let V be Z_Module; :: thesis: for a being Element of INT.Ring
for v, u being Vector of V holds a * (Sum <*v,u*>) = (a * v) + (a * u)
let a be Element of INT.Ring; :: thesis: for v, u being Vector of V holds a * (Sum <*v,u*>) = (a * v) + (a * u)
let v, u be Vector of V; :: thesis: a * (Sum <*v,u*>) = (a * v) + (a * u)
thus a * (Sum <*v,u*>) = a * (v + u) by RLVECT_1:45
.= (a * v) + (a * u) by VECTSP_1:def 14 ; :: thesis: verum