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<span class="kw">let </span><font color="Maroon" title="c1">S</font> be   <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">a9</font>, <font color="Olive" title="b3">b</font>, <font color="Olive" title="b4">b9</font>, <font color="Olive" title="b5">c</font>, <font color="Olive" title="b6">c9</font> being   <a href="gtarski1.html#NM1" title="GTARSKI1:NM.1">POINT</a> of <font color="Maroon" title="c1">S</font>  st  <a href="gtarski4.html#R1" title="GTARSKI4:pred.1">right_angle</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">b</font>,<font color="Olive" title="b5">c</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">b</font>,<font color="Olive" title="b5">c</font> <a href="gtarski1.html#R3" title="GTARSKI1:pred.3">cong</a> <font color="Olive" title="b2">a9</font>,<font color="Olive" title="b4">b9</font>,<font color="Olive" title="b6">c9</font> holds <br/> <a href="gtarski4.html#R1" title="GTARSKI4:pred.1">right_angle</a> <font color="Olive" title="b2">a9</font>,<font color="Olive" title="b4">b9</font>,<font color="Olive" title="b6">c9</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">a9</font>, <font color="Maroon" title="c4">b</font>, <font color="Maroon" title="c5">b9</font>, <font color="Maroon" title="c6">c</font>, <font color="Maroon" title="c7">c9</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="gtarski4.html#R1" title="GTARSKI4:pred.1">right_angle</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">c</font> &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">c</font> <a href="gtarski1.html#R3" title="GTARSKI1:pred.3">cong</a> <font color="Maroon" title="c3">a9</font>,<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c7">c9</font> implies  <a href="gtarski4.html#R1" title="GTARSKI4:pred.1">right_angle</a> <font color="Maroon" title="c3">a9</font>,<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c7">c9</font> )</span><br/>













<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:26"/><span class="lab"><font color="Green" title="E24">A1</font></span>: 
 <a href="gtarski4.html#R1" title="GTARSKI4:pred.1">right_angle</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">c</font>
 <span class="kw">and </span><br/><a NAME="E2:26"/><span class="lab"><font color="Green" title="E25">A2</font></span>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">c</font> <a href="gtarski1.html#R3" title="GTARSKI1:pred.3">cong</a> <font color="Maroon" title="c3">a9</font>,<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c7">c9</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="gtarski4.html#R1" title="GTARSKI4:pred.1">right_angle</a> <font color="Maroon" title="c3">a9</font>,<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c7">c9</font></span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:26_1"/>
( <font color="Maroon" title="c4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">c</font> or <font color="Maroon" title="c4">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">c</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_1_1"><span class="kw">suppose </span></a><a NAME="E1:26_1_1"/>
<font color="Maroon" title="c4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">c</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="gtarski4.html#R1" title="GTARSKI4:pred.1">right_angle</a> <font color="Maroon" title="c3">a9</font>,<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c7">c9</font></span><br/><div class="add"><a NAME="E2:26_1_1"/><span class="kw">then </span>
( <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">b</font> <a href="gtarski1.html#R2" title="GTARSKI1:pred.2">equiv</a> <font color="Maroon" title="c3">a9</font>,<font color="Maroon" title="c5">b9</font> &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">b</font> <a href="gtarski1.html#R2" title="GTARSKI1:pred.2">equiv</a> <font color="Maroon" title="c3">a9</font>,<font color="Maroon" title="c7">c9</font> &amp; <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c4">b</font> <a href="gtarski1.html#R2" title="GTARSKI1:pred.2">equiv</a> <font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c7">c9</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:26"><span class="lab"><font color="Green" title="E25">A2</font></span></a>, <a class="ref" href="gtarski1.html#D3" onmouseover="rs('gtarski1/D3')" onmouseout="rh()">GTARSKI1:def 3</a></span>;<br/><a NAME="E3:26_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">b9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">c9</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#T4" onmouseover="rs('gtarski3/T4')" onmouseout="rh()">GTARSKI3:4</a></span>;<br/><span class="kw">hence </span><a NAME="E4:26_1_1"/>
 <a href="gtarski4.html#R1" title="GTARSKI4:pred.1">right_angle</a> <font color="Maroon" title="c3">a9</font>,<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c7">c9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="gtarski4.html#T17" target="_self" onmouseover="rs('gtarski4/T17')" onmouseout="rh()">Satz8p5</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><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_1_2"><span class="kw">suppose </span></a><a NAME="E1:26_1_2"/><span class="lab"><font color="Green" title="E26">A3</font></span>: 
<font color="Maroon" title="c4">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">c</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="gtarski4.html#R1" title="GTARSKI4:pred.1">right_angle</a> <font color="Maroon" title="c3">a9</font>,<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c7">c9</font></span><br/><div class="add"><span class="kw">set </span><font color="Maroon" title="c8">d</font> =  <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">c</font>);<br/><span class="kw">set </span><font color="Maroon" title="c9">d9</font> =  <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c7">c9</font>);<br/><a NAME="E2:26_1_2"/><span class="lab"><font color="Green" title="E27">A4</font></span>: 
