let V be ComplexLinearSpace; 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; 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; ( Carrier L = {v1,v2} & v1 <> v2 implies Sum L = ((L . v1) * v1) + ((L . v2) * v2) )
assume that
A1:
Carrier L = {v1,v2}
and
A2:
v1 <> v2
; Sum L = ((L . v1) * v1) + ((L . v2) * v2)
L is C_Linear_Combination of {v1,v2}
by A1, Def4;
hence
Sum L = ((L . v1) * v1) + ((L . v2) * v2)
by A2, Th15; verum