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

<span class="kw">let </span><font color="Maroon" title="c1">C1</font>, <font color="Maroon" title="c2">C2</font> be   <a href="cat_6.html#NM2" title="CAT_6:NM.2">category</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"> <span class="p1">(<span class="default"><a href="cat_6.html#K12" title="CAT_6:func.12">id</a> <font color="Maroon" title="c1">C1</font></span>)</span> <a href="cat_8.html#K11" title="CAT_8:func.11">[x]</a> <span class="p1">(<span class="default"><a href="cat_6.html#K12" title="CAT_6:func.12">id</a> <font color="Maroon" title="c2">C2</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="cat_6.html#K12" title="CAT_6:func.12">id</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K8" title="CAT_8:func.8">[x]</a> <font color="Maroon" title="c2">C2</font></span>)</span></span><br/>

<span class="lab"><font color="Green" title="E45">A1</font></span>: <span class="p1">(<span class="default"><a href="cat_6.html#K12" title="CAT_6:func.12">id</a> <font color="Maroon" title="c1">C1</font></span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <span class="p1">(<span class="default"><a href="cat_8.html#K9" title="CAT_8:func.9">pr1</a> (<font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font>)</span>)</span> = 
 <a href="cat_8.html#K9" title="CAT_8:func.9">pr1</a> (<font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_7.html#T11" onmouseover="rs('cat_7/T11')" onmouseout="rh()">CAT_7:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="cat_8.html#K9" title="CAT_8:func.9">pr1</a> (<font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <span class="p1">(<span class="default"><a href="cat_6.html#K12" title="CAT_6:func.12">id</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K8" title="CAT_8:func.8">[x]</a> <font color="Maroon" title="c2">C2</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_7.html#T11" onmouseover="rs('cat_7/T11')" onmouseout="rh()">CAT_7:11</a></span>
;<br/>
<span class="p1">(<span class="default"><a href="cat_6.html#K12" title="CAT_6:func.12">id</a> <font color="Maroon" title="c2">C2</font></span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <span class="p1">(<span class="default"><a href="cat_8.html#K10" title="CAT_8:func.10">pr2</a> (<font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font>)</span>)</span> = 
 <a href="cat_8.html#K10" title="CAT_8:func.10">pr2</a> (<font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_7.html#T11" onmouseover="rs('cat_7/T11')" onmouseout="rh()">CAT_7:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="cat_8.html#K10" title="CAT_8:func.10">pr2</a> (<font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <span class="p1">(<span class="default"><a href="cat_6.html#K12" title="CAT_6:func.12">id</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K8" title="CAT_8:func.8">[x]</a> <font color="Maroon" title="c2">C2</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_7.html#T11" onmouseover="rs('cat_7/T11')" onmouseout="rh()">CAT_7:11</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E3:85"/>
<span class="p1">(<span class="default"><a href="cat_6.html#K12" title="CAT_6:func.12">id</a> <font color="Maroon" title="c1">C1</font></span>)</span> <a href="cat_8.html#K11" title="CAT_8:func.11">[x]</a> <span class="p1">(<span class="default"><a href="cat_6.html#K12" title="CAT_6:func.12">id</a> <font color="Maroon" title="c2">C2</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="cat_6.html#K12" title="CAT_6:func.12">id</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K8" title="CAT_8:func.8">[x]</a> <font color="Maroon" title="c2">C2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:85"><span class="lab"><font color="Green" title="E45">A1</font></span></a>, <a class="ref" href="cat_8.html#D22" target="_self" onmouseover="rs('cat_8/D22')" onmouseout="rh()">Def22</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>
