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<b>let </b><font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font>, <font color="Maroon" title="c5">c</font> be   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">W</font> <a href="waybel34.html#K4" title="WAYBEL34:func.4">-INF_category</a> </span>)</span>;<br/>

<b>assume </b><a NAME="E1:61_1"/><i><font color="Green" title="E40">A3</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="c3">a</font>,<font color="Maroon" title="c4">b</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">b</font>,<font color="Maroon" title="c5">c</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/>

<b>let </b><font color="Maroon" title="c6">f</font> be   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>;<br/><b>let </b><font color="Maroon" title="c7">g</font> be   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font>;<br/>



<a NAME="E2:61_1"/><i><font color="Green" title="E41">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="c3">a</font>,<font color="Maroon" title="c5">c</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="waybel34.html#E1:61_1"><i><font color="Green" title="E40">A3</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="E3:61_1"/><b>then </b>
(  <a href="yellow21.html#K5" title="YELLOW21:func.5">@</a> <font color="Maroon" title="c6">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">f</font> &amp;  <a href="yellow21.html#K5" title="YELLOW21:func.5">@</a> <font color="Maroon" title="c7">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">g</font> &amp;  <a href="yellow21.html#K5" title="YELLOW21:func.5">@</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c6">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">g</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c6">f</font> )
 
<b>by </b><i><a class="txt" href="waybel34.html#E1:61_1"><i><font color="Green" title="E40">A3</font></i></a>, <a class="ref" href="yellow21.html#D7" title="YELLOW21:def.7">YELLOW21:def 7</a></i>;<br/>
<a NAME="E4:61_1"/><b>then </b>
 <a href="yellow21.html#K5" title="YELLOW21:func.5">@</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c6">f</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><a href="yellow21.html#K5" title="YELLOW21:func.5">@</a> <font color="Maroon" title="c7">g</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><a href="yellow21.html#K5" title="YELLOW21:func.5">@</a> <font color="Maroon" title="c6">f</font></span>)</span>
 
<b>by </b><i><a class="txt" href="waybel34.html#E1:61_1"><i><font color="Green" title="E40">A3</font></i></a>, <a class="txt" href="waybel34.html#E2:61_1"><i><font color="Green" title="E41">A4</font></i></a>, <a class="ref" href="altcat_1.html#D14" title="ALTCAT_1:def.14">ALTCAT_1:def 14</a></i>;<br/>
<b>hence </b><a NAME="E5:61_1"/>
( <font color="Maroon">S<sub>2</sub></font>[<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">f</font>] &amp; <font color="Maroon">S<sub>2</sub></font>[<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c7">g</font>] implies <font color="Maroon">S<sub>2</sub></font>[<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c7">g</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c6">f</font>] )
 <b>by </b><i><a class="ref" href="waybel20.html#T29" title="WAYBEL20:th.29">WAYBEL20:29</a></i>;<br/>


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