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

<b>set </b><font color="Maroon">c<sub>4</sub></font> =  <a href="osalg_4.html#K16" target="_self">QuotOSAlg</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> = the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font> as   <a href="osalg_1.html#NM4">OrderSortedSet</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="osalg_1.html#T17">OSALG_1:17</a></i>;<br/>
<b>let </b><font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font> be   <a href="osalg_1.html#NM2">OperSymbol</a> of <font color="Maroon">c<sub>1</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="osalg_1.html#D23">OSALG_1:def 23</a><br/>

<b>assume </b><a NAME="E2:68_1_1"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="osalg_1.html#R6">&lt;=</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/>

<a NAME="E3:68_1_1"/><i><font color="Green">E40</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="osalg_1.html#R1">~=</a> <font color="Maroon">c<sub>7</sub></font> &amp;  <a href="msualg_1.html#K1">the_arity_of</a> <font color="Maroon">c<sub>6</sub></font> <a href="osalg_1.html#R2">&lt;=</a>  <a href="msualg_1.html#K1">the_arity_of</a> <font color="Maroon">c<sub>7</sub></font> &amp;  <a href="osalg_1.html#K1">the_result_sort_of</a> <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a>  <a href="osalg_1.html#K1">the_result_sort_of</a> <font color="Maroon">c<sub>7</sub></font> )
 
<b>by </b><i><a class="txt" href="osalg_4.html#E2:68_1_1"><i><font color="Green">E39</font></i></a>, <a class="ref" href="osalg_1.html#D22">OSALG_1:def 22</a></i>;<br/>
<a NAME="E4:68_1_1"/><i><font color="Green">E41</font></i>: 
(  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K5">Den</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="osalg_4.html#K16" target="_self">QuotOSAlg</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="msualg_1.html#K3">Args</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><a href="osalg_4.html#K16" target="_self">QuotOSAlg</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> &amp;  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K5">Den</a> <font color="Maroon">c<sub>6</sub></font>,<span class="p2">(<span class="default"><a href="osalg_4.html#K16" target="_self">QuotOSAlg</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="msualg_1.html#K3">Args</a> <font color="Maroon">c<sub>6</sub></font>,<span class="p1">(<span class="default"><a href="osalg_4.html#K16" target="_self">QuotOSAlg</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E5:68_1_1"/><i><font color="Green">E42</font></i>: 
(  <a href="msualg_1.html#K3">Args</a> <font color="Maroon">c<sub>6</sub></font>,<span class="p1">(<span class="default"><a href="osalg_4.html#K16" target="_self">QuotOSAlg</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="msualg_1.html#K3">Args</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><a href="osalg_4.html#K16" target="_self">QuotOSAlg</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> &amp;  <a href="msualg_1.html#K4">Result</a> <font color="Maroon">c<sub>6</sub></font>,<span class="p1">(<span class="default"><a href="osalg_4.html#K16" target="_self">QuotOSAlg</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="msualg_1.html#K4">Result</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><a href="osalg_4.html#K16" target="_self">QuotOSAlg</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> )
 
<b>by </b><i><a class="txt" href="osalg_4.html#E2:68_1_1"><i><font color="Green">E39</font></i></a>, <a class="ref" href="osalg_1.html#T26">OSALG_1:26</a></i>;<br/>
<a NAME="E6:68_1_1"/><b>then </b><i><font color="Green">E43</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K5">Den</a> <font color="Maroon">c<sub>6</sub></font>,<span class="p2">(<span class="default"><a href="osalg_4.html#K16" target="_self">QuotOSAlg</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K5">Den</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p3">(<span class="default"><a href="osalg_4.html#K16" target="_self">QuotOSAlg</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K8">/\</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K3">Args</a> <font color="Maroon">c<sub>6</sub></font>,<span class="p2">(<span class="default"><a href="osalg_4.html#K16" target="_self">QuotOSAlg</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="osalg_4.html#E4:68_1_1"><i><font color="Green">E41</font></i></a>, <a class="ref" href="xboole_1.html#T28">XBOOLE_1:28</a></i>;<br/>
<a NAME="E7:68_1_1"/>
(  <a href="msualg_1.html#K5">Den</a> <font color="Maroon">c<sub>6</sub></font>,<span class="p1">(<span class="default"><a href="osalg_4.html#K16" target="_self">QuotOSAlg</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_2.html#R1">=</a> <span class="p1">(<span class="default"><a href="osalg_4.html#K15" target="_self">OSQuotCharact</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="msualg_4.html#K5">.</a> <font color="Maroon">c<sub>6</sub></font> &amp;  <a href="msualg_1.html#K5">Den</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><a href="osalg_4.html#K16" target="_self">QuotOSAlg</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_2.html#R1">=</a> <span class="p1">(<span class="default"><a href="osalg_4.html#K15" target="_self">OSQuotCharact</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="msualg_4.html#K5">.</a> <font color="Maroon">c<sub>7</sub></font> )
 
