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

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be  non <a href="struct_0.html#V3">empty</a> non <a href="msualg_1.html#V2">void</a>  <a href="msualg_1.html#L1">ManySortedSign</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be  <a href="relat_1.html#V2">V5</a>  <a href="pboole.html#M1">ManySortedSet</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="funct_2.html#NM1">Function</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be  <a href="funct_1.html#V2">one-to-one</a> <a href="funct_1.html#NM1">Function</a>;<br/>







<b>assume </b><a NAME="E1:55"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="pua2mss1.html#R3">form_morphism_between</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>5</sub></font> as   <a href="funct_2.html#NM1">Function</a> of the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="ref" href="instalg1.html#T10" target="_self">Th10</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>7</sub></font> = <span class="p1">(<span class="default"><a href="msafree.html#K11">FreeMSA</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="instalg1.html#K1" target="_self">|</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>8</sub></font> = <span class="p1">(<span class="default"><a href="msafree.html#K11">FreeMSA</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="instalg1.html#K1" target="_self">|</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> as  <a href="msualg_1.html#V5">non-empty</a>  <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="txt" href="instalg1.html#E1:55"><i><font color="Green">E31</font></i></a>, <a class="ref" href="instalg1.html#T23" target="_self">Th23</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>9</sub></font> =  <a href="instalg1.html#K3" target="_self">hom</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>10</sub></font> =  <a href="instalg1.html#K3" target="_self">hom</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> as   <a href="msualg_3.html#NM1">ManySortedFunction</a> of <span class="p1">(<span class="default"><a href="msafree.html#K11">FreeMSA</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#K7">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>8</sub></font> ;<br/>
<b>thus </b><a NAME="E5:55"/>
 <a href="instalg1.html#K3" target="_self">hom</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="msualg_3.html#R1">is_homomorphism</a>  <a href="msafree.html#K11">FreeMSA</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#K7">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="msafree.html#K11">FreeMSA</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="instalg1.html#K1" target="_self">|</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="instalg1.html#E1:55"><i><font color="Green">E31</font></i></a>, <a class="ref" href="instalg1.html#D5" target="_self">Def5</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="msualg_3.html#D11">MSUALG_3:def 11</a><br/>

<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1">set</a> ] means ex <font color="Olive">b<sub>1</sub></font> being  <a href="msaterm.html#NM1">Term</a> of <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#K7">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">a<sub>1</sub></font> &amp; ( for <font color="Olive">b<sub>2</sub></font> being  <a href="msaterm.html#NM1">Term</a> of <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#K7">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> st  <a href="msaterm.html#K7">the_sort_of</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="msaterm.html#K7">the_sort_of</a> <font color="Olive">b<sub>2</sub></font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="instalg1.html#K3" target="_self">hom</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="msualg_3.html#K1">.</a> <span class="p2">(<span class="default"><a href="msaterm.html#K7">the_sort_of</a> <font color="Olive">b<sub>1</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"><span class="p2">(<span class="default"><a href="instalg1.html#K3" target="_self">hom</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="msualg_3.html#K1">.</a> <span class="p2">(<span class="default"><a href="msaterm.html#K7">the_sort_of</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>2</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> ) );<br/>
<a NAME="E6:55"/><i><font color="Green">E32</font></i>: 
 <a href="msafree.html#K11">FreeMSA</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#K7">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="msualg_1.html#G3">MSAlgebra</a>(# <span class="p1">(<span class="default"><a href="msafree.html#K8">FreeSort</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#K7">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="msafree.html#K10">FreeOper</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#K7">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> #)
 
<b>by </b><i><a class="ref" href="msafree.html#D16">MSAFREE:def 16</a></i>;<br/>
<a NAME="E7:55"/><i><font color="Green">E33</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="msualg_1.html#NM1">SortSymbol</a> of <font color="Maroon">c<sub>1</sub></font><br/>for <font color="Olive">b<sub>2</sub></font> being   <a href="subset_1.html#M1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#K7">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> holds <font color="Maroon">S<sub>1</sub></font>[ <a href="trees_4.html#K1">root-tree</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span>]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="55_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>11</sub></font> be   <a href="msualg_1.html#NM1">SortSymbol</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>12</sub></font> be    <a href="subset_1.html#M1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#K7">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font>;<br/>



