reserve V for RealLinearSpace;
reserve W,W1,W2,W3 for Subspace of V;
reserve u,u1,u2,v,v1,v2 for VECTOR of V;
reserve a,a1,a2 for Real;
reserve X,Y,x,y,y1,y2 for set;
reserve C for Coset of W;
reserve C1 for Coset of W1;
reserve C2 for Coset of W2;
reserve t1,t2 for Element of [:the carrier of V, the carrier of V:];

theorem
  for V being RealLinearSpace, W being Subspace of V, L being
Linear_Compl of W, v being VECTOR of V holds (v |-- (W,L))`1 = (v |-- (L,W))`2
by Th35,Th47;
