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