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<span class="kw">let </span><font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c2">b</font>, <font color="Maroon" title="c3">c</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">R</font>, <font color="Olive" title="b2">S</font> being   <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a>  st <font color="Olive" title="b1">R</font> is  <a href="wellord1.html#V2" title="WELLORD1:attr.2">well-ordering</a>  &amp; <font color="Olive" title="b2">S</font> is  <a href="wellord1.html#V2" title="WELLORD1:attr.2">well-ordering</a>  &amp; <font color="Maroon" title="c1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <font color="Olive" title="b1">R</font> &amp; <font color="Maroon" title="c2">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <font color="Olive" title="b2">S</font> &amp; <font color="Maroon" title="c3">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <font color="Olive" title="b2">S</font> &amp; <font color="Olive" title="b1">R</font>,<font color="Olive" title="b2">S</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="wellord1.html#R4" title="WELLORD1:pred.4">are_isomorphic</a>  &amp; <font color="Olive" title="b1">R</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">R</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Olive" title="b2">S</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="wellord1.html#R4" title="WELLORD1:pred.4">are_isomorphic</a>  holds <br/>( <font color="Olive" title="b2">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c3">c</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c2">b</font> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c2">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">S</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">R</font>, <font color="Maroon" title="c5">S</font> be   <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">R</font> is  <a href="wellord1.html#V2" title="WELLORD1:attr.2">well-ordering</a>  &amp; <font color="Maroon" title="c5">S</font> is  <a href="wellord1.html#V2" title="WELLORD1:attr.2">well-ordering</a>  &amp; <font color="Maroon" title="c1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <font color="Maroon" title="c4">R</font> &amp; <font color="Maroon" title="c2">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <font color="Maroon" title="c5">S</font> &amp; <font color="Maroon" title="c3">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <font color="Maroon" title="c5">S</font> &amp; <font color="Maroon" title="c4">R</font>,<font color="Maroon" title="c5">S</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="wellord1.html#R4" title="WELLORD1:pred.4">are_isomorphic</a>  &amp; <font color="Maroon" title="c4">R</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">R</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c5">S</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="wellord1.html#R4" title="WELLORD1:pred.4">are_isomorphic</a>  implies ( <font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c3">c</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c2">b</font> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c2">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">S</font> ) )</span><br/>









<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:62"/><span class="lab"><font color="Green" title="E57">A1</font></span>: 
<font color="Maroon" title="c4">R</font> is  <a href="wellord1.html#V2" title="WELLORD1:attr.2">well-ordering</a> 
 <span class="kw">and </span><br/><a NAME="E2:62"/><span class="lab"><font color="Green" title="E58">A2</font></span>: 
<font color="Maroon" title="c5">S</font> is  <a href="wellord1.html#V2" title="WELLORD1:attr.2">well-ordering</a> 
 <span class="kw">and </span><br/><a NAME="E3:62"/><span class="lab"><font color="Green" title="E59">A3</font></span>: 
<font color="Maroon" title="c1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <font color="Maroon" title="c4">R</font>
 <span class="kw">and </span><br/><a NAME="E4:62"/><span class="lab"><font color="Green" title="E60">A4</font></span>: 
<font color="Maroon" title="c2">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <font color="Maroon" title="c5">S</font>
 <span class="kw">and </span><br/><a NAME="E5:62"/><span class="lab"><font color="Green" title="E61">A5</font></span>: 
<font color="Maroon" title="c3">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <font color="Maroon" title="c5">S</font>
 <span class="kw">and </span><br/><a NAME="E6:62"/><span class="lab"><font color="Green" title="E62">A6</font></span>: 
<font color="Maroon" title="c4">R</font>,<font color="Maroon" title="c5">S</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="wellord1.html#R4" title="WELLORD1:pred.4">are_isomorphic</a> 
 <span class="kw">and </span><br/><a NAME="E7:62"/><span class="lab"><font color="Green" title="E63">A7</font></span>: 
