let F be Field; :: thesis: for V being VectSp of F
for W being Subspace of V
for L being Linear_Compl of W
for v being Element of V holds (v |-- W,L) `1 = (v |-- L,W) `2
let V be VectSp of F; :: thesis: for W being Subspace of V
for L being Linear_Compl of W
for v being Element 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 Element of V holds (v |-- W,L) `1 = (v |-- L,W) `2
let L be Linear_Compl of W; :: thesis: for v being Element of V holds (v |-- W,L) `1 = (v |-- L,W) `2
let v be Element of V; :: thesis: (v |-- W,L) `1 = (v |-- L,W) `2
V is_the_direct_sum_of W,L by Th48;
hence (v |-- W,L) `1 = (v |-- L,W) `2 by Th64; :: thesis: verum