<b>reconsider </b><font color="Maroon">c<sub>13</sub></font> =  <a href="trees_4.html#K1">root-tree</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="tarski.html#K4">]</a></span> as   <a href="msaterm.html#NM1">Term</a> of <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#K7">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <b>by </b><i><a class="ref" href="msaterm.html#T4">MSATERM:4</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>13</sub></font>
;<br/>

<b>thus </b><a NAME="E2:55_1"/>
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a>  <a href="trees_4.html#K1">root-tree</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="tarski.html#K4">]</a></span>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>14</sub></font> be   <a href="msaterm.html#NM1">Term</a> of <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#K7">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E3:55_1"/><i><font color="Green">E34</font></i>: 
 <a href="msaterm.html#K7">the_sort_of</a> <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a>  <a href="msaterm.html#K7">the_sort_of</a> <font color="Maroon">c<sub>14</sub></font>
 <b>and </b><br/><a NAME="E4:55_1"/><i><font color="Green">E35</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="instalg1.html#K3" target="_self">hom</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="msualg_3.html#K1">.</a> <span class="p2">(<span class="default"><a href="msaterm.html#K7">the_sort_of</a> <font color="Maroon">c<sub>13</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="instalg1.html#K3" target="_self">hom</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="msualg_3.html#K1">.</a> <span class="p2">(<span class="default"><a href="msaterm.html#K7">the_sort_of</a> <font color="Maroon">c<sub>13</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font>
 ;<br/>

<a NAME="E5:55_1"/><i><font color="Green">E36</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="instalg1.html#K3" target="_self">hom</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="msualg_3.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="trees_4.html#K1">root-tree</a> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="tarski.html#K4">]</a></span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="trees_4.html#K1">root-tree</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>12</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span>
 
<b>by </b><i><a class="txt" href="instalg1.html#E1:55"><i><font color="Green">E31</font></i></a>, <a class="ref" href="instalg1.html#D5" target="_self">Def5</a></i>;<br/>
<a NAME="E6:55_1"/><i><font color="Green">E37</font></i>: 
 <a href="msaterm.html#K7">the_sort_of</a> <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="ref" href="msaterm.html#T14">MSATERM:14</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="55_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:55_1_1"/>
<font color="Maroon">c<sub>14</sub></font> <a href="funct_1.html#K1">.</a> <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">c<sub>1</sub></font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span>
 ;<br/><a NAME="E2:55_1_1"/><b>then </b>
<font color="Maroon">c<sub>14</sub></font> is    <a href="msaterm.html#M2">CompoundTerm</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#K7">*</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="msaterm.html#D6">MSATERM:def 6</a></i>;<br/><a NAME="E3:55_1_1"/><b>then </b>
( <span class="p1">(<span class="default"><a href="trees_4.html#K1">root-tree</a> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>12</sub></font>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>12</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span> &amp;  <a href="trees_4.html#K1">root-tree</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>12</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span> is    <a href="msaterm.html#M2">CompoundTerm</a> of <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="txt" href="instalg1.html#E1:55"><i><font color="Green">E31</font></i></a>, <a class="txt" href="instalg1.html#E3:55_1"><i><font color="Green">E34</font></i></a>, <a class="txt" href="instalg1.html#E4:55_1"><i><font color="Green">E35</font></i></a>, <a class="txt" href="instalg1.html#E5:55_1"><i><font color="Green">E36</font></i></a>, <a class="txt" href="instalg1.html#E6:55_1"><i><font color="Green">E37</font></i></a>, <a class="ref" href="instalg1.html#T42" target="_self">Th42</a>, <a class="ref" href="trees_4.html#T3">TREES_4:3</a></i>;<br/><a NAME="E4:55_1_1"/><b>then </b>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>12</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</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> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">c<sub>2</sub></font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span>
 <b>by </b><i><a class="ref" href="msaterm.html#D6">MSATERM:def 6</a></i>;<br/><a NAME="E5:55_1_1"/><b>then </b>
( <font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T129">ZFMISC_1:129</a></i>;<br/><b>hence </b><a NAME="E6:55_1_1"/>
contradiction
 ;<br/></div><b>end;</b></div>
<b>then consider </b><font color="Maroon">c<sub>15</sub></font> being   <a href="msualg_1.html#NM1">SortSymbol</a> of <font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>16</sub></font> being    <a href="subset_1.html#M1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#K7">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font><b> such that </b><br/><a NAME="E9:55_1"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">c<sub>14</sub></font> <a href="funct_1.html#K1">.</a> <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>15</sub></font></span><a href="tarski.html#K4">]</a></span>
 <b>by </b><i><a class="ref" href="msaterm.html#T2">MSATERM:2</a></i>;<br/>
<a NAME="E10:55_1"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a>  <a href="trees_4.html#K1">root-tree</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>15</sub></font></span><a href="tarski.html#K4">]</a></span>
 