<font color="Maroon" title="c4">R</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">R</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c5">S</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="wellord1.html#R4" title="WELLORD1:pred.4">are_isomorphic</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c3">c</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c2">b</font> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c2">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">S</font> )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c6">Q</font> = <font color="Maroon" title="c5">S</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c2">b</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">F1</font> =  <a href="wellord1.html#K3" title="WELLORD1:func.3">canonical_isomorphism_of</a> (<font color="Maroon" title="c4">R</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span>);<br/>
<a NAME="E8:62"/><span class="lab"><font color="Green" title="E64">A8</font></span>: 
 <a href="wellord1.html#K3" title="WELLORD1:func.3">canonical_isomorphism_of</a> (<font color="Maroon" title="c4">R</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span>) <a href="wellord1.html#R3" title="WELLORD1:pred.3">is_isomorphism_of</a> <font color="Maroon" title="c4">R</font>,<font color="Maroon" title="c5">S</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c2">b</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:62"><span class="lab"><font color="Green" title="E57">A1</font></span></a>, <a class="txt" href="#E6:62"><span class="lab"><font color="Green" title="E62">A6</font></span></a>, <a class="ref" href="wellord1.html#D9" target="_self" title="WELLORD1:def.9">Def9</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c8">d</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E10:62"/><span class="lab"><font color="Green" title="E65">A9</font></span>: 
<font color="Maroon" title="c8">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span>
 <span class="kw">and </span><br/><a NAME="E11:62"/><span class="lab"><font color="Green" title="E66">A10</font></span>: 
<span class="p1">(<span class="default"><a href="wellord1.html#K3" title="WELLORD1:func.3">canonical_isomorphism_of</a> (<font color="Maroon" title="c4">R</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span>)</span>)</span> <a href="relat_1.html#K9" title="RELAT_1:func.9">.:</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">R</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c8">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:62"><span class="lab"><font color="Green" title="E59">A3</font></span></a>, <a class="ref" href="wellord1.html#T49" target="_self" title="WELLORD1:th.49">Th60</a></span>;<br/>
<a NAME="E12:62"/><span class="lab"><font color="Green" title="E67">A11</font></span>: 
<font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:62"><span class="lab"><font color="Green" title="E58">A2</font></span></a>, <a class="ref" href="wellord1.html#T32" target="_self" title="WELLORD1:th.32">Th40</a></span>;<br/>
<a NAME="E13:62"/><span class="kw">then </span><span class="lab"><font color="Green" title="E68">A12</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c8">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c8">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:62"><span class="lab"><font color="Green" title="E58">A2</font></span></a>, <a class="txt" href="#E10:62"><span class="lab"><font color="Green" title="E65">A9</font></span></a>, <a class="ref" href="wellord1.html#T27" target="_self" title="WELLORD1:th.27">Th35</a></span>;<br/>
<a NAME="E14:62"/><span class="lab"><font color="Green" title="E69">A13</font></span>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="wellord1.html#K3" title="WELLORD1:func.3">canonical_isomorphism_of</a> (<font color="Maroon" title="c4">R</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c2">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:62"><span class="lab"><font color="Green" title="E64">A8</font></span></a>, <a class="txt" href="#E12:62"><span class="lab"><font color="Green" title="E67">A11</font></span></a>, <a class="ref" href="wellord1.html#D7" target="_self" title="WELLORD1:def.7">Def7</a></span>;<br/>
<a NAME="E15:62"/><span class="kw">then </span><span class="lab"><font color="Green" title="E70">A14</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c8">d</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c2">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:62"><span class="lab"><font color="Green" title="E66">A10</font></span></a>, <a class="ref" href="relat_1.html#T111" title="RELAT_1:th.111">RELAT_1:111</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">T</font> = <font color="Maroon" title="c5">S</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c3">c</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">P</font> = <font color="Maroon" title="c4">R</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">R</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c1">a</font></span>)</span>;<br/>
<a NAME="E16:62"/><span class="lab"><font color="Green" title="E71">A15</font></span>: 
