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<span class="kw">set </span><font color="Maroon" title="c1">C</font> =  <a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 1;<br/>
<span class="kw">take </span>
 <a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 1
; <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"> (  <a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 1 is  <a href="cat_6.html#V1" title="CAT_6:attr.1">strict</a>  &amp;  not  <a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 1 is  <a href="cat_8.html#V6" title="CAT_8:attr.6">initial</a>  )</span><br/>

<a NAME="E1:51_2_1"/>
 ex <font color="Olive" title="b1">C1</font> being   <a href="cat_6.html#NM2" title="CAT_6:NM.2">category</a> st <br/> for <font color="Olive" title="b2">F</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 1</span>)</span>,<font color="Olive" title="b1">C1</font>  holds <br/>(  not <font color="Olive" title="b2">F</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  or  ex <font color="Olive" title="b3">F1</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 1</span>)</span>,<font color="Olive" title="b1">C1</font> st <br/>( <font color="Olive" title="b3">F1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp;  not <font color="Olive" title="b2">F</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b3">F1</font> ) )
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="51_2_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">take </span>
 <a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</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">  for <font color="Olive" title="b1">F</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>  holds <br/>(  not <font color="Olive" title="b1">F</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  or  ex <font color="Olive" title="b2">F1</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> st <br/>( <font color="Olive" title="b2">F1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp;  not <font color="Olive" title="b1">F</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b2">F1</font> ) )</span><br/>

<span class="kw">thus </span><a NAME="E1:51_2_1_1"/>
 for <font color="Olive" title="b1">F</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>  holds <br/>(  not <font color="Olive" title="b1">F</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  or  ex <font color="Olive" title="b2">F1</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> st <br/>( <font color="Olive" title="b2">F1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp;  not <font color="Olive" title="b1">F</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b2">F1</font> ) )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_6.html#T31" onmouseover="rs('cat_6/T31')" onmouseout="rh()">CAT_6:31</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><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E2:51_2_1"/>
(  <a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 1 is  <a href="cat_6.html#V1" title="CAT_6:attr.1">strict</a>  &amp;  not  <a href="cat_7.html#K6" title="CAT_7:func.6">OrdC</a> 1 is  <a href="cat_8.html#V6" title="CAT_8:attr.6">initial</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"> verum</span><br/>


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