let V be Z_Module; :: thesis: for v being VECTOR of V
for L being Z_Linear_Combination of V st Carrier L = {v} holds
Sum L = (L . v) * v
let v be VECTOR of V; :: thesis: for L being Z_Linear_Combination of V st Carrier L = {v} holds
Sum L = (L . v) * v
let L be Z_Linear_Combination of V; :: thesis: ( Carrier L = {v} implies Sum L = (L . v) * v )
assume Carrier L = {v} ; :: thesis: Sum L = (L . v) * v
then L is Z_Linear_Combination of {v} by Def21;
hence Sum L = (L . v) * v by Th21; :: thesis: verum