<font color="Maroon" title="c5">S</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c3">c</font></span>)</span>,<font color="Maroon" title="c4">R</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">R</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="wellord1.html#R4" title="WELLORD1:pred.4">are_isomorphic</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:62"><span class="lab"><font color="Green" title="E63">A7</font></span></a>, <a class="ref" href="wellord1.html#T40" target="_self" title="WELLORD1:th.40">Th50</a></span>;<br/>
<a NAME="E17:62"/><span class="lab"><font color="Green" title="E72">A16</font></span>: 
<font color="Maroon" title="c8">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <font color="Maroon" title="c5">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:62"><span class="lab"><font color="Green" title="E65">A9</font></span></a>, <a class="ref" href="wellord1.html#T12" target="_self" title="WELLORD1:th.12">Th19</a></span>;<br/>
<a NAME="E18:62"/>
<font color="Maroon" title="c4">R</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c1">a</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <font color="Maroon" title="c4">R</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="wellord1.html#T9" target="_self" title="WELLORD1:th.9">Th13</a></span>;<br/>
<a NAME="E19:62"/><span class="kw">then </span>
<font color="Maroon" title="c4">R</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">R</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c1">a</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="wellord1.html#K3" title="WELLORD1:func.3">canonical_isomorphism_of</a> (<font color="Maroon" title="c4">R</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span>)</span>)</span> <a href="relat_1.html#K9" title="RELAT_1:func.9">.:</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">R</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c1">a</font></span>)</span></span>)</span> <a href="wellord1.html#R4" title="WELLORD1:pred.4">are_isomorphic</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:62"><span class="lab"><font color="Green" title="E57">A1</font></span></a>, <a class="txt" href="#E8:62"><span class="lab"><font color="Green" title="E64">A8</font></span></a>, <a class="ref" href="wellord1.html#T48" target="_self" title="WELLORD1:th.48">Th59</a></span>;<br/>
<a NAME="E20:62"/><span class="kw">then </span>
<font color="Maroon" title="c5">S</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c3">c</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c8">d</font></span>)</span> <a href="wellord1.html#R4" title="WELLORD1:pred.4">are_isomorphic</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:62"><span class="lab"><font color="Green" title="E66">A10</font></span></a>, <a class="txt" href="#E16:62"><span class="lab"><font color="Green" title="E71">A15</font></span></a>, <a class="ref" href="wellord1.html#T42" target="_self" title="WELLORD1:th.42">Th52</a></span>;<br/>
<a NAME="E21:62"/><span class="kw">then </span>
<font color="Maroon" title="c5">S</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c3">c</font></span>)</span>,<font color="Maroon" title="c5">S</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c8">d</font></span>)</span> <a href="wellord1.html#R4" title="WELLORD1:pred.4">are_isomorphic</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:62"><span class="lab"><font color="Green" title="E66">A10</font></span></a>, <a class="txt" href="#E13:62"><span class="lab"><font color="Green" title="E68">A12</font></span></a>, <a class="txt" href="#E14:62"><span class="lab"><font color="Green" title="E69">A13</font></span></a>, <a class="ref" href="wellord1.html#T22" target="_self" title="WELLORD1:th.22">Th29</a>, <a class="ref" href="relat_1.html#T111" title="RELAT_1:th.111">RELAT_1:111</a></span>;<br/>
<span class="kw">hence </span><a NAME="E22:62"/>
<font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c3">c</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c2">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:62"><span class="lab"><font color="Green" title="E58">A2</font></span></a>, <a class="txt" href="#E5:62"><span class="lab"><font color="Green" title="E61">A5</font></span></a>, <a class="txt" href="#E13:62"><span class="lab"><font color="Green" title="E68">A12</font></span></a>, <a class="txt" href="#E15:62"><span class="lab"><font color="Green" title="E70">A14</font></span></a>, <a class="txt" href="#E17:62"><span class="lab"><font color="Green" title="E72">A16</font></span></a>, <a class="ref" href="wellord1.html#T47" target="_self" title="WELLORD1:th.47">Th58</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c2">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">S</font></span><br/>

<span class="kw">hence </span><a NAME="E23:62"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c2">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">S</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:62"><span class="lab"><font color="Green" title="E58">A2</font></span></a>, <a class="txt" href="#E4:62"><span class="lab"><font color="Green" title="E60">A4</font></span></a>, <a class="txt" href="#E5:62"><span class="lab"><font color="Green" title="E61">A5</font></span></a>, <a class="ref" href="wellord1.html#T29" target="_self" title="WELLORD1:th.29">Th37</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
