theorem Th61:
  X is being_plane & Y is being_plane & Z is being_plane & ( X
'||' Y & Y '||' Z or X '||' Y & Z '||' Y or Y '||' X & Y '||' Z or Y '||' X & Z
  '||' Y ) implies X '||' Z
proof
  assume that
A1: X is being_plane and
A2: Y is being_plane and
A3: Z is being_plane &( X '||' Y & Y '||' Z or X '||' Y & Z '||' Y or Y
  '||' X & Y '||' Z or Y '||' X & Z '||' Y);
  X '||' Y & Y '||' Z by A1,A2,A3,Th58;
  hence thesis by A2,Th59,Th60;
end;