<b>by </b><i><a class="txt" href="instalg1.html#E9:55_1"><i><font color="Green">E38</font></i></a>, <a class="ref" href="msaterm.html#T5">MSATERM:5</a></i>;<br/>
<a NAME="E11:55_1"/><b>then </b><i><font color="Green">E40</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>15</sub></font>
 
<b>by </b><i><a class="txt" href="instalg1.html#E3:55_1"><i><font color="Green">E34</font></i></a>, <a class="txt" href="instalg1.html#E6:55_1"><i><font color="Green">E37</font></i></a>, <a class="ref" href="msaterm.html#T14">MSATERM:14</a></i>;<br/>
<a NAME="E12:55_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="instalg1.html#K3" target="_self">hom</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="msualg_3.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a>  <a href="trees_4.html#K1">root-tree</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>16</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span>
 
<b>by </b><i><a class="txt" href="instalg1.html#E1:55"><i><font color="Green">E31</font></i></a>, <a class="txt" href="instalg1.html#E10:55_1"><i><font color="Green">E39</font></i></a>, <a class="ref" href="instalg1.html#D5" target="_self">Def5</a></i>;<br/>
<a NAME="E13:55_1"/><b>then </b>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>12</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>16</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span>
 
<b>by </b><i><a class="txt" href="instalg1.html#E4:55_1"><i><font color="Green">E35</font></i></a>, <a class="txt" href="instalg1.html#E5:55_1"><i><font color="Green">E36</font></i></a>, <a class="txt" href="instalg1.html#E6:55_1"><i><font color="Green">E37</font></i></a>, <a class="ref" href="trees_4.html#T4">TREES_4:4</a></i>;<br/>
<b>hence </b><a NAME="E14:55_1"/>
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="txt" href="instalg1.html#E10:55_1"><i><font color="Green">E39</font></i></a>, <a class="txt" href="instalg1.html#E11:55_1"><i><font color="Green">E40</font></i></a>, <a class="ref" href="zfmisc_1.html#T33">ZFMISC_1:33</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E8:55"/><i><font color="Green">E34</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="msualg_1.html#NM2">OperSymbol</a> of <font color="Maroon">c<sub>1</sub></font><br/>for <font color="Olive">b<sub>2</sub></font> being   <a href="msaterm.html#M1">ArgumentSeq</a> of  <a href="msaterm.html#K2">Sym</a> <font color="Olive">b<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#K7">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> st ( for <font color="Olive">b<sub>3</sub></font> being  <a href="msaterm.html#NM1">Term</a> of <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#K7">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> st <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Olive">b<sub>2</sub></font> holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>3</sub></font>] ) holds <br/><font color="Maroon">S<sub>1</sub></font>[<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">b<sub>1</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="trees_4.html#K4">-tree</a> <font color="Olive">b<sub>2</sub></font>]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="55_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>11</sub></font> be   <a href="msualg_1.html#NM2">OperSymbol</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>12</sub></font> be    <a href="msaterm.html#M1">ArgumentSeq</a> of  <a href="msaterm.html#K2">Sym</a> <font color="Maroon">c<sub>11</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#K7">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>;<br/>



