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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="cat_1.html#NM4" title="CAT_1:NM.4">Category</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">F1</font>, <font color="Olive" title="b2">F2</font> being    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font><br/>  for <font color="Olive" title="b3">s</font> being    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Olive" title="b1">F1</font>,<font color="Olive" title="b2">F2</font>  st <font color="Olive" title="b1">F1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Olive" title="b2">F2</font> holds <br/><span class="p1">(<span class="default"><a href="nattra_1.html#K7" title="NATTRA_1:func.7">id</a> <span class="p2">(<span class="default"><a href="cat_1.html#K11" title="CAT_1:func.11">id</a> <font color="Maroon" title="c2">B</font></span>)</span></span>)</span> <a href="isocat_1.html#K6" title="ISOCAT_1:func.6">(#)</a> <font color="Olive" title="b3">s</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b3">s</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">F1</font>, <font color="Maroon" title="c4">F2</font> be    <a href="cat_1.html#M2" title="CAT_1: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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">s</font> being    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c3">F1</font>,<font color="Maroon" title="c4">F2</font>  st <font color="Maroon" title="c3">F1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c4">F2</font> holds <br/><span class="p1">(<span class="default"><a href="nattra_1.html#K7" title="NATTRA_1:func.7">id</a> <span class="p2">(<span class="default"><a href="cat_1.html#K11" title="CAT_1:func.11">id</a> <font color="Maroon" title="c2">B</font></span>)</span></span>)</span> <a href="isocat_1.html#K6" title="ISOCAT_1:func.6">(#)</a> <font color="Olive" title="b1">s</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b1">s</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">s</font> be    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c3">F1</font>,<font color="Maroon" title="c4">F2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">F1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c4">F2</font> implies <span class="p1">(<span class="default"><a href="nattra_1.html#K7" title="NATTRA_1:func.7">id</a> <span class="p2">(<span class="default"><a href="cat_1.html#K11" title="CAT_1:func.11">id</a> <font color="Maroon" title="c2">B</font></span>)</span></span>)</span> <a href="isocat_1.html#K6" title="ISOCAT_1:func.6">(#)</a> <font color="Maroon" title="c5">s</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c5">s</font> )</span><br/>









<span class="kw">assume </span><a NAME="E1:46"/><span class="lab"><font color="Green" title="E35">A1</font></span>: 
<font color="Maroon" title="c3">F1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c4">F2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="nattra_1.html#K7" title="NATTRA_1:func.7">id</a> <span class="p2">(<span class="default"><a href="cat_1.html#K11" title="CAT_1:func.11">id</a> <font color="Maroon" title="c2">B</font></span>)</span></span>)</span> <a href="isocat_1.html#K6" title="ISOCAT_1:func.6">(#)</a> <font color="Maroon" title="c5">s</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c5">s</font></span><br/>

<a NAME="E2:46"/><span class="kw">then </span><span class="lab"><font color="Green" title="E36">A2</font></span>: 
<span class="p1">(<span class="default"><a href="cat_1.html#K11" title="CAT_1:func.11">id</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c3">F1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <span class="p1">(<span class="default"><a href="cat_1.html#K11" title="CAT_1:func.11">id</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c4">F2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="isocat_1.html#T22" target="_self" title="ISOCAT_1:th.22">Th27</a></span>;<br/>
<span class="kw">thus </span><span class="p1">(<span class="default"><a href="nattra_1.html#K7" title="NATTRA_1:func.7">id</a> <span class="p2">(<span class="default"><a href="cat_1.html#K11" title="CAT_1:func.11">id</a> <font color="Maroon" title="c2">B</font></span>)</span></span>)</span> <a href="isocat_1.html#K6" title="ISOCAT_1:func.6">(#)</a> <font color="Maroon" title="c5">s</font> = 
<span class="p1">(<span class="default"><a href="nattra_1.html#K7" title="NATTRA_1:func.7">id</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="cat_1.html#K11" title="CAT_1:func.11">id</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c4">F2</font></span>)</span></span>)</span> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cat_1.html#K11" title="CAT_1:func.11">id</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="isocat_1.html#K4" title="ISOCAT_1:func.4">*</a> <font color="Maroon" title="c5">s</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="isocat_1.html#T32" target="_self" title="ISOCAT_1:th.32">Th37</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="cat_1.html#K11" title="CAT_1:func.11">id</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="isocat_1.html#K4" title="ISOCAT_1:func.4">*</a> <font color="Maroon" title="c5">s</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:46"><span class="lab"><font color="Green" title="E36">A2</font></span></a>, <a class="ref" href="nattra_1.html#T24" title="NATTRA_1:th.24">NATTRA_1:24</a></span>
<br/>.= 
<font color="Maroon" title="c5">s</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:46"><span class="lab"><font color="Green" title="E35">A1</font></span></a>, <a class="ref" href="isocat_1.html#T35" target="_self" title="ISOCAT_1:th.35">Th40</a></span>
; <a class="txt" 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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