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 |-- L,W) `2
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 |-- L,W) `2
let L be Linear_Compl of W; :: thesis: for v being VECTOR of V holds (v |-- W,L) `1 = (v |-- L,W) `2
V is_the_direct_sum_of W,L by Th43;
hence for v being VECTOR of V holds (v |-- W,L) `1 = (v |-- L,W) `2 by Th59; :: thesis: verum