let V be ComplexLinearSpace; :: thesis: for L being C_Linear_Combination of V
for v1, v2 being VECTOR of V st Carrier L = {v1,v2} & v1 <> v2 holds
Sum L = ((L . v1) * v1) + ((L . v2) * v2)
let L be C_Linear_Combination of V; :: thesis: for v1, v2 being VECTOR of V st Carrier L = {v1,v2} & v1 <> v2 holds
Sum L = ((L . v1) * v1) + ((L . v2) * v2)
let v1, v2 be VECTOR of V; :: thesis: ( Carrier L = {v1,v2} & v1 <> v2 implies Sum L = ((L . v1) * v1) + ((L . v2) * v2) )
assume A1: ( Carrier L = {v1,v2} & v1 <> v2 ) ; :: thesis: Sum L = ((L . v1) * v1) + ((L . v2) * v2)
then L is C_Linear_Combination of {v1,v2} by Def3;
hence Sum L = ((L . v1) * v1) + ((L . v2) * v2) by A1, Th51; :: thesis: verum