<?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="gtarski2.html#NV5" title="GTARSKI2:NV.5">satisfying_Lower_Dimension_Axiom</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>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">p</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="b2">b</font>,<font color="Olive" title="b3">c</font> &amp;  <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="b1">a</font>,<font color="Olive" title="b3">c</font>),<font color="Olive" title="b4">p</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font>) holds <br/>(  <a href="gtarski4.html#R1" title="GTARSKI4:pred.1">right_angle</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b1">a</font>,<font color="Olive" title="b4">p</font> &amp; ( <font color="Olive" title="b2">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">c</font> implies <font color="Olive" title="b1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">p</font> ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font>, <font color="Maroon" title="c4">c</font>, <font color="Maroon" title="c5">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="gtarski4.html#R1" title="GTARSKI4:pred.1">right_angle</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> &amp;  <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="c2">a</font>,<font color="Maroon" title="c4">c</font>),<font color="Maroon" title="c5">p</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>) implies (  <a href="gtarski4.html#R1" title="GTARSKI4:pred.1">right_angle</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">p</font> &amp; ( <font color="Maroon" title="c3">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">c</font> implies <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">p</font> ) ) )</span><br/>









<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:44"/><span class="lab"><font color="Green" title="E34">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="c3">b</font>,<font color="Maroon" title="c4">c</font>
 <span class="kw">and </span><br/><a NAME="E2:44"/><span class="lab"><font color="Green" title="E35">A2</font></span>: 
 <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="c2">a</font>,<font color="Maroon" title="c4">c</font>),<font color="Maroon" title="c5">p</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">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">b</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">p</font> &amp; ( <font color="Maroon" title="c3">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">c</font> implies <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">p</font> ) )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c6">d</font> =  <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>);<br/>
<span class="kw">set </span><font color="Maroon" title="c7">b9</font> =  <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>);<br/>
<span class="kw">set </span><font color="Maroon" title="c8">c9</font> =  <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">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="c2">a</font>,<span class="p1">(<span class="default"><a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>)</span>)</span>);<br/>
<span class="kw">set </span><font color="Maroon" title="c10">p9</font> =  <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">p</font>);<br/>
<a NAME="E3:44"/><span class="lab"><font color="Green" title="E36">A3</font></span>: 
 <a href="gtarski4.html#R1" title="GTARSKI4:pred.1">right_angle</a>  <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>),<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="44_1"><span class="kw">proof </span></a><div class="add">

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_1_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="E1:44_1_1"/>
( <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> or <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">b</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:44_1_1_1"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</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>  <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>),<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span><br/><div class="add"><a NAME="E2:44_1_1_1"/><span class="kw">then </span>
 <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</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="gtarski3.html#T104" onmouseover="rs('gtarski3/T104')" onmouseout="rh()">GTARSKI3:104</a></span>;<br/><span class="kw">hence </span><a NAME="E3:44_1_1_1"/>
 <a href="gtarski4.html#R1" title="GTARSKI4:pred.1">right_angle</a>  <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>),<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="gtarski4.html#T13" target="_self" onmouseover="rs('gtarski4/T13')" onmouseout="rh()">Satz8p2</a>, <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="44_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:44_1_1_2"/><span class="lab"><font color="Green" title="E37">A4</font></span>: 
<font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">b</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>  <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>),<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span><br/><div class="add"><a NAME="E2:44_1_1_2"/>
 <a href="gtarski3.html#R9" title="GTARSKI3:pred.9">Middle</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</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="E3:44_1_1_2"/><span class="kw">then </span>
 <a href="gtarski1.html#R1" title="GTARSKI1:pred.1">between</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</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/><a NAME="E4:44_1_1_2"/><span class="kw">then </span>
