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<b>let </b><font color="Maroon" title="c1">V</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">C</font> be   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a>;<br/><b>let </b><font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">C</font>;<br/>







<b>assume </b><a NAME="E1:88"/><i><font color="Green" title="E63">A1</font></i>: 
 <a href="ens_1.html#K17" title="ENS_1:func.17">Hom</a> <font color="Maroon" title="c2">C</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">V</font>
 ;<br/>

<a NAME="E2:88"/>
 <a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ens_1.html#K17" title="ENS_1:func.17">Hom</a> <font color="Maroon" title="c2">C</font>
 
;<br/>
<b>then reconsider </b><font color="Maroon" title="c5">A</font> =  <a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">V</font> <b>by </b><i><a class="txt" href="ens_1.html#E1:88"><i><font color="Green" title="E63">A1</font></i></a></i>;<br/>
<b>set </b><font color="Maroon" title="c6">d</font> =  <a href="ens_1.html#K13" title="ENS_1:func.13">@</a> <font color="Maroon" title="c5">A</font>;<br/>
<span class="p1">(<span class="default"><a href="ens_1.html#K24" title="ENS_1:func.24">hom?-</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c3">a</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10" title="CAT_1:func.10">id</a> <font color="Maroon" title="c4">b</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ens_1.html#K20" title="ENS_1:func.20">hom?-</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10" title="CAT_1:func.10">id</a> <font color="Maroon" title="c4">b</font></span>)</span>
<b>by </b><i><a class="txt" href="ens_1.html#E1:88"><i><font color="Green" title="E63">A1</font></i></a>, <a class="ref" href="ens_1.html#D26" target="_self" title="ENS_1:def.26">Def26</a></i>
<br/>.= 
 <a href="cat_1.html#K10" title="CAT_1:func.10">id</a> <span class="p1">(<span class="default"><a href="ens_1.html#K13" title="ENS_1:func.13">@</a> <font color="Maroon" title="c5">A</font></span>)</span>
<b>by </b><i><a class="txt" href="ens_1.html#E1:88"><i><font color="Green" title="E63">A1</font></i></a>, <a class="txt" href="ens_1.html#E79"><i><font color="Green" title="E46">Lm8</font></i></a></i>
;<br/>
<b>hence </b><a NAME="E5:88"/>
<span class="p1">(<span class="default"><a href="cat_1.html#K12" title="CAT_1:func.12">Obj</a> <span class="p2">(<span class="default"><a href="ens_1.html#K24" title="ENS_1:func.24">hom?-</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c3">a</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>
 <b>by </b><i><a class="ref" href="cat_1.html#T103" title="CAT_1:th.103">CAT_1:103</a></i>;<br/>


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