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

<b>let </b><font color="Maroon">C</font> be   <a href="altcat_1.html#NM4">category</a>;<br/>

<a NAME="E1:74"/><i><font color="Green">E24</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="altcat_4.html#K5" target="_self">AllIso</a> <span class="p2">(<span class="default"><a href="altcat_4.html#K4" target="_self">AllCoretr</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="altcat_4.html#K4" target="_self">AllCoretr</a> <font color="Maroon">C</font></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E2:74"/><i><font color="Green">E25</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="altcat_4.html#K5" target="_self">AllIso</a> <font color="Maroon">C</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">C</font>
 
<b>by </b><i/>;<br/>
<a NAME="E3:74"/><i><font color="Green">E26</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="altcat_4.html#K4" target="_self">AllCoretr</a> <font color="Maroon">C</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">C</font>
 
<b>by </b><i><a class="txt" href="altcat_4.html#E4:74"><i><font color="Green">E32</font></i></a></i>;<br/>
<a NAME="E4:74"/><i><font color="Green">E32</font></i>: 
 <a href="altcat_4.html#K5" target="_self">AllIso</a> <font color="Maroon">C</font> is  non <a href="struct_0.html#V3">empty</a> <a href="altcat_2.html#NM2">subcategory</a> of  <a href="altcat_4.html#K4" target="_self">AllCoretr</a> <font color="Maroon">C</font>
 
<b>by </b><i/>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:74_1"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">C</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">C</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 ;<br/><b>then consider </b><font color="Maroon">o1</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">o2</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:74_1"/><i><font color="Green">E45</font></i>: 
( <font color="Maroon">o1</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">C</font> &amp; <font color="Maroon">o2</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">C</font> &amp; <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">o1</font>,<font color="Maroon">o2</font></span><a href="tarski.html#K4">]</a></span> )
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T103">ZFMISC_1:103</a></i>;<br/><b>reconsider </b><font color="Maroon">o1</font> = <font color="Maroon">o1</font>, <font color="Maroon">o2</font> = <font color="Maroon">o2</font> as   <a href="altcat_1.html#NM1">object</a> of <span class="p1">(<span class="default"><a href="altcat_4.html#K4" target="_self">AllCoretr</a> <font color="Maroon">C</font></span>)</span> <b>by </b><i>, <a class="txt" href="altcat_4.html#E4:74"><i><font color="Green">E32</font></i></a></i>;<br/><b>thus </b><a NAME="E5:74_1"/>
the <a href="altcat_1.html#U1">Arrows</a> of <span class="p1">(<span class="default"><a href="altcat_4.html#K5" target="_self">AllIso</a> <span class="p2">(<span class="default"><a href="altcat_4.html#K4" target="_self">AllCoretr</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> the <a href="altcat_1.html#U1">Arrows</a> of <span class="p1">(<span class="default"><a href="altcat_4.html#K5" target="_self">AllIso</a> <font color="Maroon">C</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_1_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:74_1_1"/>
the <a href="altcat_1.html#U1">Arrows</a> of <span class="p1">(<span class="default"><a href="altcat_4.html#K5" target="_self">AllIso</a> <span class="p2">(<span class="default"><a href="altcat_4.html#K4" target="_self">AllCoretr</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="tarski.html#R1">c=</a> the <a href="altcat_1.html#U1">Arrows</a> of <span class="p1">(<span class="default"><a href="altcat_4.html#K5" target="_self">AllIso</a> <font color="Maroon">C</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">n</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:74_1_1_1"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">n</font> <a href="hidden.html#R2">in</a> the <a href="altcat_1.html#U1">Arrows</a> of <span class="p1">(<span class="default"><a href="altcat_4.html#K5" target="_self">AllIso</a> <span class="p2">(<span class="default"><a href="altcat_4.html#K4" target="_self">AllCoretr</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
 ;<br/>

<b>reconsider </b><font color="Maroon">q1</font> = <font color="Maroon">o1</font>, <font color="Maroon">q2</font> = <font color="Maroon">o2</font> as   <a href="altcat_1.html#NM1">object</a> of <span class="p1">(<span class="default"><a href="altcat_4.html#K5" target="_self">AllIso</a> <span class="p2">(<span class="default"><a href="altcat_4.html#K4" target="_self">AllCoretr</a> <font color="Maroon">C</font></span>)</span></span>)</span> <b>by </b><i/>;<br/>
<a NAME="E3:74_1_1_1"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">n</font> <a href="hidden.html#R2">in</a> the <a href="altcat_1.html#U1">Arrows</a> of <span class="p1">(<span class="default"><a href="altcat_4.html#K5" target="_self">AllIso</a> <span class="p2">(<span class="default"><a href="altcat_4.html#K4" target="_self">AllCoretr</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">q1</font>,<font color="Maroon">q2</font>
 
