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

<b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="altcat_1.html#V6" target="_self">strict</a> <a href="altcat_1.html#V13" target="_self">quasi-discrete</a>  <a href="altcat_1.html#L2" target="_self">AltCatStr</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:61_1_2"/><i><font color="Green">E37</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E2:61_1_2"/><i><font color="Green">E38</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">c<sub>2</sub></font> holds <span class="p1"><a href="altcat_1.html#K1" target="_self">&lt;^</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>1</sub></font></span><a href="altcat_1.html#K1" target="_self">^&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>and </b><br/><a NAME="E3:61_1_2"/><i><font color="Green">E39</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E4:61_1_2"/><i><font color="Green">E40</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">c<sub>3</sub></font> holds <span class="p1"><a href="altcat_1.html#K1" target="_self">&lt;^</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>1</sub></font></span><a href="altcat_1.html#K1" target="_self">^&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span><a href="tarski.html#K1">}</a></span>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="61_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>4</sub></font> as   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="txt" href="altcat_1.html#E1:61_1_2"><i><font color="Green">E37</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>4</sub></font> as   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">c<sub>3</sub></font> <b>by </b><i><a class="txt" href="altcat_1.html#E3:61_1_2"><i><font color="Green">E39</font></i></a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="61_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:61_1_2_1_1"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> or <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="61_1_2_1_1_1"><b>suppose </b></a><a NAME="E1:61_1_2_1_1_1"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/><div class="add"><b>hence </b>the <a href="altcat_1.html#U1" target="_self">Arrows</a> of <font color="Maroon">c<sub>2</sub></font> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> = 
<span class="p1"><a href="altcat_1.html#K1" target="_self">&lt;^</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="altcat_1.html#K1" target="_self">^&gt;</a></span>

<br/>.= 
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i><a class="txt" href="altcat_1.html#E2:61_1_2"><i><font color="Green">E38</font></i></a></i>
<br/>.= 
<span class="p1"><a href="altcat_1.html#K1" target="_self">&lt;^</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="altcat_1.html#K1" target="_self">^&gt;</a></span>
<b>by </b><i><a class="txt" href="altcat_1.html#E4:61_1_2"><i><font color="Green">E40</font></i></a></i>
<br/>.= 
the <a href="altcat_1.html#U1" target="_self">Arrows</a> of <font color="Maroon">c<sub>3</sub></font> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="altcat_1.html#E1:61_1_2_1_1_1"><i><font color="Green">E41</font></i></a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="61_1_2_1_1_2"><b>suppose </b></a><a NAME="E1:61_1_2_1_1_2"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/><div class="add"><b>reconsider </b><font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>5</sub></font> as   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="txt" href="altcat_1.html#E1:61_1_2"><i><font color="Green">E37</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>9</sub></font> = <font color="Maroon">c<sub>5</sub></font> as   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">c<sub>3</sub></font> <b>by </b><i><a class="txt" href="altcat_1.html#E3:61_1_2"><i><font color="Green">E39</font></i></a></i>;<br/><b>thus </b>the <a href="altcat_1.html#U1" target="_self">Arrows</a> of <font color="Maroon">c<sub>2</sub></font> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> = 
<span class="p1"><a href="altcat_1.html#K1" target="_self">&lt;^</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font></span><a href="altcat_1.html#K1" target="_self">^&gt;</a></span>

<br/>.= 
 <a href="xboole_0.html#K1">{}</a> 
<b>by </b><i><a class="txt" href="altcat_1.html#E1:61_1_2_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="ref" href="altcat_1.html#D20" target="_self">Def20</a></i>
<br/>.= 
<span class="p1"><a href="altcat_1.html#K1" target="_self">&lt;^</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span><a href="altcat_1.html#K1" target="_self">^&gt;</a></span>
<b>by </b><i><a class="txt" href="altcat_1.html#E1:61_1_2_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="ref" href="altcat_1.html#D20" target="_self">Def20</a></i>
<br/>.= 
the <a href="altcat_1.html#U1" target="_self">Arrows</a> of <font color="Maroon">c<sub>3</sub></font> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>

