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<a NAME="E1:57_1_1"/>
<span class="p1"><a href="isocat_2.html#K15" title="ISOCAT_2:func.15">&lt;:</a><span class="default"><font color="Maroon" title="c8">t1</font>,<font color="Maroon" title="c9">t2</font></span><a href="isocat_2.html#K15" title="ISOCAT_2:func.15">:&gt;</a></span> is    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <span class="p1"><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">&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#K10" title="ISOCAT_2:func.10">:&gt;</a></span>,<span class="p1"><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">&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#K10" title="ISOCAT_2:func.10">:&gt;</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_1_1_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:57_1_1_1"/>
<span class="p1"><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">&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#K10" title="ISOCAT_2:func.10">:&gt;</a></span> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <span class="p1"><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">&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#K10" title="ISOCAT_2:func.10">:&gt;</a></span>
 <b>by </b><i><a class="txt" href="isocat_2.html#E1:57"><i><font color="Green" title="E48">A1</font></i></a>, <a class="txt" href="isocat_2.html#E2:57"><i><font color="Green" title="E49">A2</font></i></a>, <a class="ref" href="isocat_2.html#T46" target="_self" title="ISOCAT_2:th.46">Th46</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="nattra_1.html#D8" title="NATTRA_1:def.8">NATTRA_1:def 8</a><br/>

<b>thus </b><a NAME="E2:57_1_1_1"/>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Vertices</a> of <font color="Maroon" title="c1">A</font>  holds <br/>(  <a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  or for <font color="Olive">b<sub>3</sub></font> being   <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> holds  <span class="p1">(<span class="default"><span class="p2"><a href="isocat_2.html#K15" title="ISOCAT_2:func.15">&lt;:</a><span class="default"><font color="Maroon" title="c8">t1</font>,<font color="Maroon" title="c9">t2</font></span><a href="isocat_2.html#K15" title="ISOCAT_2:func.15">:&gt;</a></span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <span class="p1">(<span class="default"><span class="p2"><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">&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#K10" title="ISOCAT_2:func.10">:&gt;</a></span> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive">b<sub>3</sub></font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">&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#K10" title="ISOCAT_2:func.10">:&gt;</a></span> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive">b<sub>3</sub></font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <span class="p1">(<span class="default"><span class="p2"><a href="isocat_2.html#K15" title="ISOCAT_2:func.15">&lt;:</a><span class="default"><font color="Maroon" title="c8">t1</font>,<font color="Maroon" title="c9">t2</font></span><a href="isocat_2.html#K15" title="ISOCAT_2:func.15">:&gt;</a></span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> )
 <b>by </b><i><a class="txt" href="isocat_2.html#E1:57"><i><font color="Green" title="E48">A1</font></i></a>, <a class="txt" href="isocat_2.html#E2:57"><i><font color="Green" title="E49">A2</font></i></a>, <a class="txt" href="isocat_2.html#E60"><i><font color="Green" title="E46">Lm4</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:57_1_1"/>
<span class="p1"><a href="isocat_2.html#K15" title="ISOCAT_2:func.15">&lt;:</a><span class="default"><font color="Maroon" title="c8">t1</font>,<font color="Maroon" title="c9">t2</font></span><a href="isocat_2.html#K15" title="ISOCAT_2:func.15">:&gt;</a></span> is    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <span class="p1"><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">&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#K10" title="ISOCAT_2:func.10">:&gt;</a></span>,<span class="p1"><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">&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#K10" title="ISOCAT_2:func.10">:&gt;</a></span>
 ;<br/>


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