<b>assume </b><a NAME="E1:55_2"/><i><font color="Green">E35</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="msaterm.html#NM1">Term</a> of <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#K7">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>12</sub></font> holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>]
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>13</sub></font> = <font color="Maroon">c<sub>12</sub></font> as    <a href="subset_1.html#M1">Element</a> of  <a href="msualg_1.html#K3">Args</a> <font color="Maroon">c<sub>11</sub></font>,<span class="p1">(<span class="default"><a href="msafree.html#K11">FreeMSA</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#K7">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <b>by </b><i><a class="ref" href="instalg1.html#T2" target="_self">Th2</a></i>;<br/>
<b>take </b><font color="Maroon">c<sub>14</sub></font> = <span class="p1">(<span class="default"><a href="msaterm.html#K2">Sym</a> <font color="Maroon">c<sub>11</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#K7">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="msaterm.html#K6">-tree</a> <font color="Maroon">c<sub>12</sub></font>;<br/>

<b>thus </b><a NAME="E3:55_2"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>11</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="trees_4.html#K4">-tree</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="ref" href="msafree.html#D11">MSAFREE:def 11</a></i>;<br/>

<b>let </b><font color="Maroon">c<sub>15</sub></font> be   <a href="msaterm.html#NM1">Term</a> of <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#K7">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E4:55_2"/><i><font color="Green">E37</font></i>: 
 <a href="msaterm.html#K7">the_sort_of</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a>  <a href="msaterm.html#K7">the_sort_of</a> <font color="Maroon">c<sub>15</sub></font>
 <b>and </b><br/><a NAME="E5:55_2"/><i><font color="Green">E38</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="instalg1.html#K3" target="_self">hom</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="msualg_3.html#K1">.</a> <span class="p2">(<span class="default"><a href="msaterm.html#K7">the_sort_of</a> <font color="Maroon">c<sub>14</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="instalg1.html#K3" target="_self">hom</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="msualg_3.html#K1">.</a> <span class="p2">(<span class="default"><a href="msaterm.html#K7">the_sort_of</a> <font color="Maroon">c<sub>14</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font>
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>16</sub></font> = <span class="p1">(<span class="default"><a href="instalg1.html#K3" target="_self">hom</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="msualg_3.html#K5">#</a> <font color="Maroon">c<sub>13</sub></font> as    <a href="subset_1.html#M1">Element</a> of  <a href="msualg_1.html#K3">Args</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="msafree.html#K11">FreeMSA</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <b>by </b><i><a class="txt" href="instalg1.html#E1:55"><i><font color="Green">E31</font></i></a>, <a class="ref" href="instalg1.html#T25" target="_self">Th25</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>17</sub></font> = <font color="Maroon">c<sub>16</sub></font> as    <a href="msaterm.html#M1">ArgumentSeq</a> of  <a href="msaterm.html#K2">Sym</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font> <b>by </b><i><a class="ref" href="instalg1.html#T2" target="_self">Th2</a></i>;<br/>
<a NAME="E8:55_2"/>
 <a href="msaterm.html#K7">the_sort_of</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a>  <a href="msualg_1.html#K2">the_result_sort_of</a> <font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="ref" href="msaterm.html#T20">MSATERM:20</a></i>;<br/>
<a NAME="E9:55_2"/><b>then </b><i><font color="Green">E39</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="instalg1.html#K3" target="_self">hom</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="msualg_3.html#K1">.</a> <span class="p2">(<span class="default"><a href="msaterm.html#K7">the_sort_of</a> <font color="Maroon">c<sub>14</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="trees_4.html#K4">-tree</a> <font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="txt" href="instalg1.html#E1:55"><i><font color="Green">E31</font></i></a>, <a class="txt" href="instalg1.html#E3:55_2"><i><font color="Green">E36</font></i></a>, <a class="ref" href="instalg1.html#T41" target="_self">Th41</a></i>;<br/>
<a NAME="E10:55_2"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msaterm.html#K2">Sym</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="msaterm.html#K6">-tree</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R1">=</a>  <a href="msaterm.html#K2">Sym</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font> &amp;  <a href="msaterm.html#K2">Sym</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span> &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">c<sub>2</sub></font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span> )
 
