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<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="Red">::  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="grcat_1.html#K27" title="GRCAT_1:func.27">GroupCat</a> <font color="Maroon" title="c1">UN</font></span>)</span><br/> for <font color="Olive" title="b2">b9</font> being   <a href="grcat_1.html#M2" title="GRCAT_1:mode.2">Element</a> of  <a href="grcat_1.html#K18" title="GRCAT_1:func.18">GroupObjects</a> <font color="Maroon" title="c1">UN</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="grcat_1.html#K22" title="GRCAT_1:func.22">ID</a> <font color="Olive" title="b2">b9</font></span><br/>

<span class="kw">set </span><font color="Maroon" title="c2">C</font> =  <a href="grcat_1.html#K27" title="GRCAT_1:func.27">GroupCat</a> <font color="Maroon" title="c1">UN</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c3">V</font> =  <a href="grcat_1.html#K18" title="GRCAT_1:func.18">GroupObjects</a> <font color="Maroon" title="c1">UN</font>;<br/>
<span class="kw">let </span><font color="Maroon" title="c4">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="grcat_1.html#K27" title="GRCAT_1:func.27">GroupCat</a> <font color="Maroon" title="c1">UN</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">b9</font> being   <a href="grcat_1.html#M2" title="GRCAT_1:mode.2">Element</a> of  <a href="grcat_1.html#K18" title="GRCAT_1:func.18">GroupObjects</a> <font color="Maroon" title="c1">UN</font>  st <font color="Maroon" title="c4">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="c4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="grcat_1.html#K22" title="GRCAT_1:func.22">ID</a> <font color="Olive" title="b1">b9</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">b9</font> be    <a href="grcat_1.html#M2" title="GRCAT_1:mode.2">Element</a> of  <a href="grcat_1.html#K18" title="GRCAT_1:func.18">GroupObjects</a> <font color="Maroon" title="c1">UN</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b9</font> implies  <a href="cat_1.html#K2" title="CAT_1:func.2">id</a> <font color="Maroon" title="c4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="grcat_1.html#K22" title="GRCAT_1:func.22">ID</a> <font color="Maroon" title="c5">b9</font> )</span><br/>



<span class="kw">assume </span><a NAME="E1:103"/>
<font color="Maroon" title="c4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b9</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="cat_1.html#K2" title="CAT_1:func.2">id</a> <font color="Maroon" title="c4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="grcat_1.html#K22" title="GRCAT_1:func.22">ID</a> <font color="Maroon" title="c5">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="c4">b</font> = 
<span class="p1">(<span class="default"><a href="grcat_1.html#K25" title="GRCAT_1:func.25">ID</a> <span class="p2">(<span class="default"><a href="grcat_1.html#K18" title="GRCAT_1:func.18">GroupObjects</a> <font color="Maroon" title="c1">UN</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">b9</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_1.html#D5" title="CAT_1:def.5">CAT_1:def 5</a></span>
<br/>.= 
 <a href="grcat_1.html#K22" title="GRCAT_1:func.22">ID</a> <font color="Maroon" title="c5">b9</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="grcat_1.html#D34" target="_self" title="GRCAT_1:def.34">Def34</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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