 <a href="gtarski1.html#R6" title="GTARSKI1:pred.6">Collinear</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="gtarski1.html#D17" onmouseover="rs('gtarski1/D17')" onmouseout="rh()">GTARSKI1:def 17</a></span>;<br/><span class="kw">hence </span><a NAME="E5:44_1_1_2"/>
 <a href="gtarski4.html#R1" title="GTARSKI4:pred.1">right_angle</a>  <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>),<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:44"><span class="lab"><font color="Green" title="E34">A1</font></span></a>, <a class="txt" href="#E1:44_1_1_2"><span class="lab"><font color="Green" title="E37">A4</font></span></a>, <a class="ref" href="gtarski4.html#T15" target="_self" onmouseover="rs('gtarski4/T15')" onmouseout="rh()">Satz8p3</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>

</div><span class="kw">end;</span></div>
<a NAME="E4:44"/><span class="lab"><font color="Green" title="E37">A5</font></span>: 
 <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>),<font color="Maroon" title="c3">b</font> <a href="gtarski1.html#R2" title="GTARSKI1:pred.2">equiv</a> <font color="Maroon" title="c3">b</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>)
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="44_2"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:44_2"/>
 <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>),<font color="Maroon" title="c3">b</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="c2">a</font>,<span class="p1">(<span class="default"><a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>)</span>)</span>), <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</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/>
<span class="kw">hence </span><a NAME="E2:44_2"/>
 <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>),<font color="Maroon" title="c3">b</font> <a href="gtarski1.html#R2" title="GTARSKI1:pred.2">equiv</a> <font color="Maroon" title="c3">b</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="gtarski3.html#T101" onmouseover="rs('gtarski3/T101')" onmouseout="rh()">GTARSKI3:101</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="E5:44"/><span class="lab"><font color="Green" title="E38">A6</font></span>: 
 <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>),<font color="Maroon" title="c4">c</font> <a href="gtarski1.html#R2" title="GTARSKI1:pred.2">equiv</a> <font color="Maroon" title="c3">b</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>)
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="44_3"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:44_3"/>
 <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>),<font color="Maroon" title="c4">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="c2">a</font>,<span class="p1">(<span class="default"><a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>)</span>)</span>), <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">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/>
<span class="kw">hence </span><a NAME="E2:44_3"/>
 <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>),<font color="Maroon" title="c4">c</font> <a href="gtarski1.html#R2" title="GTARSKI1:pred.2">equiv</a> <font color="Maroon" title="c3">b</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="gtarski3.html#T101" onmouseover="rs('gtarski3/T101')" onmouseout="rh()">GTARSKI3:101</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="E6:44"/>
 <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>),<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> <a href="gtarski1.html#R3" title="GTARSKI1:pred.3">cong</a> <font color="Maroon" title="c3">b</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>), <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>)
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="44_4"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:44_4"/>
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">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="c2">a</font>,<font color="Maroon" title="c3">b</font>), <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">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/>
<span class="kw">hence </span><a NAME="E2:44_4"/>
 <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>),<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> <a href="gtarski1.html#R3" title="GTARSKI1:pred.3">cong</a> <font color="Maroon" title="c3">b</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>), <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:44"><span class="lab"><font color="Green" title="E37">A5</font></span></a>, <a class="txt" href="#E5:44"><span class="lab"><font color="Green" title="E38">A6</font></span></a>, <a class="ref" href="gtarski1.html#D3" onmouseover="rs('gtarski1/D3')" onmouseout="rh()">GTARSKI1:def 3</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="E7:44"/><span class="kw">then </span><span class="lab"><font color="Green" title="E39">A7</font></span>: 
 <a href="gtarski4.html#R1" title="GTARSKI4:pred.1">right_angle</a> <font color="Maroon" title="c3">b</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>), <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:44"><span class="lab"><font color="Green" title="E36">A3</font></span></a>, <a class="ref" href="gtarski4.html#T22" target="_self" onmouseover="rs('gtarski4/T22')" onmouseout="rh()">Satz8p10</a></span>;<br/>
<a NAME="E8:44"/><span class="lab"><font color="Green" title="E40">A8</font></span>: 
 <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<span class="p1">(<span class="default"><a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<span class="p1">(<span class="default"><a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>)</span>)</span>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="gtarski4.html#T12" target="_self" onmouseover="rs('gtarski4/T12')" onmouseout="rh()">Prelim12</a>, <a class="ref" href="gtarski3.html#T100" onmouseover="rs('gtarski3/T100')" onmouseout="rh()">GTARSKI3:100</a></span>;<br/>
