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<b>let </b><font color="Maroon" title="c1">C</font> be   <a href="altcat_1.html#NM4" title="ALTCAT_1:NM.4">category</a>;<br/><b>let </b><font color="Maroon" title="c2">o1</font>, <font color="Maroon" title="c3">o2</font>, <font color="Maroon" title="c4">o3</font>, <font color="Maroon" title="c5">o4</font> be   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">C</font>;<br/><b>let </b><font color="Maroon" title="c6">a</font> be   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c2">o1</font>,<font color="Maroon" title="c3">o2</font>;<br/><b>let </b><font color="Maroon" title="c7">b</font> be   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c3">o2</font>,<font color="Maroon" title="c4">o3</font>;<br/><b>let </b><font color="Maroon" title="c8">c</font> be   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c2">o1</font>,<font color="Maroon" title="c5">o4</font>;<br/><b>let </b><font color="Maroon" title="c9">d</font> be   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c5">o4</font>,<font color="Maroon" title="c4">o3</font>;<br/>











<b>assume </b><b>that </b><br/><a NAME="E1:5"/><i><font color="Green" title="E1">A1</font></i>: 
<font color="Maroon" title="c7">b</font> <a href="altcat_1.html#K5" title="ALTCAT_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="c9">d</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c8">c</font>
 <b>and </b><br/><a NAME="E2:5"/><i><font color="Green" title="E2">A2</font></i>: 
<font color="Maroon" title="c6">a</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">a</font> <a href="altcat_3.html#K1" title="ALTCAT_3:func.1">"</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <font color="Maroon" title="c3">o2</font>
 <b>and </b><br/><a NAME="E3:5"/><i><font color="Green" title="E3">A3</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">d</font> <a href="altcat_3.html#K1" title="ALTCAT_3:func.1">"</a> </span>)</span> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c9">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <font color="Maroon" title="c5">o4</font>
 <b>and </b><br/><a NAME="E4:5"/><i><font color="Green" title="E4">A4</font></i>: 
( <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c2">o1</font>,<font color="Maroon" title="c3">o2</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></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>  &amp; <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c3">o2</font>,<font color="Maroon" title="c2">o1</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></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>  &amp; <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c3">o2</font>,<font color="Maroon" title="c4">o3</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></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>  &amp; <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c4">o3</font>,<font color="Maroon" title="c5">o4</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></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>  &amp; <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c5">o4</font>,<font color="Maroon" title="c4">o3</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></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>  )
 ;<br/>

<a NAME="E5:5"/>
<span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c2">o1</font>,<font color="Maroon" title="c4">o3</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></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> 
 
<b>by </b><i><a class="txt" href="functor3.html#E4:5"><i><font color="Green" title="E4">A4</font></i></a>, <a class="ref" href="altcat_1.html#D4" title="ALTCAT_1:def.4">ALTCAT_1:def 4</a></i>;<br/>
<a NAME="E6:5"/><b>then </b><i><font color="Green" title="E5">A5</font></i>: 
( <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c2">o1</font>,<font color="Maroon" title="c5">o4</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></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>  &amp; <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c3">o2</font>,<font color="Maroon" title="c5">o4</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></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>  )
 
<b>by </b><i><a class="txt" href="functor3.html#E4:5"><i><font color="Green" title="E4">A4</font></i></a>, <a class="ref" href="altcat_1.html#D4" title="ALTCAT_1:def.4">ALTCAT_1:def 4</a></i>;<br/>
<font color="Maroon" title="c7">b</font> = 
<font color="Maroon" title="c7">b</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <span class="p1">(<span class="default"><a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <font color="Maroon" title="c3">o2</font></span>)</span>
<b>by </b><i><a class="txt" href="functor3.html#E4:5"><i><font color="Green" title="E4">A4</font></i></a>, <a class="ref" href="altcat_1.html#D19" title="ALTCAT_1:def.19">ALTCAT_1:def 19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">b</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c6">a</font></span>)</span> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">a</font> <a href="altcat_3.html#K1" title="ALTCAT_3:func.1">"</a> </span>)</span>
<b>by </b><i><a class="txt" href="functor3.html#E2:5"><i><font color="Green" title="E2">A2</font></i></a>, <a class="txt" href="functor3.html#E4:5"><i><font color="Green" title="E4">A4</font></i></a>, <a class="ref" href="altcat_1.html#T25" title="ALTCAT_1:th.25">ALTCAT_1:25</a></i>
;<br/>
<b>hence </b><span class="p1">(<span class="default"><font color="Maroon" title="c9">d</font> <a href="altcat_3.html#K1" title="ALTCAT_3:func.1">"</a> </span>)</span> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c7">b</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">d</font> <a href="altcat_3.html#K1" title="ALTCAT_3:func.1">"</a> </span>)</span> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">d</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">a</font> <a href="altcat_3.html#K1" title="ALTCAT_3:func.1">"</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="functor3.html#E1:5"><i><font color="Green" title="E1">A1</font></i></a>, <a class="txt" href="functor3.html#E4:5"><i><font color="Green" title="E4">A4</font></i></a>, <a class="txt" href="functor3.html#E6:5"><i><font color="Green" title="E5">A5</font></i></a>, <a class="ref" href="altcat_1.html#T25" title="ALTCAT_1:th.25">ALTCAT_1:25</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">d</font> <a href="altcat_3.html#K1" title="ALTCAT_3:func.1">"</a> </span>)</span> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c9">d</font></span>)</span> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">a</font> <a href="altcat_3.html#K1" title="ALTCAT_3:func.1">"</a> </span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="functor3.html#E4:5"><i><font color="Green" title="E4">A4</font></i></a>, <a class="txt" href="functor3.html#E6:5"><i><font color="Green" title="E5">A5</font></i></a>, <a class="ref" href="altcat_1.html#T25" title="ALTCAT_1:th.25">ALTCAT_1:25</a></i>
<br/>.= 
<font color="Maroon" title="c8">c</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">a</font> <a href="altcat_3.html#K1" title="ALTCAT_3:func.1">"</a> </span>)</span>
<b>by </b><i><a class="txt" href="functor3.html#E3:5"><i><font color="Green" title="E3">A3</font></i></a>, <a class="txt" href="functor3.html#E6:5"><i><font color="Green" title="E5">A5</font></i></a>, <a class="ref" href="altcat_1.html#T24" title="ALTCAT_1:th.24">ALTCAT_1:24</a></i>
;<br/><br/>


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