let V be RealLinearSpace; :: 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 = (- 1) * (L . v) by Def11

.= - (L . v) ; :: thesis: verum

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 = (- 1) * (L . v) by Def11

.= - (L . v) ; :: thesis: verum