reserve x,y for set;
reserve X for non empty set;
reserve a,b,c,d for Element of X;
reserve S for OAffinSpace;
reserve a,b,c,d,p,q,r,x,y,z,t,u,w for Element of S;
reserve AS for non empty AffinStruct;
reserve S for OAffinPlane;
reserve x,y,z,t,u for Element of S;

theorem
  Lambda(S) is AffinPlane
proof
  set AS = Lambda(S);
  for x,y,z,t being Element of AS st not x,y // z,t ex u being Element of
  AS st x,y // x,u & z,t // z,u by Th44;
  hence thesis by Def7,Th41;
end;
