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<b>let </b><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</font> be   <a href="altcat_1.html#NM4" title="ALTCAT_1:NM.4">category</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font> <a href="functor0.html#R1" title="FUNCTOR0:pred.1">are_isomorphic</a>  implies <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font> <a href="yellow18.html#R1" title="YELLOW18:pred.1">are_equivalent</a>  )</span><br/>

<b>assume </b><a NAME="E1:21"/><i><font color="Green" title="E6">A1</font></i>: 
<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font> <a href="functor0.html#R1" title="FUNCTOR0:pred.1">are_isomorphic</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font> <a href="yellow18.html#R1" title="YELLOW18:pred.1">are_equivalent</a> </span><br/>

<b>consider </b><font color="Maroon" title="c3">F</font> being    <a href="functor0.html#M2" title="FUNCTOR0:mode.2">Functor</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font><b> such that </b><br/><a NAME="E3:21"/><i><font color="Green" title="E7">A2</font></i>: 
( <font color="Maroon" title="c3">F</font> is <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a> &amp; <font color="Maroon" title="c3">F</font> is <a href="functor0.html#V15" title="FUNCTOR0:attr.15">covariant</a> )
 <b>by </b><i><a class="txt" href="yellow18.html#E1:21"><i><font color="Green" title="E6">A1</font></i></a>, <a class="ref" href="functor0.html#D40" title="FUNCTOR0:def.40">FUNCTOR0:def 40</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c4">F</font> = <font color="Maroon" title="c3">F</font> as  <a href="functor0.html#V15" title="FUNCTOR0:attr.15">covariant</a>  <a href="functor0.html#M2" title="FUNCTOR0:mode.2">Functor</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font> <b>by </b><i><a class="txt" href="yellow18.html#E3:21"><i><font color="Green" title="E7">A2</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon" title="c5">G</font> being    <a href="functor0.html#M2" title="FUNCTOR0:mode.2">Functor</a> of <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c1">A</font><b> such that </b><br/><a NAME="E6:21"/><i><font color="Green" title="E8">A3</font></i>: 
( <font color="Maroon" title="c5">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a>  &amp; <font color="Maroon" title="c5">G</font> is <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a> &amp; <font color="Maroon" title="c5">G</font> is <a href="functor0.html#V15" title="FUNCTOR0:attr.15">covariant</a> )
 <b>by </b><i><a class="txt" href="yellow18.html#E3:21"><i><font color="Green" title="E7">A2</font></i></a>, <a class="ref" href="functor0.html#T49" title="FUNCTOR0:th.49">FUNCTOR0:49</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">G</font> = <font color="Maroon" title="c5">G</font> as  <a href="functor0.html#V15" title="FUNCTOR0:attr.15">covariant</a>  <a href="functor0.html#M2" title="FUNCTOR0:mode.2">Functor</a> of <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c1">A</font> <b>by </b><i><a class="txt" href="yellow18.html#E6:21"><i><font color="Green" title="E8">A3</font></i></a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c4">F</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow18.html#D2" target="_self" title="YELLOW18:def.2">YELLOW18:def 2</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">G</font> being <a href="functor0.html#V15" title="FUNCTOR0:attr.15">covariant</a>  <a href="functor0.html#M2" title="FUNCTOR0:mode.2">Functor</a> of <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c1">A</font> st <br/>( <font color="Olive" title="b1">G</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c4">F</font>, <a href="functor0.html#K12" title="FUNCTOR0:func.12">id</a> <font color="Maroon" title="c1">A</font> <a href="functor3.html#R1" title="FUNCTOR3:pred.1">are_naturally_equivalent</a>  &amp; <font color="Maroon" title="c4">F</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Olive" title="b1">G</font>, <a href="functor0.html#K12" title="FUNCTOR0:func.12">id</a> <font color="Maroon" title="c2">B</font> <a href="functor3.html#R1" title="FUNCTOR3:pred.1">are_naturally_equivalent</a>  )</span><br/>

<b>take </b>
<font color="Maroon" title="c6">G</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c6">G</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c4">F</font>, <a href="functor0.html#K12" title="FUNCTOR0:func.12">id</a> <font color="Maroon" title="c1">A</font> <a href="functor3.html#R1" title="FUNCTOR3:pred.1">are_naturally_equivalent</a>  &amp; <font color="Maroon" title="c4">F</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c6">G</font>, <a href="functor0.html#K12" title="FUNCTOR0:func.12">id</a> <font color="Maroon" title="c2">B</font> <a href="functor3.html#R1" title="FUNCTOR3:pred.1">are_naturally_equivalent</a>  )</span><br/>

<b>thus </b><a NAME="E8:21"/>
( <font color="Maroon" title="c6">G</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c4">F</font>, <a href="functor0.html#K12" title="FUNCTOR0:func.12">id</a> <font color="Maroon" title="c1">A</font> <a href="functor3.html#R1" title="FUNCTOR3:pred.1">are_naturally_equivalent</a>  &amp; <font color="Maroon" title="c4">F</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c6">G</font>, <a href="functor0.html#K12" title="FUNCTOR0:func.12">id</a> <font color="Maroon" title="c2">B</font> <a href="functor3.html#R1" title="FUNCTOR3:pred.1">are_naturally_equivalent</a>  )
 <b>by </b><i><a class="txt" href="yellow18.html#E3:21"><i><font color="Green" title="E7">A2</font></i></a>, <a class="txt" href="yellow18.html#E6:21"><i><font color="Green" title="E8">A3</font></i></a>, <a class="ref" href="functor1.html#T21" title="FUNCTOR1:th.21">FUNCTOR1:21</a>, <a class="ref" href="functor1.html#T22" title="FUNCTOR1:th.22">FUNCTOR1:22</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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