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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E64">Th58</font></span>: <a NAME="T68"><span class="comment"><font color="firebrick">:: BKMODEL4:68</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">P</font>, <font color="Olive" title="b2">Q</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="bkmodel2.html#K1" title="BKMODEL2:func.1">BK_model</a>   st <font color="Olive" title="b1">P</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">Q</font> holds <br/> ex <font color="Olive" title="b3">R</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>  st <br/> for <font color="Olive" title="b4">p</font>, <font color="Olive" title="b5">q</font>, <font color="Olive" title="b6">r</font> being   non  <a href="bkmodel4.html#V1" title="BKMODEL4:attr.1">point_at_infty</a>  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="anproj_1.html#K5" title="ANPROJ_1:func.5">ProjectiveSpace</a> <span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 3</span>)</span></span>)</span>  st <font color="Olive" title="b4">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">P</font> &amp; <font color="Olive" title="b5">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">Q</font> &amp; <font color="Olive" title="b6">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">R</font> holds <br/> <a href="gtarski1.html#R1" title="GTARSKI1:pred.1">between</a>  <a href="bkmodel4.html#K5" title="BKMODEL4:func.5">RP3_to_T2</a> <font color="Olive" title="b4">p</font>, <a href="bkmodel4.html#K5" title="BKMODEL4:func.5">RP3_to_T2</a> <font color="Olive" title="b5">q</font>, <a href="bkmodel4.html#K5" title="BKMODEL4:func.5">RP3_to_T2</a> <font color="Olive" title="b6">r</font></div></div>
