let R be Ring; :: thesis: for V being RightMod of R
for v being Vector of V
for L being Linear_Combination of V holds (- L) . v = - (L . v)
let V be RightMod of R; :: thesis: for v being Vector of V
for L being Linear_Combination of V holds (- L) . v = - (L . v)
let v be Vector of V; :: thesis: for L being Linear_Combination of V holds (- L) . v = - (L . v)
let L be Linear_Combination of V; :: thesis: (- L) . v = - (L . v)
thus (- L) . v = (L . v) * (- (1_ R)) by Def10
.= - (L . v) by VECTSP_2:28 ; :: thesis: verum