;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<a NAME="E6:61_1_2"/><b>then </b><i><font color="Green">E41</font></i>: 
the <a href="altcat_1.html#U1" target="_self">Arrows</a> of <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> the <a href="altcat_1.html#U1" target="_self">Arrows</a> of <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="altcat_1.html#E1:61_1_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="altcat_1.html#E3:61_1_2"><i><font color="Green">E39</font></i></a>, <a class="ref" href="altcat_1.html#T9" target="_self">Th9</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="61_1_2_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:61_1_2_2"/><i><font color="Green">E42</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> )
 ;<br/><b>then reconsider </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>4</sub></font> as   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="txt" href="altcat_1.html#E1:61_1_2"><i><font color="Green">E37</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>4</sub></font> as   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">c<sub>3</sub></font> <b>by </b><i><a class="txt" href="altcat_1.html#E3:61_1_2"><i><font color="Green">E39</font></i></a>, <a class="txt" href="altcat_1.html#E1:61_1_2_2"><i><font color="Green">E42</font></i></a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="61_1_2_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:61_1_2_2_1"/>
( ( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> ) or <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font> or <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>6</sub></font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="61_1_2_2_1_1"><b>suppose </b></a><a NAME="E1:61_1_2_2_1_1"/><i><font color="Green">E43</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> )
 ;<br/><div class="add"><a NAME="E2:61_1_2_2_1_1"/><i><font color="Green">E44</font></i>: 
<span class="p1"><a href="altcat_1.html#K1" target="_self">&lt;^</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>8</sub></font></span><a href="altcat_1.html#K1" target="_self">^&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="txt" href="altcat_1.html#E4:61_1_2"><i><font color="Green">E40</font></i></a></i>;<br/><a NAME="E3:61_1_2_2_1_1"/><i><font color="Green">E45</font></i>: 
the <a href="altcat_1.html#U2" target="_self">Comp</a> of <font color="Maroon">c<sub>3</sub></font> <a href="altcat_1.html#K4" target="_self">.</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>8</sub></font> is   <a href="funct_2.html#NM1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2"><a href="altcat_1.html#K1" target="_self">&lt;^</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>8</sub></font></span><a href="altcat_1.html#K1" target="_self">^&gt;</a></span>,<span class="p2"><a href="altcat_1.html#K1" target="_self">&lt;^</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>8</sub></font></span><a href="altcat_1.html#K1" target="_self">^&gt;</a></span></span><a href="zfmisc_1.html#K2">:]</a></span>,<span class="p1"><a href="altcat_1.html#K1" target="_self">&lt;^</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>8</sub></font></span><a href="altcat_1.html#K1" target="_self">^&gt;</a></span>
 ;<br/><a NAME="E4:61_1_2_2_1_1"/><i><font color="Green">E46</font></i>: 
<span class="p1"><a href="altcat_1.html#K1" target="_self">&lt;^</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="altcat_1.html#K1" target="_self">^&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="txt" href="altcat_1.html#E2:61_1_2"><i><font color="Green">E38</font></i></a></i>;<br/><a NAME="E5:61_1_2_2_1_1"/>
the <a href="altcat_1.html#U2" target="_self">Comp</a> of <font color="Maroon">c<sub>2</sub></font> <a href="altcat_1.html#K4" target="_self">.</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>7</sub></font> is   <a href="funct_2.html#NM1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2"><a href="altcat_1.html#K1" target="_self">&lt;^</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="altcat_1.html#K1" target="_self">^&gt;</a></span>,<span class="p2"><a href="altcat_1.html#K1" target="_self">&lt;^</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="altcat_1.html#K1" target="_self">^&gt;</a></span></span><a href="zfmisc_1.html#K2">:]</a></span>,<span class="p1"><a href="altcat_1.html#K1" target="_self">&lt;^</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="altcat_1.html#K1" target="_self">^&gt;</a></span>
 ;<br/><b>hence </b>the <a href="altcat_1.html#U2" target="_self">Comp</a> of <font color="Maroon">c<sub>2</sub></font> <a href="multop_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> = 
<span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_2.html#K4">:-&gt;</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="altcat_1.html#E1:61_1_2_2_1_1"><i><font color="Green">E43</font></i></a>, <a class="txt" href="altcat_1.html#E4:61_1_2_2_1_1"><i><font color="Green">E46</font></i></a>, <a class="ref" href="funct_2.html#D5">FUNCT_2:def 5</a></i>
<br/>.= 
the <a href="altcat_1.html#U2" target="_self">Comp</a> of <font color="Maroon">c<sub>3</sub></font> <a href="multop_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="txt" href="altcat_1.html#E1:61_1_2_2_1_1"><i><font color="Green">E43</font></i></a>, <a class="txt" href="altcat_1.html#E2:61_1_2_2_1_1"><i><font color="Green">E44</font></i></a>, <a class="txt" href="altcat_1.html#E3:61_1_2_2_1_1"><i><font color="Green">E45</font></i></a>, <a class="ref" href="funct_2.html#D5">FUNCT_2:def 5</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="61_1_2_2_1_2"><b>suppose </b></a><a NAME="E1:61_1_2_2_1_2"/><i><font color="Green">E43</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font> or <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>6</sub></font> )
