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<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">b</font>, <font color="Olive" title="b2">c</font>, <font color="Olive" title="b3">p</font> being   <a href="gtarski1.html#NM1" title="GTARSKI1:NM.1">POINT</a> of <font color="Maroon" title="c1">S</font> holds   <a href="gtarski3.html#R9" title="GTARSKI3:pred.9">Middle</a>  <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Olive" title="b3">p</font>,<font color="Olive" title="b2">c</font>), <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Olive" title="b3">p</font>,<font color="Olive" title="b1">b</font>), <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Olive" title="b3">p</font>,<span class="p1">(<span class="default"><a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Olive" title="b1">b</font>,<font color="Olive" title="b2">c</font>)</span>)</span>)</span><br/><span class="kw">let </span><font color="Maroon" title="c2">b</font>, <font color="Maroon" title="c3">c</font>, <font color="Maroon" title="c4">p</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>  <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c3">c</font>), <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">b</font>), <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c4">p</font>,<span class="p1">(<span class="default"><a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">c</font>)</span>)</span>)</span><br/>







<a NAME="E1:15"/>
 <a href="gtarski3.html#R9" title="GTARSKI3:pred.9">Middle</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c2">b</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">c</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="gtarski3.html#D13" onmouseover="rs('gtarski3/D13')" onmouseout="rh()">GTARSKI3:def 13</a></span>;<br/>
<a NAME="E2:15"/><span class="kw">then </span>
(  <a href="gtarski1.html#R1" title="GTARSKI1:pred.1">between</a>  <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c3">c</font>), <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">b</font>), <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c4">p</font>,<span class="p1">(<span class="default"><a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">c</font>)</span>)</span>) &amp;  <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">b</font>), <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c3">c</font>) <a href="gtarski1.html#R2" title="GTARSKI1:pred.2">equiv</a>  <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">b</font>), <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c4">p</font>,<span class="p1">(<span class="default"><a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">c</font>)</span>)</span>) )
 
<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>, <a class="ref" href="gtarski3.html#T106" onmouseover="rs('gtarski3/T106')" onmouseout="rh()">GTARSKI3:106</a>, <a class="ref" href="gtarski3.html#T107" onmouseover="rs('gtarski3/T107')" onmouseout="rh()">GTARSKI3:107</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:15"/>
 <a href="gtarski3.html#R9" title="GTARSKI3:pred.9">Middle</a>  <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c3">c</font>), <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">b</font>), <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c4">p</font>,<span class="p1">(<span class="default"><a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">c</font>)</span>)</span>)
 <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>; <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/>


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