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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E35">Th31</font></span>: <a NAME="T41"><span class="comment"><font color="firebrick">:: BKMODEL2:41</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">P</font>, <font color="Olive" title="b2">PP1</font>, <font color="Olive" title="b3">PP2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="bkmodel1.html#K4" title="BKMODEL1:func.4">real_projective_plane</a><br/>  for <font color="Olive" title="b4">P1</font>, <font color="Olive" title="b5">P2</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="bkmodel1.html#K7" title="BKMODEL1:func.7">absolute</a> <br/>  for <font color="Olive" title="b6">Q</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="bkmodel1.html#K4" title="BKMODEL1:func.4">real_projective_plane</a>  st <font color="Olive" title="b4">P1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b5">P2</font> &amp; <font color="Olive" title="b2">PP1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">P1</font> &amp; <font color="Olive" title="b3">PP2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">P2</font> &amp; <font color="Olive" title="b1">P</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="bkmodel2.html#K1" title="BKMODEL2:func.1">BK_model</a>  &amp; <font color="Olive" title="b1">P</font>,<font color="Olive" title="b2">PP1</font>,<font color="Olive" title="b3">PP2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">are_collinear</a>  &amp; <font color="Olive" title="b6">Q</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="bkmodel2.html#K5" title="BKMODEL2:func.5">tangent</a> <font color="Olive" title="b4">P1</font> &amp; <font color="Olive" title="b6">Q</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="bkmodel2.html#K5" title="BKMODEL2:func.5">tangent</a> <font color="Olive" title="b5">P2</font> holds <br/> ex <font color="Olive" title="b7">R</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="bkmodel1.html#K4" title="BKMODEL1:func.4">real_projective_plane</a> st <br/>( <font color="Olive" title="b7">R</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="bkmodel1.html#K7" title="BKMODEL1:func.7">absolute</a>  &amp; <font color="Olive" title="b1">P</font>,<font color="Olive" title="b6">Q</font>,<font color="Olive" title="b7">R</font> <a href="collsp.html#R1" title="COLLSP:pred.1">are_collinear</a>  )</div></div>
