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<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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">t1</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> &amp; <font color="Olive" title="b3">t1</font> is <a href="nattra_1.html#V1" title="NATTRA_1:attr.1">invertible</a> holds <br/>for <font color="Olive" title="b4">a</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b3">t1</font> <a href="nattra_1.html#K10" title="NATTRA_1:func.10">"</a> </span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b4">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">t1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b4">a</font></span>)</span> <a href="cat_1.html#K7" title="CAT_1:func.7">"</a> </span><br/><b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">t1</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> &amp; <font color="Olive" title="b1">t1</font> is <a href="nattra_1.html#V1" title="NATTRA_1:attr.1">invertible</a> holds <br/>for <font color="Olive" title="b2">a</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">t1</font> <a href="nattra_1.html#K10" title="NATTRA_1:func.10">"</a> </span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">t1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b2">a</font></span>)</span> <a href="cat_1.html#K7" title="CAT_1:func.7">"</a> </span><br/><b>let </b><font color="Maroon" title="c5">t1</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:()"><i><font color="Red">::  thesis: </font></i></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> &amp; <font color="Maroon" title="c5">t1</font> is <a href="nattra_1.html#V1" title="NATTRA_1:attr.1">invertible</a> implies for <font color="Olive" title="b1">a</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font> holds  <span class="p1">(<span class="default"><font color="Maroon" title="c5">t1</font> <a href="nattra_1.html#K10" title="NATTRA_1:func.10">"</a> </span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</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">t1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b1">a</font></span>)</span> <a href="cat_1.html#K7" title="CAT_1:func.7">"</a>  )</span><br/>









<b>assume </b><b>that </b><br/><a NAME="E1:49"/><i><font color="Green" title="E42">A1</font></i>: 
<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>
 <b>and </b><br/><a NAME="E2:49"/><i><font color="Green" title="E43">A2</font></i>: 
<font color="Maroon" title="c5">t1</font> is <a href="nattra_1.html#V1" title="NATTRA_1:attr.1">invertible</a>
 ; <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="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font> holds  <span class="p1">(<span class="default"><font color="Maroon" title="c5">t1</font> <a href="nattra_1.html#K10" title="NATTRA_1:func.10">"</a> </span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</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">t1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b1">a</font></span>)</span> <a href="cat_1.html#K7" title="CAT_1:func.7">"</a> </span><br/>

<a NAME="E3:49"/><i><font color="Green" title="E44">A3</font></i>: 
<font color="Maroon" title="c3">F1</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Maroon" title="c4">F2</font>
 
<b>by </b><i><a class="txt" href="#E1:49"><i><font color="Green" title="E42">A1</font></i></a>, <a class="ref" href="nattra_1.html#D7" target="_self" title="NATTRA_1:def.7">Def7</a></i>;<br/>
<b>let </b><font color="Maroon" title="c6">a</font> be   <a href="cat_1.html#NM1" title="CAT_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"><font color="Maroon" title="c5">t1</font> <a href="nattra_1.html#K10" title="NATTRA_1:func.10">"</a> </span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c6">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">t1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c6">a</font></span>)</span> <a href="cat_1.html#K7" title="CAT_1:func.7">"</a> </span><br/>

<b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c5">t1</font> <a href="nattra_1.html#K10" title="NATTRA_1:func.10">"</a> </span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c6">a</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">t1</font> <a href="nattra_1.html#K9" title="NATTRA_1:func.9">"</a> </span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c6">a</font>
<b>by </b><i><a class="txt" href="#E1:49"><i><font color="Green" title="E42">A1</font></i></a>, <a class="txt" href="#E2:49"><i><font color="Green" title="E43">A2</font></i></a>, <a class="ref" href="nattra_1.html#D13" target="_self" title="NATTRA_1:def.13">Def13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">t1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c6">a</font></span>)</span> <a href="cat_1.html#K7" title="CAT_1:func.7">"</a> 
<b>by </b><i><a class="txt" href="#E2:49"><i><font color="Green" title="E43">A2</font></i></a>, <a class="txt" href="#E3:49"><i><font color="Green" title="E44">A3</font></i></a>, <a class="ref" href="nattra_1.html#D12" target="_self" title="NATTRA_1:def.12">Def12</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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