,x3,x4!]
let f be Function of REAL,REAL; :: thesis: [!(r (#) f),x0,x1,x2,x3,x4!] = r * [!f,x0,x1,x2,x3,x4!]
[!(r (#) f),x0,x1,x2,x3,x4!] = ((r * [!f,x0,x1,x2,x3!]) - [!(r (#) f),x1,x2,x3,x4!]) / (x0 - x4) by Th8
.= ((r * [!f,x0,x1,x2,x3!]) - (r * [!f,x1,x2,x3,x4!])) / (x0 - x4) by Th8
.= (r * ([!f,x0,x1,x2,x3!] - [!f,x1,x2,x3,x4!])) / (x0 - x4) ;
hence [!(r (#) f),x0,x1,x2,x3,x4!] = r * [!f,x0,x1,x2,x3,x4!] by XCMPLX_1:74; :: thesis: verum