let V be RealLinearSpace; :: thesis: for W being Subspace of V
for L being Linear_Compl of W
for v being VECTOR of V holds ((v |-- W,L) `1 ) + ((v |-- W,L) `2 ) = v
let W be Subspace of V; :: thesis: for L being Linear_Compl of W
for v being VECTOR of V holds ((v |-- W,L) `1 ) + ((v |-- W,L) `2 ) = v
let L be Linear_Compl of W; :: thesis: for v being VECTOR of V holds ((v |-- W,L) `1 ) + ((v |-- W,L) `2 ) = v
V is_the_direct_sum_of W,L by Th43;
hence for v being VECTOR of V holds ((v |-- W,L) `1 ) + ((v |-- W,L) `2 ) = v by Def6; :: thesis: verum