reserve AS for AffinSpace;
reserve a,b,c,d,a9,b9,c9,d9,p,q,r,x,y for Element of AS;
reserve A,C,K,M,N,P,Q,X,Y,Z for Subset of AS;

theorem
  M is being_line & X is being_plane implies ex q st q in X & not q in M
proof
  assume that
A1: M is being_line and
A2: X is being_plane;
  consider a,b,c such that
A3: a in X & b in X and
A4: c in X and
A5: not LIN a,b,c by A2,Th34;
  assume
A6: not ex q st q in X & not q in M;
  then
A7: c in M by A4;
  a in M & b in M by A6,A3;
  hence contradiction by A1,A5,A7,AFF_1:21;
end;
