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

<b>reconsider </b><font color="Maroon">tF</font> = <font color="Maroon">t</font> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><a href="cat_1.html#K12">Obj</a> <font color="Maroon">F</font></span>)</span> as   <a href="funct_2.html#NM1">Function</a> of the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">A</font>,the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">C</font> ;<br/>
<a NAME="E2:26_1_1"/>
<font color="Maroon">tF</font> is    <a href="nattra_1.html#M1">transformation</a> of <font color="Maroon">G1</font> <a href="cat_1.html#K14">*</a> <font color="Maroon">F</font>,<font color="Maroon">G2</font> <a href="cat_1.html#K14">*</a> <font color="Maroon">F</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1_1_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:26_1_1_1"/>
<font color="Maroon">G1</font> <a href="cat_1.html#K14">*</a> <font color="Maroon">F</font> <a href="nattra_1.html#R1">is_transformable_to</a> <font color="Maroon">G2</font> <a href="cat_1.html#K14">*</a> <font color="Maroon">F</font>
 <b>by </b><i><a class="ref" href="isocat_1.html#T1" target="_self">Th1</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">a</font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">A</font>;<br/>

<i><font color="Green">E19</font></i>: <font color="Maroon">tF</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">a</font> = 
<font color="Maroon">t</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cat_1.html#K12">Obj</a> <font color="Maroon">F</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">a</font></span>)</span>
<b>by </b><i><a class="ref" href="funct_2.html#T21">FUNCT_2:21</a></i>
<br/>.= 
<font color="Maroon">t</font> <a href="nattra_1.html#K5">.</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="cat_1.html#K13">.</a> <font color="Maroon">a</font></span>)</span>
<b>by </b><i><a class="ref" href="isocat_1.html#T1" target="_self">Th1</a>, <a class="ref" href="nattra_1.html#D5">NATTRA_1:def 5</a></i>
;<br/>
<a NAME="E3:26_1_1_1"/>
( <font color="Maroon">G1</font> <a href="cat_1.html#K13">.</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="cat_1.html#K13">.</a> <font color="Maroon">a</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">G1</font> <a href="cat_1.html#K14">*</a> <font color="Maroon">F</font></span>)</span> <a href="cat_1.html#K13">.</a> <font color="Maroon">a</font> &amp; <font color="Maroon">G2</font> <a href="cat_1.html#K13">.</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="cat_1.html#K13">.</a> <font color="Maroon">a</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">G2</font> <a href="cat_1.html#K14">*</a> <font color="Maroon">F</font></span>)</span> <a href="cat_1.html#K13">.</a> <font color="Maroon">a</font> )
 
<b>by </b><i><a class="ref" href="cat_1.html#T113">CAT_1:113</a></i>;<br/>
<b>hence </b><a NAME="E4:26_1_1_1"/>
<font color="Maroon">tF</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">a</font> is    <a href="cat_1.html#M1">Morphism</a> of <span class="p1">(<span class="default"><font color="Maroon">G1</font> <a href="cat_1.html#K14">*</a> <font color="Maroon">F</font></span>)</span> <a href="cat_1.html#K13">.</a> <font color="Maroon">a</font>,<span class="p1">(<span class="default"><font color="Maroon">G2</font> <a href="cat_1.html#K14">*</a> <font color="Maroon">F</font></span>)</span> <a href="cat_1.html#K13">.</a> <font color="Maroon">a</font>
 <b>by </b><i><a class="txt" href="isocat_1.html#E1:26"><i><font color="Green">E18</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:26_1_1"/>
<font color="Maroon">t</font> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><a href="cat_1.html#K12">Obj</a> <font color="Maroon">F</font></span>)</span> is    <a href="nattra_1.html#M1">transformation</a> of <font color="Maroon">G1</font> <a href="cat_1.html#K14">*</a> <font color="Maroon">F</font>,<font color="Maroon">G2</font> <a href="cat_1.html#K14">*</a> <font color="Maroon">F</font>
 ;<br/>


</div>
