let V be RealLinearSpace; :: thesis: for L being Linear_Combination of V st Carrier L = {} holds

Sum L = 0. V

let L be Linear_Combination of V; :: thesis: ( Carrier L = {} implies Sum L = 0. V )

assume Carrier L = {} ; :: thesis: Sum L = 0. V

then L = ZeroLC V by Def5;

hence Sum L = 0. V by Lm2; :: thesis: verum

Sum L = 0. V

let L be Linear_Combination of V; :: thesis: ( Carrier L = {} implies Sum L = 0. V )

assume Carrier L = {} ; :: thesis: Sum L = 0. V

then L = ZeroLC V by Def5;

hence Sum L = 0. V by Lm2; :: thesis: verum