<a NAME="E9:44"/>
 <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>),<font color="Maroon" title="c5">p</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>),<font color="Maroon" title="c3">b</font> <a href="gtarski3.html#R4" title="GTARSKI3:pred.4">IFS</a>  <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<span class="p1">(<span class="default"><a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>)</span>)</span>), <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">p</font>),<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="44_5"><span class="kw">proof </span></a><div class="add">

<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="44_5_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>  <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>),<font color="Maroon" title="c5">p</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>) &amp;  <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="c2">a</font>,<span class="p1">(<span class="default"><a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>)</span>)</span>), <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">p</font>),<font color="Maroon" title="c4">c</font> &amp;  <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>), <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">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="c2">a</font>,<span class="p1">(<span class="default"><a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>)</span>)</span>),<font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c5">p</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">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="c2">a</font>,<font color="Maroon" title="c5">p</font>),<font color="Maroon" title="c4">c</font> &amp;  <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>),<font color="Maroon" title="c3">b</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="c2">a</font>,<span class="p1">(<span class="default"><a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>)</span>)</span>),<font color="Maroon" title="c3">b</font> &amp;  <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>),<font color="Maroon" title="c3">b</font> <a href="gtarski1.html#R2" title="GTARSKI1:pred.2">equiv</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font> )</span></a><div class="add"><span class="kw">thus </span><a NAME="E1:44_5_1"/>
 <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="c2">a</font>,<font color="Maroon" title="c4">c</font>),<font color="Maroon" title="c5">p</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:44"><span class="lab"><font color="Green" title="E35">A2</font></span></a>, <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"> (  <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="c2">a</font>,<span class="p1">(<span class="default"><a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>)</span>)</span>), <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">p</font>),<font color="Maroon" title="c4">c</font> &amp;  <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>), <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">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="c2">a</font>,<span class="p1">(<span class="default"><a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>)</span>)</span>),<font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c5">p</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">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="c2">a</font>,<font color="Maroon" title="c5">p</font>),<font color="Maroon" title="c4">c</font> &amp;  <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>),<font color="Maroon" title="c3">b</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="c2">a</font>,<span class="p1">(<span class="default"><a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>)</span>)</span>),<font color="Maroon" title="c3">b</font> &amp;  <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>),<font color="Maroon" title="c3">b</font> <a href="gtarski1.html#R2" title="GTARSKI1:pred.2">equiv</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font> )</span><br/><a NAME="E2:44_5_1"/>
 <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="c3">b</font>,<font color="Maroon" title="c4">c</font>),<font color="Maroon" title="c5">p</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:44"><span class="lab"><font color="Green" title="E35">A2</font></span></a>, <a class="ref" href="gtarski3.html#T14" onmouseover="rs('gtarski3/T14')" onmouseout="rh()">GTARSKI3:14</a>, <a class="ref" href="gtarski3.html#D12" onmouseover="rs('gtarski3/D12')" onmouseout="rh()">GTARSKI3:def 12</a></span>;<br/><a NAME="E3:44_5_1"/><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="c2">a</font>,<span class="p1">(<span class="default"><a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>)</span>)</span>), <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">p</font>), <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<span class="p1">(<span class="default"><a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>)</span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="gtarski3.html#T106" onmouseover="rs('gtarski3/T106')" onmouseout="rh()">GTARSKI3:106</a></span>;<br/><span class="kw">hence </span><a NAME="E4:44_5_1"/>