<b>by </b><i><a class="txt" href="altcat_4.html#E1:74_1_1_1"><i><font color="Green">E46</font></i></a>, <a class="txt" href="altcat_4.html#E3:74_1_1_1"><i><font color="Green">E47</font></i></a></i>;<br/>
<a NAME="E4:74_1_1_1"/><b>then </b><i><font color="Green">E50</font></i>: 
<font color="Maroon">n</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">q1</font>,<font color="Maroon">q2</font></span><a href="altcat_1.html#K1">^&gt;</a></span>
 
;<br/>
<a NAME="E5:74_1_1_1"/><i><font color="Green">E52</font></i>: 
( <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">q1</font>,<font color="Maroon">q2</font></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="tarski.html#R1">c=</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> &amp; <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">q2</font>,<font color="Maroon">q1</font></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">o2</font>,<font color="Maroon">o1</font></span><a href="altcat_1.html#K1">^&gt;</a></span> )
 
<b>by </b><i><a class="ref" href="altcat_2.html#T32">ALTCAT_2:32</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">n2</font> = <font color="Maroon">n</font> as   <a href="altcat_1.html#NM2">Morphism</a> of <font color="Maroon">o1</font>,<font color="Maroon">o2</font> <b>by </b><i/>;<br/>
<b>reconsider </b><font color="Maroon">r1</font> = <font color="Maroon">o1</font>, <font color="Maroon">r2</font> = <font color="Maroon">o2</font> as   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">C</font> <b>by </b><i><a class="txt" href="altcat_4.html#E4:74"><i><font color="Green">E32</font></i></a></i>;<br/>
<a NAME="E8:74_1_1_1"/><i><font color="Green">E75</font></i>: 
( <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="tarski.html#R1">c=</a> <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">r1</font>,<font color="Maroon">r2</font></span><a href="altcat_1.html#K1">^&gt;</a></span> &amp; <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">o2</font>,<font color="Maroon">o1</font></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">r2</font>,<font color="Maroon">r1</font></span><a href="altcat_1.html#K1">^&gt;</a></span> )
 
<b>by </b><i><a class="ref" href="altcat_2.html#T32">ALTCAT_2:32</a></i>;<br/>
<a NAME="E9:74_1_1_1"/><b>then </b>
<span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">q1</font>,<font color="Maroon">q2</font></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">r1</font>,<font color="Maroon">r2</font></span><a href="altcat_1.html#K1">^&gt;</a></span>
 
<b>by </b><i><a class="txt" href="altcat_4.html#E4:74_1_1_1"><i><font color="Green">E50</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">n1</font> = <font color="Maroon">n</font> as   <a href="altcat_1.html#NM2">Morphism</a> of <font color="Maroon">r1</font>,<font color="Maroon">r2</font> <b>by </b><i/>;<br/>
<a NAME="E11:74_1_1_1"/>
<span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">q2</font>,<font color="Maroon">q1</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> 
 
<b>by </b><i>, </i>;<br/>
<a NAME="E12:74_1_1_1"/><b>then </b><i><font color="Green">E112</font></i>: 
( <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#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">o2</font>,<font color="Maroon">o1</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>  )
 
<b>by </b><i>, <a class="txt" href="altcat_4.html#E4:74_1_1_1"><i><font color="Green">E50</font></i></a>, <a class="ref" href="xboole_1.html#T3">XBOOLE_1:3</a></i>;<br/>
<a NAME="E13:74_1_1_1"/><b>then </b><i><font color="Green">E113</font></i>: 
( <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">r1</font>,<font color="Maroon">r2</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>  &amp; <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">r2</font>,<font color="Maroon">r1</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>  )
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T3">XBOOLE_1:3</a></i>;<br/>
<a NAME="E14:74_1_1_1"/>
<font color="Maroon">n2</font> is <a href="altcat_3.html#V3">iso</a>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E15:74_1_1_1"/><b>then </b>
<font color="Maroon">n1</font> is <a href="altcat_3.html#V3">iso</a>
 
<b>by </b><i><a class="txt" href="altcat_4.html#E5:74_1_1_1"><i><font color="Green">E52</font></i></a>, <a class="ref" href="altcat_4.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E16:74_1_1_1"/><b>then </b>
<font color="Maroon">n</font> <a href="hidden.html#R2">in</a> the <a href="altcat_1.html#U1">Arrows</a> of <span class="p1">(<span class="default"><a href="altcat_4.html#K5" target="_self">AllIso</a> <font color="Maroon">C</font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">r1</font>,<font color="Maroon">r2</font>
 
