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<span class="kw">set </span><font color="Maroon" title="c1">o</font> =  the    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>
<span class="kw">take </span>
 <a href="cat_1.html#K4" title="CAT_1:func.4">1Cat</a> ( the    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> , the    <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">  <a href="cat_1.html#K4" title="CAT_1:func.4">1Cat</a> ( the    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> , the    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ) is  <a href="nattra_1.html#V2" title="NATTRA_1:attr.2">discrete</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c2">f</font> be   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><a href="cat_1.html#K4" title="CAT_1:func.4">1Cat</a> ( the    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> , the    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> )</span>)</span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="nattra_1.html#D18" target="_self" title="NATTRA_1:def.18">NATTRA_1:def 18</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">a</font> being   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <span class="p1">(<span class="default"><a href="cat_1.html#K4" title="CAT_1:func.4">1Cat</a> ( the    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> , the    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> )</span>)</span> st <font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Olive" title="b1">a</font></span><br/>

<span class="kw">set </span><font color="Maroon" title="c3">a</font> =  the   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <span class="p1">(<span class="default"><a href="cat_1.html#K4" title="CAT_1:func.4">1Cat</a> ( the    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> , the    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> )</span>)</span>;<br/>
<span class="kw">take </span>
 the   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <span class="p1">(<span class="default"><a href="cat_1.html#K4" title="CAT_1:func.4">1Cat</a> ( the    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> , the    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> )</span>)</span>
; <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="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K6" title="CAT_1:func.6">id</a>  the   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <span class="p1">(<span class="default"><a href="cat_1.html#K4" title="CAT_1:func.4">1Cat</a> ( the    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> , the    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> )</span>)</span></span><br/>

<span class="kw">thus </span><font color="Maroon" title="c2">f</font> = 
 the    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>
<br/>.= 
 <a href="cat_1.html#K6" title="CAT_1:func.6">id</a>  the   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <span class="p1">(<span class="default"><a href="cat_1.html#K4" title="CAT_1:func.4">1Cat</a> ( the    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> , the    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> )</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</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/>


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