<b>by </b><i><a class="ref" href="msafree.html#D11">MSAFREE:def 11</a>, <a class="ref" href="trees_4.html#D4">TREES_4:def 4</a>, <a class="ref" href="zfmisc_1.html#T129">ZFMISC_1:129</a></i>;<br/>
<a NAME="E11:55_2"/><b>then </b>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="trees_4.html#K4">-tree</a> <font color="Maroon">c<sub>17</sub></font> is    <a href="msaterm.html#M2">CompoundTerm</a> of <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="msaterm.html#D6">MSATERM:def 6</a></i>;<br/>
<a NAME="E12:55_2"/><b>then </b>
<font color="Maroon">c<sub>15</sub></font> is    <a href="msaterm.html#M2">CompoundTerm</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#K7">*</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="instalg1.html#E1:55"><i><font color="Green">E31</font></i></a>, <a class="txt" href="instalg1.html#E4:55_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="instalg1.html#E5:55_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="instalg1.html#E9:55_2"><i><font color="Green">E39</font></i></a>, <a class="ref" href="instalg1.html#T42" target="_self">Th42</a></i>;<br/>
<a NAME="E13:55_2"/><b>then </b>
<font color="Maroon">c<sub>15</sub></font> <a href="funct_1.html#K1">.</a> <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">c<sub>1</sub></font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="msaterm.html#D6">MSATERM:def 6</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>18</sub></font>, <font color="Maroon">c<sub>19</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E15:55_2"/><i><font color="Green">E40</font></i>: 
( <font color="Maroon">c<sub>18</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>19</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K1">}</a></span> &amp; <font color="Maroon">c<sub>15</sub></font> <a href="funct_1.html#K1">.</a> <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>19</sub></font></span><a href="tarski.html#K4">]</a></span> )
 <b>by </b><i><a class="ref" href="zfmisc_1.html#D2">ZFMISC_1:def 2</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>20</sub></font> = <font color="Maroon">c<sub>18</sub></font> as   <a href="msualg_1.html#NM2">OperSymbol</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="txt" href="instalg1.html#E15:55_2"><i><font color="Green">E40</font></i></a></i>;<br/>
<a NAME="E17:55_2"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="funct_1.html#K1">.</a> <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>20</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span>
 
<b>by </b><i><a class="txt" href="instalg1.html#E15:55_2"><i><font color="Green">E40</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>21</sub></font> being    <a href="msaterm.html#M1">ArgumentSeq</a> of  <a href="msaterm.html#K2">Sym</a> <font color="Maroon">c<sub>20</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#K7">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span><b> such that </b><br/><a NAME="E19:55_2"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>20</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="trees_4.html#K4">-tree</a> <font color="Maroon">c<sub>21</sub></font>
 <b>by </b><i><a class="ref" href="msaterm.html#T10">MSATERM:10</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>22</sub></font> = <font color="Maroon">c<sub>21</sub></font> as    <a href="subset_1.html#M1">Element</a> of  <a href="msualg_1.html#K3">Args</a> <font color="Maroon">c<sub>20</sub></font>,<span class="p1">(<span class="default"><a href="msafree.html#K11">FreeMSA</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#K7">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <b>by </b><i><a class="ref" href="instalg1.html#T2" target="_self">Th2</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>23</sub></font> = <span class="p1">(<span class="default"><a href="instalg1.html#K3" target="_self">hom</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="msualg_3.html#K5">#</a> <font color="Maroon">c<sub>22</sub></font> as    <a href="subset_1.html#M1">Element</a> of  <a href="msualg_1.html#K3">Args</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>20</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="msafree.html#K11">FreeMSA</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <b>by </b><i><a class="txt" href="instalg1.html#E1:55"><i><font color="Green">E31</font></i></a>, <a class="ref" href="instalg1.html#T25" target="_self">Th25</a></i>;<br/>
<a NAME="E22:55_2"/>
 <a href="msualg_1.html#K2">the_result_sort_of</a> <font color="Maroon">c<sub>20</sub></font> <a href="hidden.html#R1">=</a>  <a href="msaterm.html#K7">the_sort_of</a> <font color="Maroon">c<sub>15</sub></font>
 
<b>by </b><i><a class="txt" href="instalg1.html#E17:55_2"><i><font color="Green">E41</font></i></a>, <a class="ref" href="msaterm.html#T17">MSATERM:17</a></i>;<br/>
<a NAME="E23:55_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="instalg1.html#K3" target="_self">hom</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="msualg_3.html#K1">.</a> <span class="p2">(<span class="default"><a href="msaterm.html#K7">the_sort_of</a> <font color="Maroon">c<sub>14</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>20</sub></font></span>)</span>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="trees_4.html#K4">-tree</a> <font color="Maroon">c<sub>23</sub></font>
 
