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<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(  <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">A</font>) <b>-&gt; </b>   <a href="cat_1.html#M1">Morphism</a> of <font color="Maroon">F</font> <a href="cat_1.html#K13">.</a> <font color="Maroon">a<sub>1</sub></font>,<font color="Maroon">F2</font> <a href="cat_1.html#K13">.</a> <font color="Maroon">a<sub>1</sub></font> = <span class="p1">(<span class="default"><font color="Maroon">t2</font> <a href="nattra_1.html#K5" target="_self">.</a> <font color="Maroon">a<sub>1</sub></font></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><font color="Maroon">t1</font> <a href="nattra_1.html#K5" target="_self">.</a> <font color="Maroon">a<sub>1</sub></font></span>)</span>;<br/>
<b>consider </b><font color="Maroon">t</font> being   <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">B</font><b> such that </b><br/><a NAME="E2:27_1_1"/><i><font color="Green">E25</font></i>: 
for <font color="Olive">a</font> being  <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">A</font> holds  <font color="Maroon">t</font> <a href="funct_2.html#K3">.</a> <font color="Olive">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">a</font>)
 <b>from </b><i><a class="ref" href="funct_2.html#S4">FUNCT_2:sch 4</a>();<br/></i>
<a NAME="E3:27_1_1"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">F</font> <a href="nattra_1.html#R1" target="_self">is_transformable_to</a> <font color="Maroon">F2</font>
 
<b>by </b><i>, <a class="ref" href="nattra_1.html#T2" target="_self">Th2</a>, </i>;<br/>
<a NAME="E4:27_1_1"/>
for <font color="Olive">a</font> being  <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">A</font> holds  <font color="Maroon">t</font> <a href="funct_2.html#K3">.</a> <font color="Olive">a</font> is    <a href="cat_1.html#M1">Morphism</a> of <font color="Maroon">F</font> <a href="cat_1.html#K13">.</a> <font color="Olive">a</font>,<font color="Maroon">F2</font> <a href="cat_1.html#K13">.</a> <font color="Olive">a</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1_1_1"><b>proof </b></a><div class="add">

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

<a NAME="E1:27_1_1_1"/>
<font color="Maroon">t</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">t2</font> <a href="nattra_1.html#K5" target="_self">.</a> <font color="Maroon">a</font></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><font color="Maroon">t1</font> <a href="nattra_1.html#K5" target="_self">.</a> <font color="Maroon">a</font></span>)</span>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E2:27_1_1_1"/>
<font color="Maroon">t</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">a</font> is    <a href="cat_1.html#M1">Morphism</a> of <font color="Maroon">F</font> <a href="cat_1.html#K13">.</a> <font color="Maroon">a</font>,<font color="Maroon">F2</font> <a href="cat_1.html#K13">.</a> <font color="Maroon">a</font>
 ;<br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">t'</font> = <font color="Maroon">t</font> as    <a href="nattra_1.html#M1" target="_self">transformation</a> of <font color="Maroon">F</font>,<font color="Maroon">F2</font> <b>by </b><i>, </i>;<br/>
<b>take </b>
<font color="Maroon">t'</font>
;<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/>

<b>thus </b><font color="Maroon">t'</font> <a href="nattra_1.html#K5" target="_self">.</a> <font color="Maroon">a</font> = 
<font color="Maroon">t</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">a</font>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">t2</font> <a href="nattra_1.html#K5" target="_self">.</a> <font color="Maroon">a</font></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><font color="Maroon">t1</font> <a href="nattra_1.html#K5" target="_self">.</a> <font color="Maroon">a</font></span>)</span>
<b>by </b><i/>
;<br/>


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