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

<span class="kw">let </span><font color="Maroon" title="c1">UN</font> be   <a href="classes2.html#NM1" title="CLASSES2:NM.1">Universe</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> being   <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</a><br/>  for <font color="Olive" title="b2">b</font> being   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <span class="p1">(<span class="default"><a href="modcat_1.html#K12" title="MODCAT_1:func.12">LModCat</a> (<font color="Maroon" title="c1">UN</font>,<font color="Olive" title="b1">R</font>)</span>)</span><br/>  for <font color="Olive" title="b3">b9</font> being    <a href="modcat_1.html#M2" title="MODCAT_1:mode.2">Element</a> of  <a href="modcat_1.html#K3" title="MODCAT_1:func.3">LModObjects</a> (<font color="Maroon" title="c1">UN</font>,<font color="Olive" title="b1">R</font>)  st <font color="Olive" title="b2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">b9</font> holds <br/> <a href="cat_1.html#K2" title="CAT_1:func.2">id</a> <font color="Olive" title="b2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modcat_1.html#K7" title="MODCAT_1:func.7">ID</a> <font color="Olive" title="b3">b9</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">R</font> be   <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</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">b</font> being   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <span class="p1">(<span class="default"><a href="modcat_1.html#K12" title="MODCAT_1:func.12">LModCat</a> (<font color="Maroon" title="c1">UN</font>,<font color="Maroon" title="c2">R</font>)</span>)</span><br/>  for <font color="Olive" title="b2">b9</font> being    <a href="modcat_1.html#M2" title="MODCAT_1:mode.2">Element</a> of  <a href="modcat_1.html#K3" title="MODCAT_1:func.3">LModObjects</a> (<font color="Maroon" title="c1">UN</font>,<font color="Maroon" title="c2">R</font>)  st <font color="Olive" title="b1">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b9</font> holds <br/> <a href="cat_1.html#K2" title="CAT_1:func.2">id</a> <font color="Olive" title="b1">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modcat_1.html#K7" title="MODCAT_1:func.7">ID</a> <font color="Olive" title="b2">b9</font></span><br/>



<span class="kw">set </span><font color="Maroon" title="c3">C</font> =  <a href="modcat_1.html#K12" title="MODCAT_1:func.12">LModCat</a> (<font color="Maroon" title="c1">UN</font>,<font color="Maroon" title="c2">R</font>);<br/>
<span class="kw">set </span><font color="Maroon" title="c4">V</font> =  <a href="modcat_1.html#K3" title="MODCAT_1:func.3">LModObjects</a> (<font color="Maroon" title="c1">UN</font>,<font color="Maroon" title="c2">R</font>);<br/>
<span class="kw">let </span><font color="Maroon" title="c5">b</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <span class="p1">(<span class="default"><a href="modcat_1.html#K12" title="MODCAT_1:func.12">LModCat</a> (<font color="Maroon" title="c1">UN</font>,<font color="Maroon" title="c2">R</font>)</span>)</span>; <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">b9</font> being    <a href="modcat_1.html#M2" title="MODCAT_1:mode.2">Element</a> of  <a href="modcat_1.html#K3" title="MODCAT_1:func.3">LModObjects</a> (<font color="Maroon" title="c1">UN</font>,<font color="Maroon" title="c2">R</font>)  st <font color="Maroon" title="c5">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">b9</font> holds <br/> <a href="cat_1.html#K2" title="CAT_1:func.2">id</a> <font color="Maroon" title="c5">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modcat_1.html#K7" title="MODCAT_1:func.7">ID</a> <font color="Olive" title="b1">b9</font></span><br/><span class="kw">let </span><font color="Maroon" title="c6">b9</font> be    <a href="modcat_1.html#M2" title="MODCAT_1:mode.2">Element</a> of  <a href="modcat_1.html#K3" title="MODCAT_1:func.3">LModObjects</a> (<font color="Maroon" title="c1">UN</font>,<font color="Maroon" title="c2">R</font>); <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">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">b9</font> implies  <a href="cat_1.html#K2" title="CAT_1:func.2">id</a> <font color="Maroon" title="c5">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modcat_1.html#K7" title="MODCAT_1:func.7">ID</a> <font color="Maroon" title="c6">b9</font> )</span><br/>



<span class="kw">assume </span><a NAME="E1:34"/>
<font color="Maroon" title="c5">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">b9</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="cat_1.html#K2" title="CAT_1:func.2">id</a> <font color="Maroon" title="c5">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modcat_1.html#K7" title="MODCAT_1:func.7">ID</a> <font color="Maroon" title="c6">b9</font></span><br/>

<span class="kw">hence </span> <a href="cat_1.html#K2" title="CAT_1:func.2">id</a> <font color="Maroon" title="c5">b</font> = 
<span class="p1">(<span class="default"><a href="modcat_1.html#K10" title="MODCAT_1:func.10">ID</a> <span class="p2">(<span class="default"><a href="modcat_1.html#K3" title="MODCAT_1:func.3">LModObjects</a> (<font color="Maroon" title="c1">UN</font>,<font color="Maroon" title="c2">R</font>)</span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">b9</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_1.html#D2" title="CAT_1:def.2">CAT_1:def 2</a></span>
<br/>.= 
 <a href="modcat_1.html#K7" title="MODCAT_1:func.7">ID</a> <font color="Maroon" title="c6">b9</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="modcat_1.html#D13" target="_self" title="MODCAT_1:def.13">Def13</a></span>
;<br/> <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>
