<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">S</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="gtarski1.html#V9" title="GTARSKI1:attr.9">satisfying_Tarski-model</a>   <a href="gtarski1.html#L1" title="GTARSKI1:struct.1">TarskiGeometryStruct</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="gtarski1.html#NM1" title="GTARSKI1:NM.1">POINT</a> of <font color="Maroon" title="c1">S</font>  st (  <a href="gtarski3.html#R9" title="GTARSKI3:pred.9">Middle</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> or  <a href="gtarski3.html#R9" title="GTARSKI3:pred.9">Middle</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b2">b</font> or  <a href="gtarski3.html#R9" title="GTARSKI3:pred.9">Middle</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b1">a</font> ) holds <br/><font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> be   <a href="gtarski1.html#NM1" title="GTARSKI1:NM.1">POINT</a> of <font color="Maroon" title="c1">S</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( (  <a href="gtarski3.html#R9" title="GTARSKI3:pred.9">Middle</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> or  <a href="gtarski3.html#R9" title="GTARSKI3:pred.9">Middle</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c3">b</font> or  <a href="gtarski3.html#R9" title="GTARSKI3:pred.9">Middle</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font> ) implies <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> )</span><br/>



<span class="kw">assume </span><a NAME="E1:12"/>
(  <a href="gtarski3.html#R9" title="GTARSKI3:pred.9">Middle</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> or  <a href="gtarski3.html#R9" title="GTARSKI3:pred.9">Middle</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c3">b</font> or  <a href="gtarski3.html#R9" title="GTARSKI3:pred.9">Middle</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font></span><br/>

<a NAME="E2:12"/><span class="kw">then </span>
( <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c2">a</font> <a href="gtarski1.html#R2" title="GTARSKI1:pred.2">equiv</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> or <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font> <a href="gtarski1.html#R2" title="GTARSKI1:pred.2">equiv</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c3">b</font> or  <a href="gtarski3.html#R9" title="GTARSKI3:pred.9">Middle</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="gtarski3.html#D12" onmouseover="rs('gtarski3/D12')" onmouseout="rh()">GTARSKI3:def 12</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:12"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="gtarski1.html#D7" onmouseover="rs('gtarski1/D7')" onmouseout="rh()">GTARSKI1:def 7</a>, <a class="ref" href="gtarski3.html#T3" onmouseover="rs('gtarski3/T3')" onmouseout="rh()">GTARSKI3:3</a>, <a class="ref" href="gtarski3.html#T97" onmouseover="rs('gtarski3/T97')" onmouseout="rh()">GTARSKI3:97</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
