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<a NAME="E1:20_1_1"/><i><font color="Green" title="E18">A1</font></i>: 
<font color="Maroon" title="c3">F</font> <a href="functor2.html#R2" title="FUNCTOR2:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c3">F</font>
 
<b>by </b><i><a class="ref" href="functor2.html#T9" target="_self" title="FUNCTOR2:th.9">Th9</a></i>;<br/>
<a NAME="E2:20_1_1"/>
 <a href="functor2.html#K1" title="FUNCTOR2:func.1">idt</a> <font color="Maroon" title="c3">F</font> is    <a href="functor2.html#M2" title="FUNCTOR2:mode.2">natural_transformation</a> of <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c3">F</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:20_1_1_1"/>
for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">A</font>  st <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  holds <br/>for <font color="Olive" title="b3">f</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="functor2.html#K1" title="FUNCTOR2:func.1">idt</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="functor2.html#K2" title="FUNCTOR2:func.2">!</a> <font color="Olive" title="b2">b</font></span>)</span> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K6" title="FUNCTOR0:func.6">.</a> <font color="Olive" title="b3">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K6" title="FUNCTOR0:func.6">.</a> <font color="Olive" title="b3">f</font></span>)</span> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="functor2.html#K1" title="FUNCTOR2:func.1">idt</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="functor2.html#K2" title="FUNCTOR2:func.2">!</a> <font color="Olive" title="b1">a</font></span>)</span>
 
<b>by </b><i><a class="txt" href="functor2.html#E15"><i><font color="Green" title="E13">Lm1</font></i></a></i>;<br/>
<b>hence </b><a NAME="E2:20_1_1_1"/>
 <a href="functor2.html#K1" title="FUNCTOR2:func.1">idt</a> <font color="Maroon" title="c3">F</font> is    <a href="functor2.html#M2" title="FUNCTOR2:mode.2">natural_transformation</a> of <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c3">F</font>
 <b>by </b><i><a class="txt" href="functor2.html#E1:20_1_1"><i><font color="Green" title="E18">A1</font></i></a>, <a class="ref" href="functor2.html#D7" target="_self" title="FUNCTOR2:def.7">Def7</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:20_1_1"/>
 <a href="functor2.html#K1" title="FUNCTOR2:func.1">idt</a> <font color="Maroon" title="c3">F</font> is    <a href="functor2.html#M2" title="FUNCTOR2:mode.2">natural_transformation</a> of <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c3">F</font>
 ;<br/>


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