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<a NAME="E1:54_1_1"/>
the <a href="cat_1.html#U2">Morphisms</a> of <span class="p1"><a href="cat_2.html#K11">[:</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="cat_2.html#K11">:]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">c<sub>3</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="cat_2.html#T33">CAT_2:33</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>10</sub></font> = <span class="p1"><a href="funct_3.html#K14">&lt;:</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span><a href="funct_3.html#K14">:&gt;</a></span> as   <a href="funct_2.html#NM1">Function</a> of the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="cat_1.html#U2">Morphisms</a> of <span class="p1"><a href="cat_2.html#K11">[:</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="cat_2.html#K11">:]</a></span> ;<br/>
<a NAME="E3:54_1_1"/>
<font color="Maroon">c<sub>10</sub></font> is    <a href="nattra_1.html#M1">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="54_1_1_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:54_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#R1">is_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#E1:54"><i><font color="Green">E48</font></i></a>, <a class="ref" href="isocat_2.html#T44" target="_self">Th44</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="nattra_1.html#D3">NATTRA_1:def 3</a><br/>

<b>let </b><font color="Maroon">c<sub>11</sub></font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>

<a NAME="E2:54_1_1_1"/>
<font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="cat_1.html#K6">Hom</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="cat_1.html#K13">.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span>,<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="cat_1.html#K13">.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="isocat_2.html#E1:54"><i><font color="Green">E48</font></i></a>, <a class="txt" href="isocat_2.html#E57"><i><font color="Green">Lemma46</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:54_1_1_1"/>
<font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>11</sub></font> is    <a href="cat_1.html#M1">Morphism</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> <a href="cat_1.html#K13">.</a> <font color="Maroon">c<sub>11</sub></font>,<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> <a href="cat_1.html#K13">.</a> <font color="Maroon">c<sub>11</sub></font>
 <b>by </b><i><a class="ref" href="cat_1.html#D7">CAT_1:def 7</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:54_1_1"/>
<span class="p1"><a href="funct_3.html#K14">&lt;:</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span><a href="funct_3.html#K14">:&gt;</a></span> is    <a href="nattra_1.html#M1">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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