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<b>let </b><font color="Maroon">A</font> be    <a href="altcat_1.html#L2">AltCatStr</a> , <font color="Maroon">B</font> be    <a href="altcat_1.html#L2">AltCatStr</a> ;<br/>

<b>assume </b><a NAME="E1:27"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">A</font>,<font color="Maroon">B</font> <a href="yellow20.html#R1" target="_self">have_the_same_composition</a> 
 ;<br/>

<b>let </b><font color="Maroon">a1</font> be   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">A</font>, <font color="Maroon">a2</font> be   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">A</font>;<br/><b>let </b><font color="Maroon">b1</font> be   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">B</font>, <font color="Maroon">b2</font> be   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">B</font>;<br/><b>let </b><font color="Maroon">o1</font> be   <a href="altcat_1.html#NM1">object</a> of <span class="p1">(<span class="default"><a href="yellow20.html#K2" target="_self">Intersect</a> <font color="Maroon">A</font>,<font color="Maroon">B</font></span>)</span>, <font color="Maroon">o2</font> be   <a href="altcat_1.html#NM1">object</a> of <span class="p1">(<span class="default"><a href="yellow20.html#K2" target="_self">Intersect</a> <font color="Maroon">A</font>,<font color="Maroon">B</font></span>)</span>;<br/>





<b>assume </b><a NAME="E2:27"/>
( <font color="Maroon">o1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a1</font> &amp; <font color="Maroon">o1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b1</font> &amp; <font color="Maroon">o2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a2</font> &amp; <font color="Maroon">o2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b2</font> )
 ;<br/>

<a NAME="E3:27"/><b>then </b>
<span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">o1</font>,<font color="Maroon">o2</font></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">a1</font>,<font color="Maroon">a2</font></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="xboole_0.html#K3">/\</a> <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">b1</font>,<font color="Maroon">b2</font></span><a href="altcat_1.html#K1">^&gt;</a></span>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E4:27"/>
(  not <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">a1</font>,<font color="Maroon">a2</font></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  or  not <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">b1</font>,<font color="Maroon">b2</font></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  or for <font color="Olive">f</font> being  <a href="altcat_1.html#NM2">Morphism</a> of <font color="Maroon">a1</font>,<font color="Maroon">a2</font><br/> for <font color="Olive">g</font> being  <a href="altcat_1.html#NM2">Morphism</a> of <font color="Maroon">b1</font>,<font color="Maroon">b2</font>  st <font color="Olive">f</font> <a href="hidden.html#R1">=</a> <font color="Olive">g</font> holds <br/><font color="Olive">f</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">o1</font>,<font color="Maroon">o2</font></span><a href="altcat_1.html#K1">^&gt;</a></span> )
 <b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>


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