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 & N is being_line & M,N,K is_coplanar & M,N,A
  is_coplanar & M<>N implies M,K,A is_coplanar
proof
  assume that
A1: M is being_line & N is being_line and
A2: M,N,K is_coplanar and
A3: M,N,A is_coplanar and
A4: M<>N;
  consider X such that
A5: M c= X and
A6: N c= X and
A7: K c= X and
A8: X is being_plane by A2;
  ex Y st M c= Y & N c= Y & A c= Y & Y is being_plane by A3;
  then A c= X by A1,A4,A5,A6,A8,Th26;
  hence thesis by A5,A7,A8;
end;
