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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>;<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>;<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>;<br/>









<b>assume </b><a NAME="E1:47"/><i><font color="Green" title="E40">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>
 ;<br/>

<a NAME="E2:47"/><b>then </b><i><font color="Green" title="E41">A2</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="ref" href="nattra_1.html#D7" target="_self" title="NATTRA_1:def.7">Def7</a></i>;<br/>
<b>assume </b><a NAME="E3:47"/><i><font color="Green" title="E42">A3</font></i>: 
<font color="Maroon" title="c5">t1</font> is <a href="nattra_1.html#V1" title="NATTRA_1:attr.1">invertible</a>
 ;<br/>

<b>hence </b><a NAME="E4:47"/>
<font color="Maroon" title="c4">F2</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Maroon" title="c3">F1</font>
 <b>by </b><i><a class="txt" href="nattra_1.html#E2:47"><i><font color="Green" title="E41">A2</font></i></a>, <a class="txt" href="nattra_1.html#E42"><i><font color="Green" title="E36">Lm3</font></i></a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="nattra_1.html#D7" target="_self" title="NATTRA_1:def.7">NATTRA_1:def 7</a><br/>

<b>take </b>
<font color="Maroon" title="c5">t1</font> <a href="nattra_1.html#K9" title="NATTRA_1:func.9">"</a> 
;<br/>

<b>thus </b><a NAME="E5:47"/>
for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font>  st  <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  holds <br/>for <font color="Olive" title="b3">f</font> being   <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> holds  <span class="p1">(<span class="default"><span class="p2">(<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="Olive" title="b2">b</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F2</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b3">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b3">f</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <span class="p1">(<span class="default"><span class="p2">(<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="Olive" title="b1">a</font></span>)</span>
 <b>by </b><i><a class="txt" href="nattra_1.html#E1:47"><i><font color="Green" title="E40">A1</font></i></a>, <a class="txt" href="nattra_1.html#E3:47"><i><font color="Green" title="E42">A3</font></i></a>, <a class="txt" href="nattra_1.html#E44"><i><font color="Green" title="E38">Lm4</font></i></a></i>;<br/>


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