<b>by </b><i><a class="ref" href="altcat_4.html#T13" target="_self">Th13</a>, </i>;<br/>
<b>hence </b><a NAME="E17:74_1_1_1"/>
<font color="Maroon">n</font> <a href="hidden.html#R2">in</a> the <a href="altcat_1.html#U1">Arrows</a> of <span class="p1">(<span class="default"><a href="altcat_4.html#K5" target="_self">AllIso</a> <font color="Maroon">C</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
 <b>by </b><i><a class="txt" href="altcat_4.html#E1:74_1_1_1"><i><font color="Green">E46</font></i></a></i>;<br/>


</div><b>end;</b></div>

<b>let </b><font color="Maroon">n</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E2:74_1_1"/><i><font color="Green">E114</font></i>: 
<font color="Maroon">n</font> <a href="hidden.html#R2">in</a> the <a href="altcat_1.html#U1">Arrows</a> of <span class="p1">(<span class="default"><a href="altcat_4.html#K5" target="_self">AllIso</a> <font color="Maroon">C</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
 ;<br/>

<b>reconsider </b><font color="Maroon">p1</font> = <font color="Maroon">o1</font>, <font color="Maroon">p2</font> = <font color="Maroon">o2</font> as   <a href="altcat_1.html#NM1">object</a> of <span class="p1">(<span class="default"><a href="altcat_4.html#K5" target="_self">AllIso</a> <font color="Maroon">C</font></span>)</span> <b>by </b><i>, </i>;<br/>
<a NAME="E4:74_1_1"/>
the <a href="altcat_1.html#U1">Arrows</a> of <span class="p1">(<span class="default"><a href="altcat_4.html#K5" target="_self">AllIso</a> <font color="Maroon">C</font></span>)</span> <a href="altcat_2.html#R2">cc=</a> the <a href="altcat_1.html#U1">Arrows</a> of <span class="p1">(<span class="default"><a href="altcat_4.html#K4" target="_self">AllCoretr</a> <font color="Maroon">C</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="altcat_2.html#D11">ALTCAT_2:def 11</a></i>;<br/>
<a NAME="E5:74_1_1"/><b>then </b>
the <a href="altcat_1.html#U1">Arrows</a> of <span class="p1">(<span class="default"><a href="altcat_4.html#K5" target="_self">AllIso</a> <font color="Maroon">C</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="tarski.html#R1">c=</a> the <a href="altcat_1.html#U1">Arrows</a> of <span class="p1">(<span class="default"><a href="altcat_4.html#K4" target="_self">AllCoretr</a> <font color="Maroon">C</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
 
<b>by </b><i>, <a class="txt" href="altcat_4.html#E3:74_1"><i><font color="Green">E45</font></i></a>, <a class="ref" href="altcat_2.html#D2">ALTCAT_2:def 2</a></i>;<br/>
<a NAME="E6:74_1_1"/><b>then </b>
<font color="Maroon">n</font> <a href="hidden.html#R2">in</a> the <a href="altcat_1.html#U1">Arrows</a> of <span class="p1">(<span class="default"><a href="altcat_4.html#K4" target="_self">AllCoretr</a> <font color="Maroon">C</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
 
<b>by </b><i/>;<br/>
<a NAME="E7:74_1_1"/><b>then </b><i><font color="Green">E115</font></i>: 
<font color="Maroon">n</font> <a href="hidden.html#R2">in</a> the <a href="altcat_1.html#U1">Arrows</a> of <span class="p1">(<span class="default"><a href="altcat_4.html#K4" target="_self">AllCoretr</a> <font color="Maroon">C</font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">o1</font>,<font color="Maroon">o2</font>
 
<b>by </b><i/>;<br/>
<a NAME="E8:74_1_1"/><b>then </b><i><font color="Green">E116</font></i>: 
<font color="Maroon">n</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>
 
;<br/>
<b>reconsider </b><font color="Maroon">n1</font> = <font color="Maroon">n</font> as   <a href="altcat_1.html#NM2">Morphism</a> of <font color="Maroon">o1</font>,<font color="Maroon">o2</font> <b>by </b><i/>;<br/>
<a NAME="E10:74_1_1"/><i><font color="Green">E117</font></i>: 
<font color="Maroon">n</font> <a href="hidden.html#R2">in</a> the <a href="altcat_1.html#U1">Arrows</a> of <span class="p1">(<span class="default"><a href="altcat_4.html#K5" target="_self">AllIso</a> <font color="Maroon">C</font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">o1</font>,<font color="Maroon">o2</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E11:74_1_1"/><b>then </b><i><font color="Green">E118</font></i>: 
<font color="Maroon">n</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">p1</font>,<font color="Maroon">p2</font></span><a href="altcat_1.html#K1">^&gt;</a></span>
 
