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<b>let </b><font color="Maroon" title="c5">F</font> be  <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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">F</font> <a href="functor2.html#R2" title="FUNCTOR2:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c5">F</font> &amp; <font color="Maroon" title="c5">F</font> <a href="functor2.html#R1" title="FUNCTOR2:pred.1">is_transformable_to</a> <font color="Maroon" title="c5">F</font> &amp;  ex <font color="Olive" title="b1">t</font> being   <a href="functor2.html#M2" title="FUNCTOR2:mode.2">natural_transformation</a> of <font color="Maroon" title="c5">F</font>,<font color="Maroon" title="c5">F</font> st <br/>for <font color="Olive" title="b2">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="Olive" title="b1">t</font> <a href="functor2.html#K2" title="FUNCTOR2:func.2">!</a> <font color="Olive" title="b2">a</font> is <a href="altcat_3.html#V3" title="ALTCAT_3:attr.3">iso</a> )</span><br/>

<b>thus </b><a NAME="E1:49_1_1"/>
( <font color="Maroon" title="c5">F</font> <a href="functor2.html#R2" title="FUNCTOR2:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c5">F</font> &amp; <font color="Maroon" title="c5">F</font> <a href="functor2.html#R1" title="FUNCTOR2:pred.1">is_transformable_to</a> <font color="Maroon" title="c5">F</font> )
 <b>by </b><i><a class="ref" href="functor2.html#T9" title="FUNCTOR2:th.9">FUNCTOR2:9</a></i>; <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">t</font> being   <a href="functor2.html#M2" title="FUNCTOR2:mode.2">natural_transformation</a> of <font color="Maroon" title="c5">F</font>,<font color="Maroon" title="c5">F</font> st <br/>for <font color="Olive" title="b2">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="Olive" title="b1">t</font> <a href="functor2.html#K2" title="FUNCTOR2:func.2">!</a> <font color="Olive" title="b2">a</font> is <a href="altcat_3.html#V3" title="ALTCAT_3:attr.3">iso</a></span><br/>

<b>take </b>
 <a href="functor2.html#K4" title="FUNCTOR2:func.4">idt</a> <font color="Maroon" title="c5">F</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> 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  <span class="p1">(<span class="default"><a href="functor2.html#K4" title="FUNCTOR2:func.4">idt</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="functor2.html#K2" title="FUNCTOR2:func.2">!</a> <font color="Olive" title="b1">a</font> is <a href="altcat_3.html#V3" title="ALTCAT_3:attr.3">iso</a></span><br/>

<b>let </b><font color="Maroon" title="c6">a</font> be   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">A</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="functor2.html#K4" title="FUNCTOR2:func.4">idt</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="functor2.html#K2" title="FUNCTOR2:func.2">!</a> <font color="Maroon" title="c6">a</font> is <a href="altcat_3.html#V3" title="ALTCAT_3:attr.3">iso</a></span><br/>

<a NAME="E2:49_1_1"/>
<span class="p1">(<span class="default"><a href="functor2.html#K4" title="FUNCTOR2:func.4">idt</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="functor2.html#K2" title="FUNCTOR2:func.2">!</a> <font color="Maroon" title="c6">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c6">a</font></span>)</span>
 
<b>by </b><i><a class="ref" href="functor2.html#T6" title="FUNCTOR2:th.6">FUNCTOR2:6</a></i>;<br/>
<b>hence </b><a NAME="E3:49_1_1"/>
<span class="p1">(<span class="default"><a href="functor2.html#K4" title="FUNCTOR2:func.4">idt</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="functor2.html#K2" title="FUNCTOR2:func.2">!</a> <font color="Maroon" title="c6">a</font> is <a href="altcat_3.html#V3" title="ALTCAT_3:attr.3">iso</a>
 ; <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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