 <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="c2">a</font>,<span class="p1">(<span class="default"><a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>)</span>)</span>), <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">p</font>),<font color="Maroon" title="c4">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="gtarski3.html#T101" onmouseover="rs('gtarski3/T101')" onmouseout="rh()">GTARSKI3:101</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"> (  <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>), <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">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="c2">a</font>,<span class="p1">(<span class="default"><a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>)</span>)</span>),<font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c5">p</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">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="c2">a</font>,<font color="Maroon" title="c5">p</font>),<font color="Maroon" title="c4">c</font> &amp;  <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>),<font color="Maroon" title="c3">b</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="c2">a</font>,<span class="p1">(<span class="default"><a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>)</span>)</span>),<font color="Maroon" title="c3">b</font> &amp;  <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>),<font color="Maroon" title="c3">b</font> <a href="gtarski1.html#R2" title="GTARSKI1:pred.2">equiv</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font> )</span><br/><a NAME="E5:44_5_1"/>
 <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>), <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">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="c2">a</font>,<span class="p1">(<span class="default"><a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>)</span>)</span>), <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<span class="p1">(<span class="default"><a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>)</span>)</span>)
 <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="E6:44_5_1"/><span class="kw">then </span>
 <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>), <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>) <a href="gtarski1.html#R2" title="GTARSKI1:pred.2">equiv</a> <font color="Maroon" title="c4">c</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<span class="p1">(<span class="default"><a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>)</span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="gtarski3.html#T101" onmouseover="rs('gtarski3/T101')" onmouseout="rh()">GTARSKI3:101</a></span>;<br/><span class="kw">hence </span><a NAME="E7:44_5_1"/>
 <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>), <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">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="c2">a</font>,<span class="p1">(<span class="default"><a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>)</span>)</span>),<font color="Maroon" title="c4">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="gtarski3.html#T7" onmouseover="rs('gtarski3/T7')" onmouseout="rh()">GTARSKI3:7</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="c5">p</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">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="c2">a</font>,<font color="Maroon" title="c5">p</font>),<font color="Maroon" title="c4">c</font> &amp;  <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>),<font color="Maroon" title="c3">b</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="c2">a</font>,<span class="p1">(<span class="default"><a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>)</span>)</span>),<font color="Maroon" title="c3">b</font> &amp;  <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>),<font color="Maroon" title="c3">b</font> <a href="gtarski1.html#R2" title="GTARSKI1:pred.2">equiv</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font> )</span><br/><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="44_5_1_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"> ( <font color="Maroon" title="c5">p</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">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="c2">a</font>,<font color="Maroon" title="c5">p</font>), <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<span class="p1">(<span class="default"><a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>)</span>)</span>) &amp;  <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">p</font>), <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<span class="p1">(<span class="default"><a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>)</span>)</span>) <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="c2">a</font>,<font color="Maroon" title="c5">p</font>),<font color="Maroon" title="c4">c</font> )</span></a><div class="add"><span class="kw">thus </span><a NAME="E1:44_5_1_1"/>
<font color="Maroon" title="c5">p</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">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="c2">a</font>,<font color="Maroon" title="c5">p</font>), <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<span class="p1">(<span class="default"><a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>)</span>)</span>)
 <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>; <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#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">p</font>), <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<span class="p1">(<span class="default"><a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>)</span>)</span>) <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="c2">a</font>,<font color="Maroon" title="c5">p</font>),<font color="Maroon" title="c4">c</font></span><br/><a NAME="E2:44_5_1_1"/><span class="lab"><font color="Green" title="E41">A9</font></span>: 