;<br/>
<b>reconsider </b><font color="Maroon">n2</font> = <font color="Maroon">n</font> as   <a href="altcat_1.html#NM2">Morphism</a> of <font color="Maroon">p1</font>,<font color="Maroon">p2</font> <b>by </b><i/>;<br/>
<a NAME="E13:74_1_1"/><i><font color="Green">E119</font></i>: 
<font color="Maroon">n2</font> <a href="altcat_3.html#K1">"</a>  <a href="hidden.html#R2">in</a> <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">p2</font>,<font color="Maroon">p1</font></span><a href="altcat_1.html#K1">^&gt;</a></span>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E14:74_1_1"/><i><font color="Green">E120</font></i>: 
<span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">p2</font>,<font color="Maroon">p1</font></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">o2</font>,<font color="Maroon">o1</font></span><a href="altcat_1.html#K1">^&gt;</a></span>
 
<b>by </b><i>, <a class="ref" href="altcat_2.html#T32">ALTCAT_2:32</a></i>;<br/>
<a NAME="E15:74_1_1"/>
<font color="Maroon">n2</font> is <a href="altcat_3.html#V3">iso</a>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E16:74_1_1"/><b>then </b>
<font color="Maroon">n1</font> is <a href="altcat_3.html#V3">iso</a>
 
<b>by </b><i>, , , <a class="ref" href="altcat_4.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E17:74_1_1"/><b>then </b>
<font color="Maroon">n</font> <a href="hidden.html#R2">in</a> the <a href="altcat_1.html#U1">Arrows</a> of <span class="p1">(<span class="default"><a href="altcat_4.html#K5" target="_self">AllIso</a> <span class="p2">(<span class="default"><a href="altcat_4.html#K4" target="_self">AllCoretr</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">o1</font>,<font color="Maroon">o2</font>
 
<b>by </b><i>, , <a class="ref" href="altcat_4.html#T13" target="_self">Th13</a>, </i>;<br/>
<b>hence </b><a NAME="E18:74_1_1"/>
<font color="Maroon">n</font> <a href="hidden.html#R2">in</a> the <a href="altcat_1.html#U1">Arrows</a> of <span class="p1">(<span class="default"><a href="altcat_4.html#K5" target="_self">AllIso</a> <span class="p2">(<span class="default"><a href="altcat_4.html#K4" target="_self">AllCoretr</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div></div><b>end;</b></div>
<a NAME="E6:74"/><b>then </b><i><font color="Green">E121</font></i>: 
the <a href="altcat_1.html#U1">Arrows</a> of <span class="p1">(<span class="default"><a href="altcat_4.html#K5" target="_self">AllIso</a> <span class="p2">(<span class="default"><a href="altcat_4.html#K4" target="_self">AllCoretr</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="altcat_1.html#U1">Arrows</a> of <span class="p1">(<span class="default"><a href="altcat_4.html#K5" target="_self">AllIso</a> <font color="Maroon">C</font></span>)</span>
 
<b>by </b><i>, , , <a class="ref" href="pboole.html#T3">PBOOLE:3</a></i>;<br/>
<a NAME="E7:74"/>
 <a href="altcat_4.html#K5" target="_self">AllIso</a> <span class="p1">(<span class="default"><a href="altcat_4.html#K4" target="_self">AllCoretr</a> <font color="Maroon">C</font></span>)</span> is  non <a href="struct_0.html#V3">empty</a> <a href="altcat_1.html#V2">transitive</a>  <a href="altcat_2.html#M1">SubCatStr</a> of <font color="Maroon">C</font>
 
<b>by </b><i><a class="ref" href="altcat_2.html#T22">ALTCAT_2:22</a></i>;<br/>
<a NAME="E8:74"/><b>then </b>
 <a href="altcat_4.html#K5" target="_self">AllIso</a> <span class="p1">(<span class="default"><a href="altcat_4.html#K4" target="_self">AllCoretr</a> <font color="Maroon">C</font></span>)</span> is    <a href="altcat_2.html#M1">SubCatStr</a> of  <a href="altcat_4.html#K5" target="_self">AllIso</a> <font color="Maroon">C</font>
 
<b>by </b><i>, , , , <a class="ref" href="altcat_2.html#T25">ALTCAT_2:25</a></i>;<br/>
<b>hence </b><a NAME="E9:74"/>
 <a href="altcat_4.html#K5" target="_self">AllIso</a> <span class="p1">(<span class="default"><a href="altcat_4.html#K4" target="_self">AllCoretr</a> <font color="Maroon">C</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="altcat_4.html#K5" target="_self">AllIso</a> <font color="Maroon">C</font>
 <b>by </b><i>, , , , <a class="ref" href="altcat_2.html#T26">ALTCAT_2:26</a></i>;<br/>


</div>