( <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">b</font> <a href="gtarski1.html#R2" title="GTARSKI1:pred.2">equiv</a> <font color="Maroon" title="c3">a9</font>,<font color="Maroon" title="c5">b9</font> &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c6">c</font> <a href="gtarski1.html#R2" title="GTARSKI1:pred.2">equiv</a> <font color="Maroon" title="c3">a9</font>,<font color="Maroon" title="c7">c9</font> &amp; <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">c</font> <a href="gtarski1.html#R2" title="GTARSKI1:pred.2">equiv</a> <font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c7">c9</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:26"><span class="lab"><font color="Green" title="E25">A2</font></span></a>, <a class="ref" href="gtarski1.html#D3" onmouseover="rs('gtarski1/D3')" onmouseout="rh()">GTARSKI1:def 3</a></span>;<br/><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="26_1_2_1"><span class="kw">now </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"> (  <a href="gtarski1.html#R1" title="GTARSKI1:pred.1">between</a> <font color="Maroon" title="c6">c</font>,<font color="Maroon" title="c4">b</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">c</font>) &amp;  <a href="gtarski1.html#R1" title="GTARSKI1:pred.1">between</a> <font color="Maroon" title="c7">c9</font>,<font color="Maroon" title="c5">b9</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c7">c9</font>) &amp; <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c2">a</font> <a href="gtarski1.html#R2" title="GTARSKI1:pred.2">equiv</a> <font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c3">a9</font> &amp; <font color="Maroon" title="c6">c</font>,<font color="Maroon" title="c4">b</font> <a href="gtarski1.html#R2" title="GTARSKI1:pred.2">equiv</a> <font color="Maroon" title="c7">c9</font>,<font color="Maroon" title="c5">b9</font> &amp; <font color="Maroon" title="c6">c</font>,<font color="Maroon" title="c2">a</font> <a href="gtarski1.html#R2" title="GTARSKI1:pred.2">equiv</a> <font color="Maroon" title="c7">c9</font>,<font color="Maroon" title="c3">a9</font> &amp; <font color="Maroon" title="c4">b</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">c</font>) <a href="gtarski1.html#R2" title="GTARSKI1:pred.2">equiv</a> <font color="Maroon" title="c5">b9</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c7">c9</font>) )</span></a><div class="add"><a NAME="E1:26_1_2_1"/>
(  <a href="gtarski3.html#R9" title="GTARSKI3:pred.9">Middle</a> <font color="Maroon" title="c6">c</font>,<font color="Maroon" title="c4">b</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">c</font>) &amp;  <a href="gtarski3.html#R9" title="GTARSKI3:pred.9">Middle</a> <font color="Maroon" title="c7">c9</font>,<font color="Maroon" title="c5">b9</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c7">c9</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/><span class="kw">hence </span><a NAME="E2:26_1_2_1"/>
(  <a href="gtarski1.html#R1" title="GTARSKI1:pred.1">between</a> <font color="Maroon" title="c6">c</font>,<font color="Maroon" title="c4">b</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">c</font>) &amp;  <a href="gtarski1.html#R1" title="GTARSKI1:pred.1">between</a> <font color="Maroon" title="c7">c9</font>,<font color="Maroon" title="c5">b9</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c7">c9</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>; <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="c4">b</font>,<font color="Maroon" title="c2">a</font> <a href="gtarski1.html#R2" title="GTARSKI1:pred.2">equiv</a> <font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c3">a9</font> &amp; <font color="Maroon" title="c6">c</font>,<font color="Maroon" title="c4">b</font> <a href="gtarski1.html#R2" title="GTARSKI1:pred.2">equiv</a> <font color="Maroon" title="c7">c9</font>,<font color="Maroon" title="c5">b9</font> &amp; <font color="Maroon" title="c6">c</font>,<font color="Maroon" title="c2">a</font> <a href="gtarski1.html#R2" title="GTARSKI1:pred.2">equiv</a> <font color="Maroon" title="c7">c9</font>,<font color="Maroon" title="c3">a9</font> &amp; <font color="Maroon" title="c4">b</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">c</font>) <a href="gtarski1.html#R2" title="GTARSKI1:pred.2">equiv</a> <font color="Maroon" title="c5">b9</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c7">c9</font>) )</span><br/><span class="kw">thus </span><a NAME="E3:26_1_2_1"/>
( <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c2">a</font> <a href="gtarski1.html#R2" title="GTARSKI1:pred.2">equiv</a> <font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c3">a9</font> &amp; <font color="Maroon" title="c6">c</font>,<font color="Maroon" title="c4">b</font> <a href="gtarski1.html#R2" title="GTARSKI1:pred.2">equiv</a> <font color="Maroon" title="c7">c9</font>,<font color="Maroon" title="c5">b9</font> &amp; <font color="Maroon" title="c6">c</font>,<font color="Maroon" title="c2">a</font> <a href="gtarski1.html#R2" title="GTARSKI1:pred.2">equiv</a> <font color="Maroon" title="c7">c9</font>,<font color="Maroon" title="c3">a9</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:26_1_2"><span class="lab"><font color="Green" title="E27">A4</font></span></a>, <a class="ref" href="gtarski4.html#T1" target="_self" onmouseover="rs('gtarski4/T1')" onmouseout="rh()">Prelim01</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"> <font color="Maroon" title="c4">b</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">c</font>) <a href="gtarski1.html#R2" title="GTARSKI1:pred.2">equiv</a> <font color="Maroon" title="c5">b9</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c7">c9</font>)</span><br/><a NAME="E4:26_1_2_1"/>