<b>by </b><i><a class="txt" href="instalg1.html#E1:55"><i><font color="Green">E31</font></i></a>, <a class="txt" href="instalg1.html#E4:55_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="instalg1.html#E5:55_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="instalg1.html#E19:55_2"><i><font color="Green">E42</font></i></a>, <a class="ref" href="instalg1.html#T41" target="_self">Th41</a></i>;<br/>
<a NAME="E24:55_2"/><b>then </b><i><font color="Green">E43</font></i>: 
( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>20</sub></font></span>)</span>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span> &amp; <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>23</sub></font> )
 
<b>by </b><i><a class="txt" href="instalg1.html#E9:55_2"><i><font color="Green">E39</font></i></a>, <a class="ref" href="trees_4.html#T15">TREES_4:15</a></i>;<br/>
<a NAME="E25:55_2"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>20</sub></font>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T33">ZFMISC_1:33</a></i>;<br/>
<a NAME="E26:55_2"/><b>then </b><i><font color="Green">E44</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>20</sub></font>
 
<b>by </b><i><a class="ref" href="funct_2.html#T25">FUNCT_2:25</a></i>;<br/>
<a NAME="E27:55_2"/><b>then </b><i><font color="Green">E45</font></i>: 
(  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>12</sub></font> <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>11</sub></font></span>)</span> &amp;  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>21</sub></font> <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>11</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="msaterm.html#T22">MSATERM:22</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="55_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>24</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:55_2_1"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">c<sub>24</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>11</sub></font></span>)</span>
 ;<br/><b>then reconsider </b><font color="Maroon">c<sub>25</sub></font> = <font color="Maroon">c<sub>12</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>24</sub></font>, <font color="Maroon">c<sub>26</sub></font> = <font color="Maroon">c<sub>21</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>24</sub></font> as   <a href="msaterm.html#NM1">Term</a> of <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#K7">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <b>by </b><i><a class="txt" href="instalg1.html#E27:55_2"><i><font color="Green">E45</font></i></a>, <a class="ref" href="msaterm.html#T22">MSATERM:22</a></i>;<br/><a NAME="E3:55_2_1"/>
<font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="txt" href="instalg1.html#E27:55_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="instalg1.html#E1:55_2_1"><i><font color="Green">E46</font></i></a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/><a NAME="E4:55_2_1"/><b>then </b><i><font color="Green">E47</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">c<sub>25</sub></font>]
 <b>by </b><i><a class="txt" href="instalg1.html#E1:55_2"><i><font color="Green">E35</font></i></a></i>;<br/><a NAME="E5:55_2_1"/><i><font color="Green">E48</font></i>: 
(  <a href="msaterm.html#K7">the_sort_of</a> <font color="Maroon">c<sub>25</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>11</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>24</sub></font> &amp;  <a href="msaterm.html#K7">the_sort_of</a> <font color="Maroon">c<sub>26</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>11</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>24</sub></font> )
 <b>by </b><i><a class="txt" href="instalg1.html#E26:55_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="instalg1.html#E27:55_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="instalg1.html#E1:55_2_1"><i><font color="Green">E46</font></i></a>, <a class="ref" href="msaterm.html#T23">MSATERM:23</a></i>;<br/><a NAME="E6:55_2_1"/>
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> <a href="msualg_3.html#K6">#</a> <font color="Maroon">c<sub>13</sub></font>
 ;<br/><a NAME="E7:55_2_1"/><b>then </b>
( <font color="Maroon">c<sub>16</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>24</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="instalg1.html#K3" target="_self">hom</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="msualg_3.html#K1">.</a> <span class="p2">(<span class="default"><a href="msaterm.html#K7">the_sort_of</a> <font color="Maroon">c<sub>25</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>25</sub></font> &amp; <font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> <a href="msualg_3.html#K6">#</a> <font color="Maroon">c<sub>22</sub></font> )
 <b>by </b><i><a class="txt" href="instalg1.html#E27:55_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="instalg1.html#E1:55_2_1"><i><font color="Green">E46</font></i></a>, <a class="txt" href="instalg1.html#E5:55_2_1"><i><font color="Green">E48</font></i></a>, <a class="ref" href="msualg_3.html#D8">MSUALG_3:def 8</a></i>;<br/><a NAME="E8:55_2_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="instalg1.html#K3" target="_self">hom</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="msualg_3.html#K1">.</a> <span class="p2">(<span class="default"><a href="msaterm.html#K7">the_sort_of</a> <font color="Maroon">c<sub>25</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="instalg1.html#K3" target="_self">hom</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="msualg_3.html#K1">.</a> <span class="p2">(<span class="default"><a href="msaterm.html#K7">the_sort_of</a> <font color="Maroon">c<sub>25</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>26</sub></font>
 <b>by </b><i><a class="txt" href="instalg1.html#E24:55_2"><i><font color="Green">E43</font></i></a>, <a class="txt" href="instalg1.html#E26:55_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="instalg1.html#E27:55_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="instalg1.html#E1:55_2_1"><i><font color="Green">E46</font></i></a>, <a class="txt" href="instalg1.html#E5:55_2_1"><i><font color="Green">E48</font></i></a>, <a class="ref" href="msualg_3.html#D8">MSUALG_3:def 8</a></i>;<br/><b>hence </b><a NAME="E9:55_2_1"/>
<font color="Maroon">c<sub>12</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>24</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>21</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>24</sub></font>
 <b>by </b><i><a class="txt" href="instalg1.html#E4:55_2_1"><i><font color="Green">E47</font></i></a>, <a class="txt" href="instalg1.html#E5:55_2_1"><i><font color="Green">E48</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E29:55_2"/>
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="instalg1.html#E3:55_2"><i><font color="Green">E36</font></i></a>, <a class="txt" href="instalg1.html#E19:55_2"><i><font color="Green">E42</font></i></a>, <a class="txt" href="instalg1.html#E26:55_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="instalg1.html#E27:55_2"><i><font color="Green">E45</font></i></a>, <a class="ref" href="finseq_1.html#T17">FINSEQ_1:17</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E9:55"/><i><font color="Green">E35</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="msaterm.html#NM1">Term</a> of <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#K7">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> holds <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>]
 
