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;
reserve p,p1,p2,q,q1,r,r1,r2 for Element of AMSpace(V,w,y);
reserve x,a,b,c,d,p,q,y for Element of POS;
reserve A,K,M for Subset of POS;

theorem Th44:
  (a,b _|_ K implies K is being_line) &
  (K _|_ M implies K is being_line & M is being_line )
proof
  for a,b,K st a,b _|_ K holds K is being_line;
  then K _|_ M implies K is being_line & M is being_line;
  hence thesis;
end;