<b>by </b><i><a class="ref" href="msualg_1.html#D11">MSUALG_1:def 11</a></i>;<br/>
<a NAME="E8:68_1_1"/><b>then </b><i><font color="Green">E44</font></i>: 
(  <a href="msualg_1.html#K5">Den</a> <font color="Maroon">c<sub>6</sub></font>,<span class="p1">(<span class="default"><a href="osalg_4.html#K16" target="_self">QuotOSAlg</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_2.html#R1">=</a>  <a href="osalg_4.html#K14" target="_self">OSQuotCharact</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp;  <a href="msualg_1.html#K5">Den</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><a href="osalg_4.html#K16" target="_self">QuotOSAlg</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_2.html#R1">=</a>  <a href="osalg_4.html#K14" target="_self">OSQuotCharact</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font> )
 
<b>by </b><i><a class="ref" href="osalg_4.html#D21" target="_self">Def21</a></i>;<br/>
<a NAME="E9:68_1_1"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="osalg_1.html#K1">the_result_sort_of</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="osalg_1.html#K1">the_result_sort_of</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="osalg_4.html#E3:68_1_1"><i><font color="Green">E40</font></i></a>, <a class="ref" href="osalg_1.html#D19">OSALG_1:def 19</a></i>;<br/>
<a NAME="E10:68_1_1"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">c<sub>1</sub></font> )
 
;<br/>
<a NAME="E11:68_1_1"/><b>then </b><i><font color="Green">E46</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E12:68_1_1"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K1">the_arity_of</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K1">the_arity_of</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="osalg_4.html#E3:68_1_1"><i><font color="Green">E40</font></i></a>, <a class="ref" href="osalg_1.html#D7">OSALG_1:def 7</a></i>;<br/>
<a NAME="E13:68_1_1"/><b>then </b><i><font color="Green">E47</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K1">the_arity_of</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K1">the_arity_of</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_3.html#T31">FINSEQ_3:31</a></i>;<br/>
<a NAME="E14:68_1_1"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K5">Den</a> <font color="Maroon">c<sub>6</sub></font>,<span class="p2">(<span class="default"><a href="osalg_4.html#K16" target="_self">QuotOSAlg</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> holds <br/><span class="p1">(<span class="default"><a href="msualg_1.html#K5">Den</a> <font color="Maroon">c<sub>6</sub></font>,<span class="p2">(<span class="default"><a href="osalg_4.html#K16" target="_self">QuotOSAlg</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K5">Den</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="osalg_4.html#K16" target="_self">QuotOSAlg</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="68_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>8</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:68_1_1_1"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K5">Den</a> <font color="Maroon">c<sub>6</sub></font>,<span class="p2">(<span class="default"><a href="osalg_4.html#K16" target="_self">QuotOSAlg</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
 ;<br/>

<a NAME="E2:68_1_1_1"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a>  <a href="msualg_1.html#K3">Args</a> <font color="Maroon">c<sub>6</sub></font>,<span class="p1">(<span class="default"><a href="osalg_4.html#K16" target="_self">QuotOSAlg</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="osalg_4.html#E1:68_1_1_1"><i><font color="Green">E48</font></i></a></i>;<br/>
<a NAME="E3:68_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a>  <a href="msualg_1.html#K3">Args</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><a href="osalg_4.html#K16" target="_self">QuotOSAlg</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="osalg_4.html#E5:68_1_1"><i><font color="Green">E42</font></i></a></i>;<br/>
<a NAME="E4:68_1_1_1"/><b>then </b><i><font color="Green">E50</font></i>: 
( <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="osalg_4.html#K7" target="_self">OSClass</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="pboole.html#K6">#</a> </span>)</span> <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="osalg_4.html#K7" target="_self">OSClass</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="pboole.html#K6">#</a> </span>)</span> <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font> )
 
