reserve V for RealLinearSpace;
reserve u,u1,u2,v,v1,v2,w,w1,y for VECTOR of V;
reserve a,a1,a2,b,b1,b2,c1,c2 for Real;
reserve x,z for set;
reserve p,p1,q,q1 for Element of Lambda(OASpace(V));
reserve POS for non empty ParOrtStr;

theorem
  the carrier of AMSpace(V,w,y) = the carrier of V & the CONGR of
  AMSpace(V,w,y) = lambda(DirPar(V)) & the orthogonality of AMSpace(V,w,y) =
  Orthogonality(V,w,y);
