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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>  st <font color="Olive" title="b1">F1</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Olive" title="b2">F2</font> holds <br/> for <font color="Olive" title="b3">t</font> being    <a href="nattra_1.html#M1" title="NATTRA_1:mode.1">transformation</a> of <font color="Olive" title="b1">F1</font>,<font color="Olive" title="b2">F2</font> holds <br/> ( <span class="p1">(<span class="default"><a href="nattra_1.html#K4" title="NATTRA_1:func.4">id</a> <font color="Olive" title="b2">F2</font></span>)</span> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Olive" title="b3">t</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b3">t</font> &amp; <font color="Olive" title="b3">t</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <span class="p1">(<span class="default"><a href="nattra_1.html#K4" title="NATTRA_1:func.4">id</a> <font color="Olive" title="b1">F1</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b3">t</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"> ( <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> implies  for <font color="Olive" title="b1">t</font> being    <a href="nattra_1.html#M1" title="NATTRA_1:mode.1">transformation</a> of <font color="Maroon" title="c3">F1</font>,<font color="Maroon" title="c4">F2</font> holds <br/> ( <span class="p1">(<span class="default"><a href="nattra_1.html#K4" title="NATTRA_1:func.4">id</a> <font color="Maroon" title="c4">F2</font></span>)</span> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Olive" title="b1">t</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b1">t</font> &amp; <font color="Olive" title="b1">t</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <span class="p1">(<span class="default"><a href="nattra_1.html#K4" title="NATTRA_1:func.4">id</a> <font color="Maroon" title="c3">F1</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b1">t</font> ) )</span><br/>







<span class="kw">assume </span><a NAME="E1:29"/><span class="lab"><font color="Green" title="E24">A1</font></span>: 
<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>
 ; <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">t</font> being    <a href="nattra_1.html#M1" title="NATTRA_1:mode.1">transformation</a> of <font color="Maroon" title="c3">F1</font>,<font color="Maroon" title="c4">F2</font> holds <br/> ( <span class="p1">(<span class="default"><a href="nattra_1.html#K4" title="NATTRA_1:func.4">id</a> <font color="Maroon" title="c4">F2</font></span>)</span> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Olive" title="b1">t</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b1">t</font> &amp; <font color="Olive" title="b1">t</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <span class="p1">(<span class="default"><a href="nattra_1.html#K4" title="NATTRA_1:func.4">id</a> <font color="Maroon" title="c3">F1</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b1">t</font> )</span><br/>

<span class="kw">let </span><font color="Maroon" title="c5">t</font> be    <a href="nattra_1.html#M1" title="NATTRA_1:mode.1">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"> ( <span class="p1">(<span class="default"><a href="nattra_1.html#K4" title="NATTRA_1:func.4">id</a> <font color="Maroon" title="c4">F2</font></span>)</span> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Maroon" title="c5">t</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c5">t</font> &amp; <font color="Maroon" title="c5">t</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <span class="p1">(<span class="default"><a href="nattra_1.html#K4" title="NATTRA_1:func.4">id</a> <font color="Maroon" title="c3">F1</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c5">t</font> )</span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="nattra_1.html#K4" title="NATTRA_1:func.4">id</a> <font color="Maroon" title="c4">F2</font></span>)</span> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Maroon" title="c5">t</font></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> <font color="Maroon" title="c5">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c6">a</font></span><br/><a NAME="E1:29_1"/><span class="lab"><font color="Green" title="E25">A2</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c3">F1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c6">a</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c6">a</font></span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:29"><span class="lab"><font color="Green" title="E24">A1</font></span></a>, <a class="ref" href="nattra_1.html#D2" target="_self" title="NATTRA_1:def.2">Def2</a></span>;<br/><span class="kw">thus </span><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="nattra_1.html#K4" title="NATTRA_1:func.4">id</a> <font color="Maroon" title="c4">F2</font></span>)</span> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Maroon" title="c5">t</font></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"><span class="p2">(<span class="default"><a href="nattra_1.html#K4" title="NATTRA_1:func.4">id</a> <font color="Maroon" title="c4">F2</font></span>)</span> <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#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c6">a</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:29"><span class="lab"><font color="Green" title="E24">A1</font></span></a>, <a class="ref" href="nattra_1.html#D6" target="_self" title="NATTRA_1:def.6">Def6</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c6">a</font></span>)</span></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c6">a</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="nattra_1.html#T20" target="_self" title="NATTRA_1:th.20">Th21</a></span>
<br/>.= 
<font color="Maroon" title="c5">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c6">a</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:29_1"><span class="lab"><font color="Green" title="E25">A2</font></span></a>, <a class="ref" href="cat_1.html#T28" title="CAT_1:th.28">CAT_1:28</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/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:29"/>
<span class="p1">(<span class="default"><a href="nattra_1.html#K4" title="NATTRA_1:func.4">id</a> <font color="Maroon" title="c4">F2</font></span>)</span> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Maroon" title="c5">t</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c5">t</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:29"><span class="lab"><font color="Green" title="E24">A1</font></span></a>, <a class="ref" href="nattra_1.html#T19" target="_self" title="NATTRA_1:th.19">Th20</a></span>; <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="c5">t</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <span class="p1">(<span class="default"><a href="nattra_1.html#K4" title="NATTRA_1:func.4">id</a> <font color="Maroon" title="c3">F1</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c5">t</font></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c5">t</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <span class="p2">(<span class="default"><a href="nattra_1.html#K4" title="NATTRA_1:func.4">id</a> <font color="Maroon" title="c3">F1</font></span>)</span></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> <font color="Maroon" title="c5">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c6">a</font></span><br/><a NAME="E1:29_2"/><span class="lab"><font color="Green" title="E25">A3</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c3">F1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c6">a</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c6">a</font></span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:29"><span class="lab"><font color="Green" title="E24">A1</font></span></a>, <a class="ref" href="nattra_1.html#D2" target="_self" title="NATTRA_1:def.2">Def2</a></span>;<br/><span class="kw">thus </span><span class="p1">(<span class="default"><font color="Maroon" title="c5">t</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <span class="p2">(<span class="default"><a href="nattra_1.html#K4" title="NATTRA_1:func.4">id</a> <font color="Maroon" title="c3">F1</font></span>)</span></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">t</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#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="nattra_1.html#K4" title="NATTRA_1:func.4">id</a> <font color="Maroon" title="c3">F1</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c6">a</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:29"><span class="lab"><font color="Green" title="E24">A1</font></span></a>, <a class="ref" href="nattra_1.html#D6" target="_self" title="NATTRA_1:def.6">Def6</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">t</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#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c6">a</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="nattra_1.html#T20" target="_self" title="NATTRA_1:th.20">Th21</a></span>
<br/>.= 
<font color="Maroon" title="c5">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c6">a</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:29_2"><span class="lab"><font color="Green" title="E25">A3</font></span></a>, <a class="ref" href="cat_1.html#T29" title="CAT_1:th.29">CAT_1:29</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/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E5:29"/>
<font color="Maroon" title="c5">t</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <span class="p1">(<span class="default"><a href="nattra_1.html#K4" title="NATTRA_1:func.4">id</a> <font color="Maroon" title="c3">F1</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c5">t</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:29"><span class="lab"><font color="Green" title="E24">A1</font></span></a>, <a class="ref" href="nattra_1.html#T19" target="_self" title="NATTRA_1:th.19">Th20</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/>


</div>
