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<span class="kw">consider </span><font color="Maroon" title="c2">C</font> being   <a href="cat_6.html#V1" title="CAT_6:attr.1">strict</a>   <a href="cat_7.html#V6" title="CAT_7:attr.6">preorder</a>  <a href="cat_6.html#NM2" title="CAT_6:NM.2">category</a><span class="kw"> such that </span><br/><a NAME="E2:63_1_1"/><span class="lab"><font color="Green" title="E36">A1</font></span>: 
(  <a href="cat_6.html#K5" title="CAT_6:func.5">Ob</a> <font color="Maroon" title="c2">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">O</font> &amp; (  for <font color="Olive" title="b1">o1</font>, <font color="Olive" title="b2">o2</font> being   <a href="cat_6.html#NM3" title="CAT_6:NM.3">Object</a> of <font color="Maroon" title="c2">C</font>  st <font color="Olive" title="b1">o1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">o2</font> holds <br/> <a href="cat_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Olive" title="b1">o1</font>,<font color="Olive" title="b2">o2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">o1</font>,<font color="Olive" title="b2">o2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> ) &amp;  <a href="cat_7.html#K5" title="CAT_7:func.5">RelOb</a> <font color="Maroon" title="c2">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="wellord2.html#K1" title="WELLORD2:func.1">RelIncl</a> <font color="Maroon" title="c1">O</font> &amp;  <a href="cat_6.html#K1" title="CAT_6:func.1">Mor</a> <font color="Maroon" title="c2">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">O</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"> { <span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">o1</font>,<font color="Olive" title="b2">o2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">o1</font>, <font color="Olive" title="b2">o2</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">O</font> : <font color="Olive" title="b1">o1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">o2</font> </span> } </span>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_7.html#T37" target="_self" onmouseover="rs('cat_7/T37')" onmouseout="rh()">Th37</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c2">C</font>
; <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"> ( <font color="Maroon" title="c2">C</font> is  <a href="cat_6.html#V1" title="CAT_6:attr.1">strict</a>  &amp; <font color="Maroon" title="c2">C</font> is <font color="Maroon" title="c1">O</font> <a href="cat_7.html#V7" title="CAT_7:attr.7">-ordered</a>  &amp; <font color="Maroon" title="c2">C</font> is  <a href="cat_7.html#V6" title="CAT_7:attr.6">preorder</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E3:63_1_1"/>
( <font color="Maroon" title="c2">C</font> is  <a href="cat_6.html#V1" title="CAT_6:attr.1">strict</a>  &amp; <font color="Maroon" title="c2">C</font> is <font color="Maroon" title="c1">O</font> <a href="cat_7.html#V7" title="CAT_7:attr.7">-ordered</a>  &amp; <font color="Maroon" title="c2">C</font> is  <a href="cat_7.html#V6" title="CAT_7:attr.6">preorder</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:63_1_1"><span class="lab"><font color="Green" title="E36">A1</font></span></a>, <a class="ref" href="wellord1.html#T38" onmouseover="rs('wellord1/T38')" onmouseout="rh()">WELLORD1:38</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/>


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