let V be RealLinearSpace; :: thesis: for a being Real
for L being Linear_Combination of V holds a * (vector ((LC_RLSpace V),L)) = a * L
let a be Real; :: thesis: for L being Linear_Combination of V holds a * (vector ((LC_RLSpace V),L)) = a * L
let L be Linear_Combination of V; :: thesis: a * (vector ((LC_RLSpace V),L)) = a * L
A1: @ (@ L) = L ;
L in the carrier of (LC_RLSpace V) by Def14;
then L in LC_RLSpace V ;
hence a * (vector ((LC_RLSpace V),L)) = (LCMult V) . [a,(@ L)] by Def1
.= a * L by A1, Def18 ;
:: thesis: verum