<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">C1</font>, <font color="Maroon" title="c2">C2</font> be   <a href="cat_6.html#NM2" title="CAT_6:NM.2">category</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"> <span class="p1">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span> <a href="cat_8.html#NK8" title="CAT_8:NK.8">[|x|]</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>, <a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>), <a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>) <a href="cat_8.html#R2" title="CAT_8:pred.2">is_product_of</a> <font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font></span><br/>

<span class="kw">set </span><font color="Maroon" title="c3">F1</font> = <font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">F2</font> = <font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a> ;<br/>
<a NAME="E1:73"/><span class="lab"><font color="Green" title="E39">A1</font></span>: 
 <a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>) is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_7.html#T52" onmouseover="rs('cat_7/T52')" onmouseout="rh()">CAT_7:52</a></span>;<br/>
<a NAME="E2:73"/><span class="lab"><font color="Green" title="E40">A2</font></span>: 
 <a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>) is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_7.html#T52" onmouseover="rs('cat_7/T52')" onmouseout="rh()">CAT_7:52</a></span>;<br/>
<a NAME="E3:73"/>
 for <font color="Olive" title="b1">D1</font> being   <a href="cat_6.html#NM2" title="CAT_6:NM.2">category</a><br/>  for <font color="Olive" title="b2">G1</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Olive" title="b1">D1</font>,<font color="Maroon" title="c1">C1</font><br/>  for <font color="Olive" title="b3">G2</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Olive" title="b1">D1</font>,<font color="Maroon" title="c2">C2</font>  st <font color="Olive" title="b2">G1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Olive" title="b3">G2</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  holds <br/> ex <font color="Olive" title="b4">H</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Olive" title="b1">D1</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span> <a href="cat_8.html#NK8" title="CAT_8:NK.8">[|x|]</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span></span>)</span> st <br/>( <font color="Olive" title="b4">H</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b4">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b2">G1</font> &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b4">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b3">G2</font> &amp; (  for <font color="Olive" title="b5">H1</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Olive" title="b1">D1</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span> <a href="cat_8.html#NK8" title="CAT_8:NK.8">[|x|]</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span></span>)</span>  st <font color="Olive" title="b5">H1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b5">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b2">G1</font> &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b5">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b3">G2</font> holds <br/><font color="Olive" title="b4">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b5">H1</font> ) )
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="73_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c5">D1</font> be   <a href="cat_6.html#NM2" title="CAT_6:NM.2">category</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">G1</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c5">D1</font>,<font color="Maroon" title="c1">C1</font><br/>  for <font color="Olive" title="b2">G2</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c5">D1</font>,<font color="Maroon" title="c2">C2</font>  st <font color="Olive" title="b1">G1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Olive" title="b2">G2</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  holds <br/> ex <font color="Olive" title="b3">H</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c5">D1</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span> <a href="cat_8.html#NK8" title="CAT_8:NK.8">[|x|]</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span></span>)</span> st <br/>( <font color="Olive" title="b3">H</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b3">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b1">G1</font> &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b3">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b2">G2</font> &amp; (  for <font color="Olive" title="b4">H1</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c5">D1</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span> <a href="cat_8.html#NK8" title="CAT_8:NK.8">[|x|]</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span></span>)</span>  st <font color="Olive" title="b4">H1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b4">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b1">G1</font> &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b4">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b2">G2</font> holds <br/><font color="Olive" title="b3">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b4">H1</font> ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c6">G1</font> be   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c5">D1</font>,<font color="Maroon" title="c1">C1</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">  for <font color="Olive" title="b1">G2</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c5">D1</font>,<font color="Maroon" title="c2">C2</font>  st <font color="Maroon" title="c6">G1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Olive" title="b1">G2</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  holds <br/> ex <font color="Olive" title="b2">H</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c5">D1</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span> <a href="cat_8.html#NK8" title="CAT_8:NK.8">[|x|]</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span></span>)</span> st <br/>( <font color="Olive" title="b2">H</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b2">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c6">G1</font> &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b2">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b1">G2</font> &amp; (  for <font color="Olive" title="b3">H1</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c5">D1</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span> <a href="cat_8.html#NK8" title="CAT_8:NK.8">[|x|]</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span></span>)</span>  st <font color="Olive" title="b3">H1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b3">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c6">G1</font> &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b3">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b1">G2</font> holds <br/><font color="Olive" title="b2">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b3">H1</font> ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c7">G2</font> be   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c5">D1</font>,<font color="Maroon" title="c2">C2</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="c6">G1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Maroon" title="c7">G2</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  implies  ex <font color="Olive" title="b1">H</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c5">D1</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span> <a href="cat_8.html#NK8" title="CAT_8:NK.8">[|x|]</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span></span>)</span> st <br/>( <font color="Olive" title="b1">H</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b1">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c6">G1</font> &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b1">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c7">G2</font> &amp; (  for <font color="Olive" title="b2">H1</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c5">D1</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span> <a href="cat_8.html#NK8" title="CAT_8:NK.8">[|x|]</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span></span>)</span>  st <font color="Olive" title="b2">H1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b2">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c6">G1</font> &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b2">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c7">G2</font> holds <br/><font color="Olive" title="b1">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b2">H1</font> ) ) )</span><br/>





