<?xml version="1.0"?>
<div class="add">

<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> be   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">C</font>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:15"/><i><font color="Green" title="E5">A1</font></i>: 
<font color="Maroon" title="c2">o1</font> is <a href="altcat_3.html#V6" title="ALTCAT_3:attr.6">initial</a>
 <b>and </b><br/><a NAME="E2:15"/><i><font color="Green" title="E6">A2</font></i>: 
<font color="Maroon" title="c3">o2</font> is <a href="altcat_3.html#V7" title="ALTCAT_3:attr.7">terminal</a>
 ;<br/>

<b>assume </b><a NAME="E3:15"/>
<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> 
 ;<br/>

<b>then consider </b><font color="Maroon" title="c4">m</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E5:15"/><i><font color="Green" title="E7">A3</font></i>: 
<font color="Maroon" title="c4">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <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>
 <b>by </b><i><a class="ref" href="xboole_0.html#D1" title="XBOOLE_0:def.1">XBOOLE_0:def 1</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c5">m</font> = <font color="Maroon" title="c4">m</font> as   <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="c2">o1</font> <b>by </b><i><a class="txt" href="altcat_4.html#E5:15"><i><font color="Green" title="E7">A3</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon" title="c6">l</font> being   <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><b> such that </b><br/><a NAME="E8:15"/><i><font color="Green" title="E8">A4</font></i>: 
<font color="Maroon" title="c6">l</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <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>
 <b>and </b><br/><a NAME="E9:15"/>
for <font color="Olive" title="b1">M1</font> being  <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>  st <font color="Olive" title="b1">M1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <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> holds <br/><font color="Maroon" title="c6">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">M1</font>
 <b>by </b><i><a class="txt" href="altcat_4.html#E1:15"><i><font color="Green" title="E5">A1</font></i></a>, <a class="ref" href="altcat_3.html#T25" title="ALTCAT_3:th.25">ALTCAT_3:25</a></i>;<br/>
<a NAME="E10:15"/>
for <font color="Olive" title="b1">o3</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">C</font>  ex <font color="Olive" title="b2">M</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c3">o2</font>,<font color="Olive" title="b1">o3</font> st <br/>( <font color="Olive" title="b2">M</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <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="Olive" title="b1">o3</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> &amp; ( for <font color="Olive" title="b3">M1</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c3">o2</font>,<font color="Olive" title="b1">o3</font>  st <font color="Olive" title="b3">M1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <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="Olive" title="b1">o3</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> holds <br/><font color="Olive" title="b2">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">M1</font> ) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c7">o3</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>consider </b><font color="Maroon" title="c8">M</font> being   <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="c7">o3</font><b> such that </b><br/><a NAME="E2:15_1"/><i><font color="Green" title="E9">A5</font></i>: 
( <font color="Maroon" title="c8">M</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <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="c7">o3</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> &amp; ( for <font color="Olive" title="b1">M1</font> being  <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="c7">o3</font>  st <font color="Olive" title="b1">M1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <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="c7">o3</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> holds <br/><font color="Maroon" title="c8">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">M1</font> ) )
 <b>by </b><i><a class="txt" href="altcat_4.html#E1:15"><i><font color="Green" title="E5">A1</font></i></a>, <a class="ref" href="altcat_3.html#T25" title="ALTCAT_3:th.25">ALTCAT_3:25</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c8">M</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c5">m</font>
;<br/>

<a NAME="E3:15_1"/>
<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="c7">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="altcat_4.html#E5:15"><i><font color="Green" title="E7">A3</font></i></a>, <a class="txt" href="altcat_4.html#E2:15_1"><i><font color="Green" title="E9">A5</font></i></a>, <a class="ref" href="altcat_1.html#D4" title="ALTCAT_1:def.4">ALTCAT_1:def 4</a></i>;<br/>
<b>hence </b><a NAME="E4:15_1"/>
<font color="Maroon" title="c8">M</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c5">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <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="c7">o3</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span>
 ;<br/>

