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<span class="kw">let </span><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</font>, <font color="Maroon" title="c3">C</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">G1</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">F2</font>, <font color="Olive" title="b4">G2</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="c3">C</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">G1</font> &amp; <font color="Olive" title="b3">F2</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Olive" title="b4">G2</font> holds <br/><span class="p1"><a href="isocat_2.html#K8" title="ISOCAT_2:func.8">&lt;:</a><span class="default"><font color="Olive" title="b1">F1</font>,<font color="Olive" title="b3">F2</font></span><a href="isocat_2.html#K8" title="ISOCAT_2:func.8">:&gt;</a></span> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <span class="p1"><a href="isocat_2.html#K8" title="ISOCAT_2:func.8">&lt;:</a><span class="default"><font color="Olive" title="b2">G1</font>,<font color="Olive" title="b4">G2</font></span><a href="isocat_2.html#K8" title="ISOCAT_2:func.8">:&gt;</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">F1</font>, <font color="Maroon" title="c5">G1</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">F2</font>, <font color="Olive" title="b2">G2</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="c3">C</font>  st <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">G1</font> &amp; <font color="Olive" title="b1">F2</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Olive" title="b2">G2</font> holds <br/><span class="p1"><a href="isocat_2.html#K8" title="ISOCAT_2:func.8">&lt;:</a><span class="default"><font color="Maroon" title="c4">F1</font>,<font color="Olive" title="b1">F2</font></span><a href="isocat_2.html#K8" title="ISOCAT_2:func.8">:&gt;</a></span> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <span class="p1"><a href="isocat_2.html#K8" title="ISOCAT_2:func.8">&lt;:</a><span class="default"><font color="Maroon" title="c5">G1</font>,<font color="Olive" title="b2">G2</font></span><a href="isocat_2.html#K8" title="ISOCAT_2:func.8">:&gt;</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c6">F2</font>, <font color="Maroon" title="c7">G2</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="c3">C</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="c4">F1</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Maroon" title="c5">G1</font> &amp; <font color="Maroon" title="c6">F2</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Maroon" title="c7">G2</font> implies <span class="p1"><a href="isocat_2.html#K8" title="ISOCAT_2:func.8">&lt;:</a><span class="default"><font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c6">F2</font></span><a href="isocat_2.html#K8" title="ISOCAT_2:func.8">:&gt;</a></span> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <span class="p1"><a href="isocat_2.html#K8" title="ISOCAT_2:func.8">&lt;:</a><span class="default"><font color="Maroon" title="c5">G1</font>,<font color="Maroon" title="c7">G2</font></span><a href="isocat_2.html#K8" title="ISOCAT_2:func.8">:&gt;</a></span> )</span><br/>









<span class="kw">assume </span><a NAME="E1:50"/><span class="lab"><font color="Green" title="E42">A1</font></span>: 
( <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">G1</font> &amp; <font color="Maroon" title="c6">F2</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Maroon" title="c7">G2</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"><a href="isocat_2.html#K8" title="ISOCAT_2:func.8">&lt;:</a><span class="default"><font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c6">F2</font></span><a href="isocat_2.html#K8" title="ISOCAT_2:func.8">:&gt;</a></span> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <span class="p1"><a href="isocat_2.html#K8" title="ISOCAT_2:func.8">&lt;:</a><span class="default"><font color="Maroon" title="c5">G1</font>,<font color="Maroon" title="c7">G2</font></span><a href="isocat_2.html#K8" title="ISOCAT_2:func.8">:&gt;</a></span></span><br/>

<span class="kw">let </span><font color="Maroon" title="c8">a</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="nattra_1.html#D2" title="NATTRA_1:def.2">NATTRA_1:def 2</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<span class="p1">(<span class="default"><span class="p2"><a href="isocat_2.html#K8" title="ISOCAT_2:func.8">&lt;:</a><span class="default"><font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c6">F2</font></span><a href="isocat_2.html#K8" title="ISOCAT_2:func.8">:&gt;</a></span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c8">a</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2"><a href="isocat_2.html#K8" title="ISOCAT_2:func.8">&lt;:</a><span class="default"><font color="Maroon" title="c5">G1</font>,<font color="Maroon" title="c7">G2</font></span><a href="isocat_2.html#K8" title="ISOCAT_2:func.8">:&gt;</a></span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c8">a</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><br/>

<span class="kw">thus </span><a NAME="E2:50"/>
 not  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<span class="p1">(<span class="default"><span class="p2"><a href="isocat_2.html#K8" title="ISOCAT_2:func.8">&lt;:</a><span class="default"><font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c6">F2</font></span><a href="isocat_2.html#K8" title="ISOCAT_2:func.8">:&gt;</a></span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c8">a</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2"><a href="isocat_2.html#K8" title="ISOCAT_2:func.8">&lt;:</a><span class="default"><font color="Maroon" title="c5">G1</font>,<font color="Maroon" title="c7">G2</font></span><a href="isocat_2.html#K8" title="ISOCAT_2:func.8">:&gt;</a></span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c8">a</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="#E1:50"><span class="lab"><font color="Green" title="E42">A1</font></span></a>, <a class="txt" href="isocat_2.html#E48"><span class="lab"><font color="Green" title="E40">Lm3</font></span></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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