<?xml version="1.0"?>
<div>:: <span class="kw">deftheorem </span>   defines <a href="gtarski5.html#R1" title="GTARSKI5:pred.1">between</a> <a onclick="hs(this)" href="javascript:()">GTARSKI5:def 1 : <br/></a><span> for <font color="Olive" title="b1">S</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="gtarski1.html#L1" title="GTARSKI1:struct.1">TarskiGeometryStruct</a> <br/>  for <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font> being   <a href="gtarski1.html#NM1" title="GTARSKI1:NM.1">POINT</a> of <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b4">A</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">S</font> holds <br/> (  <a href="gtarski5.html#R1" title="GTARSKI5:pred.1">between</a> <font color="Olive" title="b2">a</font>,<font color="Olive" title="b4">A</font>,<font color="Olive" title="b3">b</font> iff ( <font color="Olive" title="b4">A</font> <a href="gtarski3.html#R8" title="GTARSKI3:pred.8">is_line</a>  &amp;  not <font color="Olive" title="b2">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b4">A</font> &amp;  not <font color="Olive" title="b3">b</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b4">A</font> &amp;  ex <font color="Olive" title="b5">t</font> being   <a href="gtarski1.html#NM1" title="GTARSKI1:NM.1">POINT</a> of <font color="Olive" title="b1">S</font> st <br/>( <font color="Olive" title="b5">t</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b4">A</font> &amp;  <a href="gtarski1.html#R1" title="GTARSKI1:pred.1">between</a> <font color="Olive" title="b2">a</font>,<font color="Olive" title="b5">t</font>,<font color="Olive" title="b3">b</font> ) ) );<br/></span></div>
