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<span class="kw">let </span><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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/>

<span class="kw">assume </span><a NAME="E1:21"/>
<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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/>

<span class="kw">then </span><span class="kw">consider </span><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><span class="kw"> such that </span><br/><a NAME="E3:21"/><span class="lab"><font color="Green" title="E6">A1</font></span>: 
( <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>  )
 ;<br/>
<span class="kw">reconsider </span><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> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:21"><span class="lab"><font color="Green" title="E6">A1</font></span></a></span>;<br/>
<span class="kw">consider </span><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><span class="kw"> such that </span><br/><a NAME="E6:21"/><span class="lab"><font color="Green" title="E7">A2</font></span>: 
<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#K14" title="FUNCTOR0:func.14">"</a> 
 <span class="kw">and </span><br/><a NAME="E7:21"/><span class="lab"><font color="Green" title="E8">A3</font></span>: 
( <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>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:21"><span class="lab"><font color="Green" title="E6">A1</font></span></a>, <a class="ref" href="functor0.html#T48" onmouseover="rs('functor0/T48')" onmouseout="rh()">FUNCTOR0:48</a></span>;<br/>
<span class="kw">reconsider </span><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> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:21"><span class="lab"><font color="Green" title="E8">A3</font></span></a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c4">F</font>
; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="yellow18.html#D2" target="_self" onmouseover="rs('yellow18/D2')" onmouseout="rh()">YELLOW18:def 2</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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#K11" title="FUNCTOR0:func.11">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#K11" title="FUNCTOR0:func.11">id</a> <font color="Maroon" title="c2">B</font> <a href="functor3.html#R1" title="FUNCTOR3:pred.1">are_naturally_equivalent</a>  )</span><br/>

<span class="kw">take </span>
<font color="Maroon" title="c6">G</font>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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#K11" title="FUNCTOR0:func.11">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#K11" title="FUNCTOR0:func.11">id</a> <font color="Maroon" title="c2">B</font> <a href="functor3.html#R1" title="FUNCTOR3:pred.1">are_naturally_equivalent</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E9:21"/>
( <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#K11" title="FUNCTOR0:func.11">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#K11" title="FUNCTOR0:func.11">id</a> <font color="Maroon" title="c2">B</font> <a href="functor3.html#R1" title="FUNCTOR3:pred.1">are_naturally_equivalent</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:21"><span class="lab"><font color="Green" title="E6">A1</font></span></a>, <a class="txt" href="#E6:21"><span class="lab"><font color="Green" title="E7">A2</font></span></a>, <a class="ref" href="functor1.html#T18" onmouseover="rs('functor1/T18')" onmouseout="rh()">FUNCTOR1:18</a>, <a class="ref" href="functor1.html#T19" onmouseover="rs('functor1/T19')" onmouseout="rh()">FUNCTOR1:19</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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