 ;<br/><div class="add"><b>reconsider </b><font color="Maroon">c<sub>9</sub></font> = <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>10</sub></font> = <font color="Maroon">c<sub>6</sub></font> as   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="txt" href="altcat_1.html#E1:61_1_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="altcat_1.html#E1:61_1_2_2"><i><font color="Green">E42</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>11</sub></font> = <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>12</sub></font> = <font color="Maroon">c<sub>6</sub></font> as   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">c<sub>3</sub></font> <b>by </b><i><a class="txt" href="altcat_1.html#E3:61_1_2"><i><font color="Green">E39</font></i></a>, <a class="txt" href="altcat_1.html#E1:61_1_2_2"><i><font color="Green">E42</font></i></a></i>;<br/><a NAME="E4:61_1_2_2_1_2"/>
( <span class="p1"><a href="altcat_1.html#K1" target="_self">&lt;^</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="altcat_1.html#K1" target="_self">^&gt;</a></span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  or <span class="p1"><a href="altcat_1.html#K1" target="_self">&lt;^</a><span class="default"><font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font></span><a href="altcat_1.html#K1" target="_self">^&gt;</a></span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 <b>by </b><i><a class="txt" href="altcat_1.html#E1:61_1_2_2_1_2"><i><font color="Green">E43</font></i></a>, <a class="ref" href="altcat_1.html#D20" target="_self">Def20</a></i>;<br/><a NAME="E5:61_1_2_2_1_2"/><b>then </b><i><font color="Green">E44</font></i>: 
<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2"><a href="altcat_1.html#K1" target="_self">&lt;^</a><span class="default"><font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font></span><a href="altcat_1.html#K1" target="_self">^&gt;</a></span>,<span class="p2"><a href="altcat_1.html#K1" target="_self">&lt;^</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="altcat_1.html#K1" target="_self">^&gt;</a></span></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T113">ZFMISC_1:113</a></i>;<br/><a NAME="E6:61_1_2_2_1_2"/><i><font color="Green">E45</font></i>: 
the <a href="altcat_1.html#U2" target="_self">Comp</a> of <font color="Maroon">c<sub>3</sub></font> <a href="altcat_1.html#K4" target="_self">.</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font> is   <a href="funct_2.html#NM1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2"><a href="altcat_1.html#K1" target="_self">&lt;^</a><span class="default"><font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font></span><a href="altcat_1.html#K1" target="_self">^&gt;</a></span>,<span class="p2"><a href="altcat_1.html#K1" target="_self">&lt;^</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="altcat_1.html#K1" target="_self">^&gt;</a></span></span><a href="zfmisc_1.html#K2">:]</a></span>,<span class="p1"><a href="altcat_1.html#K1" target="_self">&lt;^</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>12</sub></font></span><a href="altcat_1.html#K1" target="_self">^&gt;</a></span>
 ;<br/><a NAME="E7:61_1_2_2_1_2"/>
( <span class="p1"><a href="altcat_1.html#K1" target="_self">&lt;^</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span><a href="altcat_1.html#K1" target="_self">^&gt;</a></span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  or <span class="p1"><a href="altcat_1.html#K1" target="_self">&lt;^</a><span class="default"><font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font></span><a href="altcat_1.html#K1" target="_self">^&gt;</a></span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 <b>by </b><i><a class="txt" href="altcat_1.html#E1:61_1_2_2_1_2"><i><font color="Green">E43</font></i></a>, <a class="ref" href="altcat_1.html#D20" target="_self">Def20</a></i>;<br/><a NAME="E8:61_1_2_2_1_2"/><b>then </b><i><font color="Green">E46</font></i>: 
<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2"><a href="altcat_1.html#K1" target="_self">&lt;^</a><span class="default"><font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font></span><a href="altcat_1.html#K1" target="_self">^&gt;</a></span>,<span class="p2"><a href="altcat_1.html#K1" target="_self">&lt;^</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span><a href="altcat_1.html#K1" target="_self">^&gt;</a></span></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T113">ZFMISC_1:113</a></i>;<br/><a NAME="E9:61_1_2_2_1_2"/>
the <a href="altcat_1.html#U2" target="_self">Comp</a> of <font color="Maroon">c<sub>2</sub></font> <a href="altcat_1.html#K4" target="_self">.</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font> is   <a href="funct_2.html#NM1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2"><a href="altcat_1.html#K1" target="_self">&lt;^</a><span class="default"><font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font></span><a href="altcat_1.html#K1" target="_self">^&gt;</a></span>,<span class="p2"><a href="altcat_1.html#K1" target="_self">&lt;^</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span><a href="altcat_1.html#K1" target="_self">^&gt;</a></span></span><a href="zfmisc_1.html#K2">:]</a></span>,<span class="p1"><a href="altcat_1.html#K1" target="_self">&lt;^</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>10</sub></font></span><a href="altcat_1.html#K1" target="_self">^&gt;</a></span>
 ;<br/><b>hence </b><a NAME="E10:61_1_2_2_1_2"/>
the <a href="altcat_1.html#U2" target="_self">Comp</a> of <font color="Maroon">c<sub>2</sub></font> <a href="multop_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> the <a href="altcat_1.html#U2" target="_self">Comp</a> of <font color="Maroon">c<sub>3</sub></font> <a href="multop_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="altcat_1.html#E5:61_1_2_2_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="altcat_1.html#E6:61_1_2_2_1_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="altcat_1.html#E8:61_1_2_2_1_2"><i><font color="Green">E46</font></i></a>, <a class="ref" href="partfun1.html#T58">PARTFUN1:58</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E8:61_1_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="altcat_1.html#E1:61_1_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="altcat_1.html#E3:61_1_2"><i><font color="Green">E39</font></i></a>, <a class="txt" href="altcat_1.html#E6:61_1_2"><i><font color="Green">E41</font></i></a>, <a class="ref" href="altcat_1.html#T10" target="_self">Th10</a></i>;<br/>


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