<b>by </b><i><a class="txt" href="osalg_4.html#E2:68_1_1_1"><i><font color="Green">E49</font></i></a>, <a class="ref" href="msualg_1.html#D9">MSUALG_1:def 9</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>9</sub></font> being    <a href="subset_1.html#M1">Element</a> of  <a href="msualg_1.html#K3">Args</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font><b> such that </b><br/><a NAME="E6:68_1_1_1"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="osalg_4.html#K9" target="_self">#_os</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="ref" href="osalg_4.html#T15" target="_self">Th15</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>10</sub></font> being    <a href="subset_1.html#M1">Element</a> of  <a href="msualg_1.html#K3">Args</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>2</sub></font><b> such that </b><br/><a NAME="E8:68_1_1_1"/><i><font color="Green">E52</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="osalg_4.html#K9" target="_self">#_os</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="osalg_4.html#E4:68_1_1_1"><i><font color="Green">E50</font></i></a>, <a class="ref" href="osalg_4.html#T15" target="_self">Th15</a></i>;<br/>
<a NAME="E9:68_1_1_1"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>9</sub></font> holds <br/><span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> <a href="msualg_4.html#K2">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_1.html#K1">the_arity_of</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Olive">b<sub>1</sub></font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="68_1_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>11</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>assume </b><a NAME="E1:68_1_1_1_1"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>9</sub></font>
 ;<br/>

<a NAME="E2:68_1_1_1_1"/><i><font color="Green">E54</font></i>: 
( <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K1">the_arity_of</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K1">the_arity_of</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> )
 
<b>by </b><i><a class="txt" href="osalg_4.html#E13:68_1_1"><i><font color="Green">E47</font></i></a>, <a class="txt" href="osalg_4.html#E1:68_1_1_1_1"><i><font color="Green">E53</font></i></a>, <a class="ref" href="msualg_6.html#T2">MSUALG_6:2</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>12</sub></font> being    <a href="subset_1.html#M1">Element</a> of the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_1.html#K1">the_arity_of</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span><b> such that </b><br/><a NAME="E4:68_1_1_1_1"/><i><font color="Green">E55</font></i>: 
( <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="osalg_4.html#K9" target="_self">#_os</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a>  <a href="osalg_4.html#K8" target="_self">OSClass</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>12</sub></font> )
 <b>by </b><i><a class="ref" href="osalg_4.html#D15" target="_self">Def15</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>13</sub></font> being    <a href="subset_1.html#M1">Element</a> of the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_1.html#K1">the_arity_of</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span><b> such that </b><br/><a NAME="E6:68_1_1_1_1"/><i><font color="Green">E56</font></i>: 
( <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="osalg_4.html#K9" target="_self">#_os</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a>  <a href="osalg_4.html#K8" target="_self">OSClass</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>13</sub></font> )
 <b>by </b><i><a class="txt" href="osalg_4.html#E2:68_1_1_1_1"><i><font color="Green">E54</font></i></a>, <a class="ref" href="osalg_4.html#D15" target="_self">Def15</a></i>;<br/>
<a NAME="E7:68_1_1_1_1"/><i><font color="Green">E57</font></i>: 
( <span class="p1">(<span class="default"><a href="msualg_1.html#K1">the_arity_of</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K1">the_arity_of</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font> &amp; <span class="p1">(<span class="default"><a href="msualg_1.html#K1">the_arity_of</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K1">the_arity_of</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font> )
 
<b>by </b><i><a class="txt" href="osalg_4.html#E2:68_1_1_1_1"><i><font color="Green">E54</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>14</sub></font> = <span class="p1">(<span class="default"><a href="msualg_1.html#K1">the_arity_of</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font>, <font color="Maroon">c<sub>15</sub></font> = <span class="p1">(<span class="default"><a href="msualg_1.html#K1">the_arity_of</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font> as   <a href="osalg_1.html#NM1">SortSymbol</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="txt" href="osalg_4.html#E2:68_1_1_1_1"><i><font color="Green">E54</font></i></a>, <a class="ref" href="partfun1.html#T27">PARTFUN1:27</a></i>;<br/>
<a NAME="E9:68_1_1_1_1"/><i><font color="Green">E58</font></i>: 
<font color="Maroon">c<sub>14</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>15</sub></font>
 
