let V be RealLinearSpace; :: thesis: for a being Real

for A being Subset of V

for L being Linear_Combination of V st L is Linear_Combination of A holds

a * L is Linear_Combination of A

let a be Real; :: thesis: for A being Subset of V

for L being Linear_Combination of V st L is Linear_Combination of A holds

a * L is Linear_Combination of A

let A be Subset of V; :: thesis: for L being Linear_Combination of V st L is Linear_Combination of A holds

a * L is Linear_Combination of A

let L be Linear_Combination of V; :: thesis: ( L is Linear_Combination of A implies a * L is Linear_Combination of A )

assume A1: L is Linear_Combination of A ; :: thesis: a * L is Linear_Combination of A

for A being Subset of V

for L being Linear_Combination of V st L is Linear_Combination of A holds

a * L is Linear_Combination of A

let a be Real; :: thesis: for A being Subset of V

for L being Linear_Combination of V st L is Linear_Combination of A holds

a * L is Linear_Combination of A

let A be Subset of V; :: thesis: for L being Linear_Combination of V st L is Linear_Combination of A holds

a * L is Linear_Combination of A

let L be Linear_Combination of V; :: thesis: ( L is Linear_Combination of A implies a * L is Linear_Combination of A )

assume A1: L is Linear_Combination of A ; :: thesis: a * L is Linear_Combination of A

now :: thesis: a * L is Linear_Combination of A

hence
a * L is Linear_Combination of A
; :: thesis: verumend;