%include_equality
%include_excluded_middle

types point

datatype col point point point
datatype cop point point point point
datatype bet point point point
datatype cong point point point point
datatype cong3 point point point point point point
datatype afs point point point point point point point point
datatype bet4 point point point point
datatype ifs point point point point point point point point
datatype fs point point point point point point point point
datatype le point point point point
datatype lt point point point point
datatype gt point point point point
datatype ge point point point point
datatype out point point point
datatype is_midpoint point point point
datatype is_symmetric point point point
datatype is_image point point point point
datatype is_image_spec point point point point
datatype is_image_spec_in point point point point point
datatype is_image_spec_in_gen point point point point point
datatype per point point point
datatype perp_in point point point point point
datatype perp point point point point
datatype two_sides point point point point
datatype one_side point point point point
datatype point_on_line point point point
datatype point_on_plane3p point point point point
datatype point_on_plane2l point point point point point
datatype same_lines point point point point
datatype same_planes3p point point point point point point
datatype line_on_plane3p point point point point point
datatype same_planes2l point point point point point point point point
datatype line_on_plane2l point point point point point point
datatype same_planes2l3p point point point point point point point
datatype distinct point point point
datatype cong_angle point point point point point point
datatype point_in_angle point point point point
datatype le_angle point point point point point point
datatype ge_angle point point point point point point
datatype lt_angle point point point point point point
datatype gt_angle point point point point point point
datatype cong4 point point point point point point point point
datatype acute point point point
datatype obtuse point point point
datatype inter point point point point point
datatype intersect point point point point
datatype two_sides3p point point point point point
datatype one_side3p point point point point point 
datatype right_angle3p3p point point point point point point
datatype right_angle2p3p_in point point point point point point
datatype right_angle2p3p point point point point point 
datatype cop_lines point point point point
datatype cop_lines3l point point point point point point
datatype int point point point point
datatype parallel point point point point
datatype parallel_broad point point point point
datatype parallel_planes point point point point point point
datatype point_on_ray point point point
datatype parallel_normal point point point point point
