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<span class="kw">let </span><font color="Maroon" title="c1">C</font>, <font color="Maroon" title="c2">D</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">F</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">D</font>  st <font color="Olive" title="b1">F</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  holds <br/>( <font color="Olive" title="b1">F</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <span class="p1">(<span class="default"><a href="cat_6.html#K12" title="CAT_6:func.12">id</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b1">F</font> &amp; <span class="p1">(<span class="default"><a href="cat_6.html#K12" title="CAT_6:func.12">id</a> <font color="Maroon" title="c2">D</font></span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b1">F</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b1">F</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">F</font> be   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">D</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="c3">F</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  implies ( <font color="Maroon" title="c3">F</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <span class="p1">(<span class="default"><a href="cat_6.html#K12" title="CAT_6:func.12">id</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c3">F</font> &amp; <span class="p1">(<span class="default"><a href="cat_6.html#K12" title="CAT_6:func.12">id</a> <font color="Maroon" title="c2">D</font></span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c3">F</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c3">F</font> ) )</span><br/>



<span class="kw">assume </span><a NAME="E1:17"/><span class="lab"><font color="Green" title="E12">A1</font></span>: 
<font color="Maroon" title="c3">F</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"> ( <font color="Maroon" title="c3">F</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <span class="p1">(<span class="default"><a href="cat_6.html#K12" title="CAT_6:func.12">id</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c3">F</font> &amp; <span class="p1">(<span class="default"><a href="cat_6.html#K12" title="CAT_6:func.12">id</a> <font color="Maroon" title="c2">D</font></span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c3">F</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c3">F</font> )</span><br/>

<span class="kw">thus </span><font color="Maroon" title="c3">F</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <span class="p1">(<span class="default"><a href="cat_6.html#K12" title="CAT_6:func.12">id</a> <font color="Maroon" title="c1">C</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="cat_6.html#K12" title="CAT_6:func.12">id</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="relset_1.html#K4" title="RELSET_1:func.4">*</a> <font color="Maroon" title="c3">F</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:17"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="ref" href="cat_6.html#D27" onmouseover="rs('cat_6/D27')" onmouseout="rh()">CAT_6:def 27</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font></span>)</span> <a href="relset_1.html#K4" title="RELSET_1:func.4">*</a> <font color="Maroon" title="c3">F</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="struct_0.html#D4" onmouseover="rs('struct_0/D4')" onmouseout="rh()">STRUCT_0:def 4</a></span>
<br/>.= 
<font color="Maroon" title="c3">F</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T17" onmouseover="rs('funct_2/T17')" onmouseout="rh()">FUNCT_2:17</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"> <span class="p1">(<span class="default"><a href="cat_6.html#K12" title="CAT_6:func.12">id</a> <font color="Maroon" title="c2">D</font></span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c3">F</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c3">F</font></span><br/>

<span class="kw">thus </span><span class="p1">(<span class="default"><a href="cat_6.html#K12" title="CAT_6:func.12">id</a> <font color="Maroon" title="c2">D</font></span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c3">F</font> = 
<font color="Maroon" title="c3">F</font> <a href="relset_1.html#K4" title="RELSET_1:func.4">*</a> <span class="p1">(<span class="default"><a href="cat_6.html#K12" title="CAT_6:func.12">id</a> <font color="Maroon" title="c2">D</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:17"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="ref" href="cat_6.html#D27" onmouseover="rs('cat_6/D27')" onmouseout="rh()">CAT_6:def 27</a></span>
<br/>.= 
<font color="Maroon" title="c3">F</font> <a href="relset_1.html#K4" title="RELSET_1:func.4">*</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">D</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="struct_0.html#D4" onmouseover="rs('struct_0/D4')" onmouseout="rh()">STRUCT_0:def 4</a></span>
<br/>.= 
<font color="Maroon" title="c3">F</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T17" onmouseover="rs('funct_2/T17')" onmouseout="rh()">FUNCT_2:17</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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