<font color="Maroon" title="c5">p</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>) <a href="gtarski1.html#R2" title="GTARSKI1:pred.2">equiv</a> <font color="Maroon" title="c5">p</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:44"><span class="lab"><font color="Green" title="E35">A2</font></span></a>, <a class="ref" href="gtarski3.html#D12" onmouseover="rs('gtarski3/D12')" onmouseout="rh()">GTARSKI3:def 12</a></span>;<br/><a NAME="E3:44_5_1_1"/>
<font color="Maroon" title="c5">p</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">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="c2">a</font>,<font color="Maroon" title="c5">p</font>), <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<span class="p1">(<span class="default"><a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>)</span>)</span>)
 <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="E4:44_5_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E42">A10</font></span>: 
<font color="Maroon" title="c5">p</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">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="c2">a</font>,<font color="Maroon" title="c5">p</font>),<font color="Maroon" title="c4">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="gtarski3.html#T101" onmouseover="rs('gtarski3/T101')" onmouseout="rh()">GTARSKI3:101</a></span>;<br/><a NAME="E5:44_5_1_1"/>
<font color="Maroon" title="c5">p</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">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="c2">a</font>,<font color="Maroon" title="c5">p</font>), <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<span class="p1">(<span class="default"><a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>)</span>)</span>)
 <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="E6:44_5_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">p</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">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="c2">a</font>,<font color="Maroon" title="c5">p</font>), <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<span class="p1">(<span class="default"><a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>)</span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:44_5_1_1"><span class="lab"><font color="Green" title="E41">A9</font></span></a>, <a class="ref" href="gtarski3.html#T5" onmouseover="rs('gtarski3/T5')" onmouseout="rh()">GTARSKI3:5</a></span>;<br/><a NAME="E7:44_5_1_1"/><span class="kw">then </span>
 <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">p</font>), <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<span class="p1">(<span class="default"><a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>)</span>)</span>) <a href="gtarski1.html#R2" title="GTARSKI1:pred.2">equiv</a> <font color="Maroon" title="c5">p</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>)
 <span class="kw">by</span> <span class="lab"><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="E8:44_5_1_1"/>
 <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">p</font>), <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<span class="p1">(<span class="default"><a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>)</span>)</span>) <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="c2">a</font>,<font color="Maroon" title="c5">p</font>),<font color="Maroon" title="c4">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:44_5_1_1"><span class="lab"><font color="Green" title="E42">A10</font></span></a>, <a class="ref" href="gtarski3.html#T5" onmouseover="rs('gtarski3/T5')" onmouseout="rh()">GTARSKI3:5</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><span class="kw">hence </span><a NAME="E9:44_5_1"/>
<font color="Maroon" title="c5">p</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">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="c2">a</font>,<font color="Maroon" title="c5">p</font>),<font color="Maroon" title="c4">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="gtarski3.html#T5" onmouseover="rs('gtarski3/T5')" onmouseout="rh()">GTARSKI3:5</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"> (  <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>),<font color="Maroon" title="c3">b</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="c2">a</font>,<span class="p1">(<span class="default"><a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>)</span>)</span>),<font color="Maroon" title="c3">b</font> &amp;  <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>),<font color="Maroon" title="c3">b</font> <a href="gtarski1.html#R2" title="GTARSKI1:pred.2">equiv</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font> )</span><br/><a NAME="E10:44_5_1"/>
 <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>),<font color="Maroon" title="c3">b</font> <a href="gtarski1.html#R2" title="GTARSKI1:pred.2">equiv</a> <font color="Maroon" title="c3">b</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<span class="p1">(<span class="default"><a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>)</span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:44"><span class="lab"><font color="Green" title="E40">A8</font></span></a>, <a class="txt" href="#E7:44"><span class="lab"><font color="Green" title="E39">A7</font></span></a>, <a class="ref" href="gtarski3.html#T6" onmouseover="rs('gtarski3/T6')" onmouseout="rh()">GTARSKI3:6</a></span>;<br/><span class="kw">hence </span><a NAME="E11:44_5_1"/>
