let V be Z_Module; :: thesis: for v being VECTOR of V
for L being Z_Linear_Combination of V holds (- L) . v = - (L . v)
let v be VECTOR of V; :: thesis: for L being Z_Linear_Combination of V holds (- L) . v = - (L . v)
let L be Z_Linear_Combination of V; :: thesis: (- L) . v = - (L . v)
thus (- L) . v = (- 1) * (L . v) by Def26
.= - (L . v) ; :: thesis: verum