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<a NAME="E1:58_1_1"/>
<span class="p1"><a href="isocat_2.html#K15" target="_self">&lt;:</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span><a href="isocat_2.html#K15" target="_self">:&gt;</a></span> is    <a href="nattra_1.html#M2">natural_transformation</a> of <span class="p1"><a href="isocat_2.html#K10" target="_self">&lt;:</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="isocat_2.html#K10" target="_self">:&gt;</a></span>,<span class="p1"><a href="isocat_2.html#K10" target="_self">&lt;:</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="isocat_2.html#K10" target="_self">:&gt;</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1_1_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:58_1_1_1"/>
<span class="p1"><a href="isocat_2.html#K10" target="_self">&lt;:</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="isocat_2.html#K10" target="_self">:&gt;</a></span> <a href="nattra_1.html#R2">is_naturally_transformable_to</a> <span class="p1"><a href="isocat_2.html#K10" target="_self">&lt;:</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="isocat_2.html#K10" target="_self">:&gt;</a></span>
 <b>by </b><i><a class="txt" href="isocat_2.html#E1:58"><i><font color="Green">E52</font></i></a>, <a class="txt" href="isocat_2.html#E2:58"><i><font color="Green">E53</font></i></a>, <a class="ref" href="isocat_2.html#T46" target="_self">Th46</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="nattra_1.html#D8">NATTRA_1:def 8</a><br/>

<b>thus </b><a NAME="E2:58_1_1_1"/>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="subset_1.html#M1">Element</a> of the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font> holds <br/>(  <a href="cat_1.html#K6">Hom</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  or for <font color="Olive">b<sub>3</sub></font> being   <a href="cat_1.html#M1">Morphism</a> of <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> holds <span class="p1">(<span class="default"><span class="p2"><a href="isocat_2.html#K15" target="_self">&lt;:</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span><a href="isocat_2.html#K15" target="_self">:&gt;</a></span> <a href="nattra_1.html#K5">.</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><span class="p2"><a href="isocat_2.html#K10" target="_self">&lt;:</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="isocat_2.html#K10" target="_self">:&gt;</a></span> <a href="nattra_1.html#K3">.</a> <font color="Olive">b<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="isocat_2.html#K10" target="_self">&lt;:</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="isocat_2.html#K10" target="_self">:&gt;</a></span> <a href="nattra_1.html#K3">.</a> <font color="Olive">b<sub>3</sub></font></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><span class="p2"><a href="isocat_2.html#K15" target="_self">&lt;:</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span><a href="isocat_2.html#K15" target="_self">:&gt;</a></span> <a href="nattra_1.html#K5">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> )
 <b>by </b><i><a class="txt" href="isocat_2.html#E1:58"><i><font color="Green">E52</font></i></a>, <a class="txt" href="isocat_2.html#E2:58"><i><font color="Green">E53</font></i></a>, <a class="txt" href="isocat_2.html#E61"><i><font color="Green">Lemma50</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:58_1_1"/>
<span class="p1"><a href="isocat_2.html#K15" target="_self">&lt;:</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span><a href="isocat_2.html#K15" target="_self">:&gt;</a></span> is    <a href="nattra_1.html#M2">natural_transformation</a> of <span class="p1"><a href="isocat_2.html#K10" target="_self">&lt;:</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="isocat_2.html#K10" target="_self">:&gt;</a></span>,<span class="p1"><a href="isocat_2.html#K10" target="_self">&lt;:</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="isocat_2.html#K10" target="_self">:&gt;</a></span>
 ;<br/>


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