 <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>),<font color="Maroon" title="c3">b</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="c2">a</font>,<span class="p1">(<span class="default"><a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>)</span>)</span>),<font color="Maroon" title="c3">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="gtarski3.html#T7" onmouseover="rs('gtarski3/T7')" onmouseout="rh()">GTARSKI3:7</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">  <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>),<font color="Maroon" title="c3">b</font> <a href="gtarski1.html#R2" title="GTARSKI1:pred.2">equiv</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font></span><br/><a NAME="E12:44_5_1"/>
 <a href="gtarski3.html#R9" title="GTARSKI3:pred.9">Middle</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">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="E13:44_5_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">b</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>) <a href="gtarski1.html#R2" title="GTARSKI1:pred.2">equiv</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="gtarski3.html#T4" onmouseover="rs('gtarski3/T4')" onmouseout="rh()">GTARSKI3:4</a>, <a class="ref" href="gtarski3.html#D12" onmouseover="rs('gtarski3/D12')" onmouseout="rh()">GTARSKI3:def 12</a></span>;<br/><a NAME="E14:44_5_1"/><span class="kw">then </span>
 <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>),<font color="Maroon" title="c3">b</font> <a href="gtarski1.html#R2" title="GTARSKI1:pred.2">equiv</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="gtarski3.html#T6" onmouseover="rs('gtarski3/T6')" onmouseout="rh()">GTARSKI3:6</a></span>;<br/><span class="kw">hence </span><a NAME="E15:44_5_1"/>
 <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>),<font color="Maroon" title="c3">b</font> <a href="gtarski1.html#R2" title="GTARSKI1:pred.2">equiv</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="gtarski3.html#T7" onmouseover="rs('gtarski3/T7')" onmouseout="rh()">GTARSKI3:7</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>
<span class="kw">hence </span><a NAME="E2:44_5"/>
 <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>),<font color="Maroon" title="c5">p</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>),<font color="Maroon" title="c3">b</font> <a href="gtarski3.html#R4" title="GTARSKI3:pred.4">IFS</a>  <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<span class="p1">(<span class="default"><a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>)</span>)</span>), <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">p</font>),<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="gtarski3.html#D5" onmouseover="rs('gtarski3/D5')" onmouseout="rh()">GTARSKI3:def 5</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="E10:44"/><span class="kw">then </span>
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">p</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="c2">a</font>,<font color="Maroon" title="c5">p</font>),<font color="Maroon" title="c3">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="gtarski3.html#T6" onmouseover="rs('gtarski3/T6')" onmouseout="rh()">GTARSKI3:6</a>, <a class="ref" href="gtarski3.html#T41" onmouseover="rs('gtarski3/T41')" onmouseout="rh()">GTARSKI3:41</a></span>;<br/>
<span class="kw">hence </span><a NAME="E11:44"/>
 <a href="gtarski4.html#R1" title="GTARSKI4:pred.1">right_angle</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">p</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="gtarski3.html#T7" onmouseover="rs('gtarski3/T7')" onmouseout="rh()">GTARSKI3:7</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="c3">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">c</font> implies <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">p</font> )</span><br/>

<span class="kw">thus </span><a NAME="E12:44"/>
( <font color="Maroon" title="c3">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">c</font> implies <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">p</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"> verum</span><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="44_6"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:44_6"/><span class="lab"><font color="Green" title="E41">A11</font></span>: 
<font color="Maroon" title="c3">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">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"> <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">p</font></span><br/>

<span class="kw">assume </span><a NAME="E2:44_6"/><span class="lab"><font color="Green" title="E42">A12</font></span>: 
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">p</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"> contradiction</span><br/>

<font color="Maroon" title="c4">c</font> = 
 <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<span class="p1">(<span class="default"><a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="gtarski3.html#T101" onmouseover="rs('gtarski3/T101')" onmouseout="rh()">GTARSKI3:101</a></span>
<br/>.= 
 <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:44_6"><span class="lab"><font color="Green" title="E42">A12</font></span></a>, <a class="txt" href="#E2:44"><span class="lab"><font color="Green" title="E35">A2</font></span></a>, <a class="ref" href="gtarski3.html#D13" onmouseover="rs('gtarski3/D13')" onmouseout="rh()">GTARSKI3:def 13</a></span>
;<br/>
<a NAME="E4:44_6"/><span class="kw">then </span>
 <a href="gtarski3.html#R9" title="GTARSKI3:pred.9">Middle</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">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/>
<span class="kw">hence </span><a NAME="E5:44_6"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="ref" href="gtarski3.html#T97" onmouseover="rs('gtarski3/T97')" onmouseout="rh()">GTARSKI3:97</a>, <a class="txt" href="#E1:44_6"><span class="lab"><font color="Green" title="E41">A11</font></span></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>