<b>let </b><font color="Maroon" title="c9">M1</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="c7">o3</font>;<br/>

<b>assume </b><a NAME="E5:15_1"/><i><font color="Green" title="E10">A6</font></i>: 
<font color="Maroon" title="c9">M1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <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="c7">o3</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span>
 ;<br/>

<b>consider </b><font color="Maroon" title="c10">i2</font> being   <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="c3">o2</font><b> such that </b><br/><a NAME="E7:15_1"/>
<font color="Maroon" title="c10">i2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <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="c3">o2</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span>
 <b>and </b><br/><a NAME="E8:15_1"/><i><font color="Green" title="E11">A7</font></i>: 
for <font color="Olive" title="b1">M1</font> being  <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="c3">o2</font>  st <font color="Olive" title="b1">M1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <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="c3">o2</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> holds <br/><font color="Maroon" title="c10">i2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">M1</font>
 <b>by </b><i><a class="txt" href="altcat_4.html#E2:15"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="altcat_3.html#T27" title="ALTCAT_3:th.27">ALTCAT_3:27</a></i>;<br/>
<b>thus </b><font color="Maroon" title="c8">M</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c5">m</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">M1</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c6">l</font></span>)</span> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c5">m</font>
<b>by </b><i><a class="txt" href="altcat_4.html#E2:15_1"><i><font color="Green" title="E9">A5</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c9">M1</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">l</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c5">m</font></span>)</span>
<b>by </b><i><a class="txt" href="altcat_4.html#E5:15"><i><font color="Green" title="E7">A3</font></i></a>, <a class="txt" href="altcat_4.html#E8:15"><i><font color="Green" title="E8">A4</font></i></a>, <a class="txt" href="altcat_4.html#E5:15_1"><i><font color="Green" title="E10">A6</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="c9">M1</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c10">i2</font>
<b>by </b><i><a class="txt" href="altcat_4.html#E8:15_1"><i><font color="Green" title="E11">A7</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c9">M1</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="altcat_4.html#E8:15_1"><i><font color="Green" title="E11">A7</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c9">M1</font>
<b>by </b><i><a class="txt" href="altcat_4.html#E5:15_1"><i><font color="Green" title="E10">A6</font></i></a>, <a class="ref" href="altcat_1.html#D19" title="ALTCAT_1:def.19">ALTCAT_1:def 19</a></i>
;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E11:15"/>
<font color="Maroon" title="c3">o2</font> is <a href="altcat_3.html#V6" title="ALTCAT_3:attr.6">initial</a>
 <b>by </b><i><a class="ref" href="altcat_3.html#T25" title="ALTCAT_3:th.25">ALTCAT_3:25</a></i>;<br/>

<a NAME="E12:15"/>
for <font color="Olive" title="b1">o3</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">C</font>  ex <font color="Olive" title="b2">M</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Olive" title="b1">o3</font>,<font color="Maroon" title="c2">o1</font> st <br/>( <font color="Olive" title="b2">M</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Olive" title="b1">o3</font>,<font color="Maroon" title="c2">o1</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> &amp; ( for <font color="Olive" title="b3">M1</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Olive" title="b1">o3</font>,<font color="Maroon" title="c2">o1</font>  st <font color="Olive" title="b3">M1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Olive" title="b1">o3</font>,<font color="Maroon" title="c2">o1</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> holds <br/><font color="Olive" title="b2">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">M1</font> ) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c7">o3</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>consider </b><font color="Maroon" title="c8">M</font> being   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c7">o3</font>,<font color="Maroon" title="c3">o2</font><b> such that </b><br/><a NAME="E2:15_2"/><i><font color="Green" title="E9">A8</font></i>: 
( <font color="Maroon" title="c8">M</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c7">o3</font>,<font color="Maroon" title="c3">o2</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> &amp; ( for <font color="Olive" title="b1">M1</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c7">o3</font>,<font color="Maroon" title="c3">o2</font>  st <font color="Olive" title="b1">M1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c7">o3</font>,<font color="Maroon" title="c3">o2</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> holds <br/><font color="Maroon" title="c8">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">M1</font> ) )
 <b>by </b><i><a class="txt" href="altcat_4.html#E2:15"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="altcat_3.html#T27" title="ALTCAT_3:th.27">ALTCAT_3:27</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c5">m</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c8">M</font>
;<br/>