<b>by </b><i><a class="txt" href="osalg_4.html#E3:68_1_1"><i><font color="Green">E40</font></i></a>, <a class="txt" href="osalg_4.html#E2:68_1_1_1_1"><i><font color="Green">E54</font></i></a>, <a class="ref" href="osalg_1.html#D7">OSALG_1:def 7</a></i>;<br/>
<a NAME="E10:68_1_1_1_1"/><b>then </b>
the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_1.html#K1">the_arity_of</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_1.html#K1">the_arity_of</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="osalg_4.html#E7:68_1_1_1_1"><i><font color="Green">E57</font></i></a>, <a class="ref" href="osalg_1.html#D19">OSALG_1:def 19</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>16</sub></font> = <font color="Maroon">c<sub>12</sub></font> as    <a href="subset_1.html#M1">Element</a> of the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_1.html#K1">the_arity_of</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<a NAME="E12:68_1_1_1_1"/>
 <a href="osalg_4.html#K8" target="_self">OSClass</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a>  <a href="osalg_4.html#K8" target="_self">OSClass</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="txt" href="osalg_4.html#E6:68_1_1_1"><i><font color="Green">E51</font></i></a>, <a class="txt" href="osalg_4.html#E8:68_1_1_1"><i><font color="Green">E52</font></i></a>, <a class="txt" href="osalg_4.html#E4:68_1_1_1_1"><i><font color="Green">E55</font></i></a>, <a class="txt" href="osalg_4.html#E6:68_1_1_1_1"><i><font color="Green">E56</font></i></a>, <a class="txt" href="osalg_4.html#E7:68_1_1_1_1"><i><font color="Green">E57</font></i></a>, <a class="txt" href="osalg_4.html#E9:68_1_1_1_1"><i><font color="Green">E58</font></i></a>, <a class="ref" href="osalg_4.html#T14" target="_self">Th14</a></i>;<br/>
<b>hence </b><a NAME="E13:68_1_1_1_1"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> <a href="msualg_4.html#K2">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_1.html#K1">the_arity_of</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="osalg_4.html#E4:68_1_1_1_1"><i><font color="Green">E55</font></i></a>, <a class="txt" href="osalg_4.html#E6:68_1_1_1_1"><i><font color="Green">E56</font></i></a>, <a class="ref" href="osalg_4.html#T13" target="_self">Th13</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E10:68_1_1_1"/><b>then </b><i><font color="Green">E53</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="msualg_1.html#K5">Den</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="msualg_1.html#K5">Den</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> <a href="msualg_4.html#K2">.</a> <span class="p1">(<span class="default"><a href="osalg_1.html#K1">the_result_sort_of</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="osalg_4.html#E2:68_1_1"><i><font color="Green">E39</font></i></a>, <a class="ref" href="osalg_4.html#D28" target="_self">Def28</a></i>;<br/>
<a NAME="E11:68_1_1_1"/><i><font color="Green">E54</font></i>: 
( <span class="p1">(<span class="default"><a href="osalg_4.html#K14" target="_self">OSQuotCharact</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="osalg_4.html#K9" target="_self">#_os</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="osalg_4.html#K10" target="_self">OSQuotRes</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K5">Den</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font> &amp; <span class="p1">(<span class="default"><a href="osalg_4.html#K14" target="_self">OSQuotCharact</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="osalg_4.html#K9" target="_self">#_os</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="osalg_4.html#K10" target="_self">OSQuotRes</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K5">Den</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font> )
 
