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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"> ( <font color="Maroon" title="c1">A</font> is  <a href="nattra_1.html#V2" title="NATTRA_1:attr.2">discrete</a>  implies  <a href="nattra_1.html#K12" title="NATTRA_1:func.12">Functors</a> (<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c1">A</font>) is  <a href="nattra_1.html#V2" title="NATTRA_1:attr.2">discrete</a>  )</span><br/>



<span class="kw">assume </span><a NAME="E1:72"/><span class="lab"><font color="Green" title="E56">A1</font></span>: 
<font color="Maroon" title="c1">A</font> is  <a href="nattra_1.html#V2" title="NATTRA_1:attr.2">discrete</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="nattra_1.html#K12" title="NATTRA_1:func.12">Functors</a> (<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c1">A</font>) is  <a href="nattra_1.html#V2" title="NATTRA_1:attr.2">discrete</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c3">f</font> be   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K12" title="NATTRA_1:func.12">Functors</a> (<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c1">A</font>)</span>)</span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="nattra_1.html#D18" target="_self" title="NATTRA_1:def.18">NATTRA_1:def 18</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">a</font> being   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K12" title="NATTRA_1:func.12">Functors</a> (<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c1">A</font>)</span>)</span> st <font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Olive" title="b1">a</font></span><br/>

<a NAME="E2:72"/>
<font color="Maroon" title="c3">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K12" title="NATTRA_1:func.12">Functors</a> (<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c1">A</font>)</span>)</span>
 
;<br/>
<a NAME="E3:72"/><span class="kw">then </span>
<font color="Maroon" title="c3">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="nattra_1.html#K11" title="NATTRA_1:func.11">NatTrans</a> (<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c1">A</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nattra_1.html#D17" target="_self" title="NATTRA_1:def.17">Def18</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">F1</font>, <font color="Maroon" title="c5">F2</font> being    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c6">t</font> being    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font><span class="kw"> such that </span><br/><a NAME="E5:72"/><span class="lab"><font color="Green" title="E57">A2</font></span>: 
<font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<font color="Maroon" title="c6">t</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">and </span><br/><a NAME="E6:72"/><span class="lab"><font color="Green" title="E58">A3</font></span>: 
<font color="Maroon" title="c4">F1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c5">F2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nattra_1.html#D16" target="_self" title="NATTRA_1:def.16">Def16</a></span>;<br/>
<a NAME="E7:72"/>
<font color="Maroon" title="c4">F1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_2.html#K7" title="CAT_2:func.7">Funct</a> (<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c1">A</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_2.html#D2" title="CAT_2:def.2">CAT_2:def 2</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c7">a</font> = <font color="Maroon" title="c4">F1</font> as   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K12" title="NATTRA_1:func.12">Functors</a> (<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c1">A</font>)</span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="nattra_1.html#D17" target="_self" title="NATTRA_1:def.17">Def18</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c7">a</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">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c7">a</font></span><br/>

<a NAME="E9:72"/>
<font color="Maroon" title="c4">F1</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Maroon" title="c5">F2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:72"><span class="lab"><font color="Green" title="E58">A3</font></span></a>, <a class="ref" href="nattra_1.html#D7" target="_self" title="NATTRA_1:def.7">Def7</a></span>;<br/>
<a NAME="E10:72"/><span class="kw">then </span><span class="lab"><font color="Green" title="E59">A4</font></span>: 
<font color="Maroon" title="c4">F1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c5">F2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:72"><span class="lab"><font color="Green" title="E56">A1</font></span></a>, <a class="ref" href="nattra_1.html#T42" target="_self" title="NATTRA_1:th.42">Th49</a></span>;<br/>
<a NAME="E11:72"/><span class="kw">then </span>
<font color="Maroon" title="c6">t</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="nattra_1.html#K7" title="NATTRA_1:func.7">id</a> <font color="Maroon" title="c4">F1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:72"><span class="lab"><font color="Green" title="E56">A1</font></span></a>, <a class="ref" href="nattra_1.html#T43" target="_self" title="NATTRA_1:th.43">Th50</a></span>;<br/>
<span class="kw">hence </span><a NAME="E12:72"/>
<font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c7">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:72"><span class="lab"><font color="Green" title="E57">A2</font></span></a>, <a class="txt" href="#E10:72"><span class="lab"><font color="Green" title="E59">A4</font></span></a>, <a class="ref" href="nattra_1.html#D17" target="_self" title="NATTRA_1:def.17">Def18</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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