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

<b>let </b><font color="Maroon" title="c6">P</font>, <font color="Maroon" title="c7">R</font> be    <a href="functor3.html#M1" title="FUNCTOR3:mode.1">natural_equivalence</a> of <font color="Maroon" title="c4">F2</font>,<font color="Maroon" title="c3">F1</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:56_1_2"/><i><font color="Green" title="E32">A5</font></i>: 
for <font color="Olive" title="b1">a</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">A</font> holds  <font color="Maroon" title="c6">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">e</font> <a href="functor2.html#K2" title="FUNCTOR2:func.2">!</a> <font color="Olive" title="b1">a</font></span>)</span> <a href="altcat_3.html#K1" title="ALTCAT_3:func.1">"</a> 
 <b>and </b><br/><a NAME="E2:56_1_2"/><i><font color="Green" title="E33">A6</font></i>: 
for <font color="Olive" title="b1">a</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">A</font> holds  <font color="Maroon" title="c7">R</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">e</font> <a href="functor2.html#K2" title="FUNCTOR2:func.2">!</a> <font color="Olive" title="b1">a</font></span>)</span> <a href="altcat_3.html#K1" title="ALTCAT_3:func.1">"</a> 
 ;<br/>

<a NAME="E3:56_1_2"/><i><font color="Green" title="E34">A7</font></i>: 
<font color="Maroon" title="c4">F2</font> <a href="functor2.html#R1" title="FUNCTOR2:pred.1">is_transformable_to</a> <font color="Maroon" title="c3">F1</font>
 
<b>by </b><i><a class="txt" href="functor3.html#E1:56"><i><font color="Green" title="E31">A1</font></i></a>, <a class="ref" href="functor3.html#D4" target="_self" title="FUNCTOR3:def.4">Def4</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="56_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c8">a</font> be   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">A</font>;<br/><b>thus </b><font color="Maroon" title="c6">P</font> <a href="functor2.html#K2" title="FUNCTOR2:func.2">!</a> <font color="Maroon" title="c8">a</font> = 
<font color="Maroon" title="c6">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">a</font>
<b>by </b><i><a class="txt" href="functor3.html#E3:56_1_2"><i><font color="Green" title="E34">A7</font></i></a>, <a class="ref" href="functor2.html#D4" title="FUNCTOR2:def.4">FUNCTOR2:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">e</font> <a href="functor2.html#K2" title="FUNCTOR2:func.2">!</a> <font color="Maroon" title="c8">a</font></span>)</span> <a href="altcat_3.html#K1" title="ALTCAT_3:func.1">"</a> 
<b>by </b><i><a class="txt" href="functor3.html#E1:56_1_2"><i><font color="Green" title="E32">A5</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c7">R</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">a</font>
<b>by </b><i><a class="txt" href="functor3.html#E2:56_1_2"><i><font color="Green" title="E33">A6</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c7">R</font> <a href="functor2.html#K2" title="FUNCTOR2:func.2">!</a> <font color="Maroon" title="c8">a</font>
<b>by </b><i><a class="txt" href="functor3.html#E3:56_1_2"><i><font color="Green" title="E34">A7</font></i></a>, <a class="ref" href="functor2.html#D4" title="FUNCTOR2:def.4">FUNCTOR2:def 4</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:56_1_2"/>
<font color="Maroon" title="c6">P</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c7">R</font>
 <b>by </b><i><a class="txt" href="functor3.html#E3:56_1_2"><i><font color="Green" title="E34">A7</font></i></a>, <a class="ref" href="functor2.html#T5" title="FUNCTOR2:th.5">FUNCTOR2:5</a></i>;<br/>


</div>