<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">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">b</font>,<font color="Maroon" title="c4">b</font>), <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">c</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="gtarski3.html#T105" onmouseover="rs('gtarski3/T105')" onmouseout="rh()">GTARSKI3:105</a></span>;<br/><a NAME="E5:26_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E28">A5</font></span>: 
<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c7">c9</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">b</font>,<font color="Maroon" title="c4">b</font>), <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">c</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:26_1_2"><span class="lab"><font color="Green" title="E27">A4</font></span></a>, <a class="ref" href="gtarski1.html#D6" onmouseover="rs('gtarski1/D6')" onmouseout="rh()">GTARSKI1:def 6</a></span>;<br/><a NAME="E6:26_1_2_1"/>
<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c7">c9</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="c5">b9</font>,<font color="Maroon" title="c5">b9</font>), <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c7">c9</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="gtarski3.html#T105" onmouseover="rs('gtarski3/T105')" onmouseout="rh()">GTARSKI3:105</a></span>;<br/><a NAME="E7:26_1_2_1"/><span class="kw">then </span>
 <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c4">b</font>), <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">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="c5">b9</font>,<font color="Maroon" title="c5">b9</font>), <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c7">c9</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:26_1_2_1"><span class="lab"><font color="Green" title="E28">A5</font></span></a>, <a class="ref" href="gtarski1.html#D6" onmouseover="rs('gtarski1/D6')" onmouseout="rh()">GTARSKI1:def 6</a></span>;<br/><a NAME="E8:26_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">b</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">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="c5">b9</font>,<font color="Maroon" title="c5">b9</font>), <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c7">c9</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="gtarski3.html#T104" onmouseover="rs('gtarski3/T104')" onmouseout="rh()">GTARSKI3:104</a></span>;<br/><span class="kw">hence </span><a NAME="E9:26_1_2_1"/>
<font color="Maroon" title="c4">b</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">c</font>) <a href="gtarski1.html#R2" title="GTARSKI1:pred.2">equiv</a> <font color="Maroon" title="c5">b9</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c7">c9</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="gtarski3.html#T104" onmouseover="rs('gtarski3/T104')" onmouseout="rh()">GTARSKI3:104</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><span class="kw">end;</span></div><a NAME="E4:26_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c6">c</font>,<font color="Maroon" title="c4">b</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">c</font>),<font color="Maroon" title="c2">a</font> <a href="gtarski3.html#R1" title="GTARSKI3:pred.1">AFS</a> <font color="Maroon" title="c7">c9</font>,<font color="Maroon" title="c5">b9</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c7">c9</font>),<font color="Maroon" title="c3">a9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="gtarski3.html#D2" onmouseover="rs('gtarski3/D2')" onmouseout="rh()">GTARSKI3:def 2</a></span>;<br/><a NAME="E5:26_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E28">A6</font></span>: 
<font color="Maroon" title="c2">a</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">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="c5">b9</font>,<font color="Maroon" title="c7">c9</font>),<font color="Maroon" title="c3">a9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:26_1_2"><span class="lab"><font color="Green" title="E26">A3</font></span></a>, <a class="ref" href="gtarski3.html#T6" onmouseover="rs('gtarski3/T6')" onmouseout="rh()">GTARSKI3:6</a>, <a class="ref" href="gtarski3.html#T10" onmouseover="rs('gtarski3/T10')" onmouseout="rh()">GTARSKI3:10</a></span>;<br/><a NAME="E6:26_1_2"/>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c6">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="c5">b9</font>,<font color="Maroon" title="c7">c9</font>),<font color="Maroon" title="c3">a9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:26"><span class="lab"><font color="Green" title="E24">A1</font></span></a>, <a class="txt" href="#E5:26_1_2"><span class="lab"><font color="Green" title="E28">A6</font></span></a>, <a class="ref" href="gtarski4.html#T3" target="_self" onmouseover="rs('gtarski4/T3')" onmouseout="rh()">Prelim03</a></span>;<br/><span class="kw">hence </span><a NAME="E7:26_1_2"/>
 <a href="gtarski4.html#R1" title="GTARSKI4:pred.1">right_angle</a> <font color="Maroon" title="c3">a9</font>,<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c7">c9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:26_1_2"><span class="lab"><font color="Green" title="E27">A4</font></span></a>, <a class="ref" href="gtarski4.html#T3" target="_self" onmouseover="rs('gtarski4/T3')" onmouseout="rh()">Prelim03</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><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

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