<b>by </b><i><a class="txt" href="osalg_4.html#E4:68_1_1_1"><i><font color="Green">E50</font></i></a>, <a class="txt" href="osalg_4.html#E6:68_1_1_1"><i><font color="Green">E51</font></i></a>, <a class="txt" href="osalg_4.html#E8:68_1_1_1"><i><font color="Green">E52</font></i></a>, <a class="ref" href="osalg_4.html#D20" target="_self">Def20</a></i>;<br/>
 <a href="msualg_1.html#K4">Result</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font> = 
<span class="p1">(<span class="default">the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font> <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="ref" href="msualg_1.html#D10">MSUALG_1:def 10</a></i>
<br/>.= 
the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default">the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">c<sub>1</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="osalg_4.html#E11:68_1_1"><i><font color="Green">E46</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="osalg_1.html#K1">the_result_sort_of</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="msualg_1.html#D7">MSUALG_1:def 7</a></i>
;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>11</sub></font> = <span class="p1">(<span class="default"><a href="msualg_1.html#K5">Den</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font> as    <a href="subset_1.html#M1">Element</a> of the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="osalg_1.html#K1">the_result_sort_of</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> ;<br/>
<a NAME="E14:68_1_1_1"/>
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a>  <a href="msualg_1.html#K3">Args</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 
;<br/>
<a NAME="E15:68_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K5">Den</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<b>then </b><i><font color="Green">E55</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="osalg_4.html#K10" target="_self">OSQuotRes</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K5">Den</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font> = 
<span class="p1">(<span class="default"><a href="osalg_4.html#K10" target="_self">OSQuotRes</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
 <a href="osalg_4.html#K8" target="_self">OSClass</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="ref" href="osalg_4.html#D16" target="_self">Def16</a></i>
;<br/>
 <a href="msualg_1.html#K4">Result</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>2</sub></font> = 
<span class="p1">(<span class="default">the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font> <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="ref" href="msualg_1.html#D10">MSUALG_1:def 10</a></i>
<br/>.= 
the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default">the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">c<sub>1</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="osalg_4.html#E11:68_1_1"><i><font color="Green">E46</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="osalg_1.html#K1">the_result_sort_of</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="msualg_1.html#D7">MSUALG_1:def 7</a></i>
;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>12</sub></font> = <span class="p1">(<span class="default"><a href="msualg_1.html#K5">Den</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>10</sub></font> as    <a href="subset_1.html#M1">Element</a> of the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="osalg_1.html#K1">the_result_sort_of</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> ;<br/>
<a NAME="E19:68_1_1_1"/>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a>  <a href="msualg_1.html#K3">Args</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 
;<br/>
<a NAME="E20:68_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K5">Den</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<b>then </b><i><font color="Green">E56</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="osalg_4.html#K10" target="_self">OSQuotRes</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K5">Den</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font> = 
<span class="p1">(<span class="default"><a href="osalg_4.html#K10" target="_self">OSQuotRes</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font>
<b>by </b><i><a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
 <a href="osalg_4.html#K8" target="_self">OSClass</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>12</sub></font>
<b>by </b><i><a class="ref" href="osalg_4.html#D16" target="_self">Def16</a></i>
;<br/>
<b>reconsider </b><font color="Maroon">c<sub>13</sub></font> = <font color="Maroon">c<sub>11</sub></font> as    <a href="subset_1.html#M1">Element</a> of the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="osalg_1.html#K1">the_result_sort_of</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <b>by </b><i><a class="txt" href="osalg_4.html#E9:68_1_1"><i><font color="Green">E45</font></i></a>, <a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
 <a href="osalg_4.html#K8" target="_self">OSClass</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>11</sub></font> = 
 <a href="osalg_4.html#K8" target="_self">OSClass</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>13</sub></font>
<b>by </b><i><a class="txt" href="osalg_4.html#E3:68_1_1"><i><font color="Green">E40</font></i></a>, <a class="ref" href="osalg_4.html#T14" target="_self">Th14</a></i>
<br/>.= 
 <a href="osalg_4.html#K8" target="_self">OSClass</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>12</sub></font>
<b>by </b><i><a class="txt" href="osalg_4.html#E10:68_1_1_1"><i><font color="Green">E53</font></i></a>, <a class="ref" href="osalg_4.html#T13" target="_self">Th13</a></i>
;<br/>
<b>hence </b><a NAME="E24:68_1_1_1"/>
<span class="p1">(<span class="default"><a href="msualg_1.html#K5">Den</a> <font color="Maroon">c<sub>6</sub></font>,<span class="p2">(<span class="default"><a href="osalg_4.html#K16" target="_self">QuotOSAlg</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K5">Den</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="osalg_4.html#K16" target="_self">QuotOSAlg</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="osalg_4.html#E8:68_1_1"><i><font color="Green">E44</font></i></a>, <a class="txt" href="osalg_4.html#E6:68_1_1_1"><i><font color="Green">E51</font></i></a>, <a class="txt" href="osalg_4.html#E8:68_1_1_1"><i><font color="Green">E52</font></i></a>, <a class="txt" href="osalg_4.html#E11:68_1_1_1"><i><font color="Green">E54</font></i></a>, <a class="txt" href="osalg_4.html#E16:68_1_1_1"><i><font color="Green">E55</font></i></a>, <a class="txt" href="osalg_4.html#E21:68_1_1_1"><i><font color="Green">E56</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E15:68_1_1"/>
<span class="p1">(<span class="default"><a href="msualg_1.html#K5">Den</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="osalg_4.html#K16" target="_self">QuotOSAlg</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="partfun1.html#K2">|</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K3">Args</a> <font color="Maroon">c<sub>6</sub></font>,<span class="p2">(<span class="default"><a href="osalg_4.html#K16" target="_self">QuotOSAlg</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="msualg_1.html#K5">Den</a> <font color="Maroon">c<sub>6</sub></font>,<span class="p1">(<span class="default"><a href="osalg_4.html#K16" target="_self">QuotOSAlg</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="osalg_4.html#E6:68_1_1"><i><font color="Green">E43</font></i></a>, <a class="ref" href="funct_1.html#T68">FUNCT_1:68</a></i>;<br/>


</div>
