let R be Ring; :: thesis: for V being RightMod of R
for v being Vector of V
for L being Linear_Combination of V st Carrier L = {v} holds
Sum L = v * (L . v)
let V be RightMod of R; :: thesis: for v being Vector of V
for L being Linear_Combination of V st Carrier L = {v} holds
Sum L = v * (L . v)
let v be Vector of V; :: thesis: for L being Linear_Combination of V st Carrier L = {v} holds
Sum L = v * (L . v)
let L be Linear_Combination of V; :: thesis: ( Carrier L = {v} implies Sum L = v * (L . v) )
assume Carrier L = {v} ; :: thesis: Sum L = v * (L . v)
then L is Linear_Combination of {v} by Def5;
hence Sum L = v * (L . v) by Th32; :: thesis: verum