<span class="kw">assume </span><a NAME="E1:73_1"/><span class="lab"><font color="Green" title="E41">A3</font></span>: 
( <font color="Maroon" title="c6">G1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Maroon" title="c7">G2</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</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">  ex <font color="Olive" title="b1">H</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c5">D1</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span> <a href="cat_8.html#NK8" title="CAT_8:NK.8">[|x|]</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span></span>)</span> st <br/>( <font color="Olive" title="b1">H</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b1">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c6">G1</font> &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b1">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c7">G2</font> &amp; (  for <font color="Olive" title="b2">H1</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c5">D1</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span> <a href="cat_8.html#NK8" title="CAT_8:NK.8">[|x|]</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span></span>)</span>  st <font color="Olive" title="b2">H1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b2">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c6">G1</font> &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b2">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c7">G2</font> holds <br/><font color="Olive" title="b1">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b2">H1</font> ) )</span><br/>

<a NAME="E2:73_1"/><span class="lab"><font color="Green" title="E42">A4</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span> <a href="cat_8.html#NK8" title="CAT_8:NK.8">[|x|]</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>, <a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>), <a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>) <a href="cat_7.html#R3" title="CAT_7:pred.3">is_pullback_of</a> <font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a> ,<font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_7.html#T52" onmouseover="rs('cat_7/T52')" onmouseout="rh()">CAT_7:52</a></span>;<br/>
<a NAME="E3:73_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c6">G1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c7">G2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:73_1"><span class="lab"><font color="Green" title="E41">A3</font></span></a>, <a class="ref" href="cat_8.html#T29" target="_self" onmouseover="rs('cat_8/T29')" onmouseout="rh()">Th29</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c8">H</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c5">D1</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span> <a href="cat_8.html#NK8" title="CAT_8:NK.8">[|x|]</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span></span>)</span><span class="kw"> such that </span><br/><a NAME="E5:73_1"/><span class="lab"><font color="Green" title="E43">A5</font></span>: 
( <font color="Maroon" title="c8">H</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c8">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c6">G1</font> &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c8">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c7">G2</font> &amp; (  for <font color="Olive" title="b1">H1</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c5">D1</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span> <a href="cat_8.html#NK8" title="CAT_8:NK.8">[|x|]</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span></span>)</span>  st <font color="Olive" title="b1">H1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b1">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c6">G1</font> &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b1">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c7">G2</font> holds <br/><font color="Maroon" title="c8">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b1">H1</font> ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:73_1"><span class="lab"><font color="Green" title="E42">A4</font></span></a>, <a class="txt" href="#E1:73_1"><span class="lab"><font color="Green" title="E41">A3</font></span></a>, <a class="txt" href="#E1:73"><span class="lab"><font color="Green" title="E39">A1</font></span></a>, <a class="txt" href="#E2:73"><span class="lab"><font color="Green" title="E40">A2</font></span></a>, <a class="ref" href="cat_7.html#D20" onmouseover="rs('cat_7/D20')" onmouseout="rh()">CAT_7:def 20</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c8">H</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="c8">H</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c8">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c6">G1</font> &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c8">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c7">G2</font> &amp; (  for <font color="Olive" title="b1">H1</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c5">D1</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span> <a href="cat_8.html#NK8" title="CAT_8:NK.8">[|x|]</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span></span>)</span>  st <font color="Olive" title="b1">H1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b1">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c6">G1</font> &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b1">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c7">G2</font> holds <br/><font color="Maroon" title="c8">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b1">H1</font> ) )</span><br/>

<span class="kw">thus </span><a NAME="E6:73_1"/>
( <font color="Maroon" title="c8">H</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c8">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c6">G1</font> &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c8">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c7">G2</font> &amp; (  for <font color="Olive" title="b1">H1</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c5">D1</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span> <a href="cat_8.html#NK8" title="CAT_8:NK.8">[|x|]</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span></span>)</span>  st <font color="Olive" title="b1">H1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b1">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c6">G1</font> &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b1">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c7">G2</font> holds <br/><font color="Maroon" title="c8">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b1">H1</font> ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:73_1"><span class="lab"><font color="Green" title="E43">A5</font></span></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="E4:73"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span> <a href="cat_8.html#NK8" title="CAT_8:NK.8">[|x|]</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>, <a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>), <a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K2" title="CAT_8:func.2">-&gt;OrdC1</a></span>)</span>) <a href="cat_8.html#R2" title="CAT_8:pred.2">is_product_of</a> <font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:73"><span class="lab"><font color="Green" title="E39">A1</font></span></a>, <a class="txt" href="#E2:73"><span class="lab"><font color="Green" title="E40">A2</font></span></a>, <a class="ref" href="cat_8.html#D17" target="_self" onmouseover="rs('cat_8/D17')" onmouseout="rh()">Def17</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>