<a NAME="E3:15_2"/>
<span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c7">o3</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> 
 
<b>by </b><i><a class="txt" href="altcat_4.html#E5:15"><i><font color="Green" title="E7">A3</font></i></a>, <a class="txt" href="altcat_4.html#E2:15_2"><i><font color="Green" title="E9">A8</font></i></a>, <a class="ref" href="altcat_1.html#D4" title="ALTCAT_1:def.4">ALTCAT_1:def 4</a></i>;<br/>
<b>hence </b><a NAME="E4:15_2"/>
<font color="Maroon" title="c5">m</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c8">M</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c7">o3</font>,<font color="Maroon" title="c2">o1</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span>
 ;<br/>

<b>let </b><font color="Maroon" title="c9">M1</font> be   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c7">o3</font>,<font color="Maroon" title="c2">o1</font>;<br/>

<b>assume </b><a NAME="E5:15_2"/><i><font color="Green" title="E10">A9</font></i>: 
<font color="Maroon" title="c9">M1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c7">o3</font>,<font color="Maroon" title="c2">o1</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span>
 ;<br/>

<b>consider </b><font color="Maroon" title="c10">i1</font> being   <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="c2">o1</font><b> such that </b><br/><a NAME="E7:15_2"/>
<font color="Maroon" title="c10">i1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <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="c2">o1</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span>
 <b>and </b><br/><a NAME="E8:15_2"/><i><font color="Green" title="E11">A10</font></i>: 
for <font color="Olive" title="b1">M1</font> being  <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="c2">o1</font>  st <font color="Olive" title="b1">M1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <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="c2">o1</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> holds <br/><font color="Maroon" title="c10">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">M1</font>
 <b>by </b><i><a class="txt" href="altcat_4.html#E1:15"><i><font color="Green" title="E5">A1</font></i></a>, <a class="ref" href="altcat_3.html#T25" title="ALTCAT_3:th.25">ALTCAT_3:25</a></i>;<br/>
<b>thus </b><font color="Maroon" title="c5">m</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c8">M</font> = 
<font color="Maroon" title="c5">m</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">l</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c9">M1</font></span>)</span>
<b>by </b><i><a class="txt" href="altcat_4.html#E2:15_2"><i><font color="Green" title="E9">A8</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">m</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c6">l</font></span>)</span> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c9">M1</font>
<b>by </b><i><a class="txt" href="altcat_4.html#E5:15"><i><font color="Green" title="E7">A3</font></i></a>, <a class="txt" href="altcat_4.html#E8:15"><i><font color="Green" title="E8">A4</font></i></a>, <a class="txt" href="altcat_4.html#E5:15_2"><i><font color="Green" title="E10">A9</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="c10">i1</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c9">M1</font>
<b>by </b><i><a class="txt" href="altcat_4.html#E8:15_2"><i><font color="Green" title="E11">A10</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <font color="Maroon" title="c2">o1</font></span>)</span> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c9">M1</font>
<b>by </b><i><a class="txt" href="altcat_4.html#E8:15_2"><i><font color="Green" title="E11">A10</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c9">M1</font>
<b>by </b><i><a class="txt" href="altcat_4.html#E5:15_2"><i><font color="Green" title="E10">A9</font></i></a>, <a class="ref" href="altcat_1.html#T24" title="ALTCAT_1:th.24">ALTCAT_1:24</a></i>
;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E13:15"/>
<font color="Maroon" title="c2">o1</font> is <a href="altcat_3.html#V7" title="ALTCAT_3:attr.7">terminal</a>
 <b>by </b><i><a class="ref" href="altcat_3.html#T27" title="ALTCAT_3:th.27">ALTCAT_3:27</a></i>;<br/>


</div>