<b>from </b><i><a class="ref" href="msaterm.html#S1">MSATERM:sch 1</a>(<a class="txt" href="instalg1.html#E7:55"><i><font color="Green">E33</font></i></a>, <a class="txt" href="instalg1.html#E8:55"><i><font color="Green">E34</font></i></a>);<br/></i>
<b>let </b><font color="Maroon">c<sub>11</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="msualg_3.html#D2">MSUALG_3:def 2</a><br/><b>let </b><font color="Maroon">c<sub>12</sub></font> be   <a href="funct_1.html#NM1">Function</a>;<br/>



<b>assume </b><a NAME="E10:55"/>
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="instalg1.html#K3" target="_self">hom</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>13</sub></font> = <font color="Maroon">c<sub>11</sub></font> as   <a href="msualg_1.html#NM1">SortSymbol</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/>
<b>assume </b><a NAME="E12:55"/><i><font color="Green">E36</font></i>: 
<span class="p1">(<span class="default"><a href="instalg1.html#K3" target="_self">hom</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</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> <font color="Maroon">c<sub>12</sub></font>
 ;<br/>

<b>then </b><i><font color="Green">E37</font></i>:  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>12</sub></font> = 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="msualg_3.html#K1">.</a> <font color="Maroon">c<sub>13</sub></font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="msafree.html#K8">FreeSort</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#K7">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>13</sub></font>
<b>by </b><i><a class="txt" href="instalg1.html#E6:55"><i><font color="Green">E32</font></i></a>, <a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>
<br/>.= 
 <a href="msafree.html#K7">FreeSort</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#K7">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<font color="Maroon">c<sub>13</sub></font>
<b>by </b><i><a class="ref" href="msafree.html#D13">MSAFREE:def 13</a></i>
;<br/>
<a NAME="E14:55"/><i><font color="Green">E38</font></i>: 
 <a href="msafree.html#K7">FreeSort</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#K7">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<font color="Maroon">c<sub>13</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>1</sub></font> <a href="msaterm.html#K1">-Terms</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#K7">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="msaterm.html#T12">MSATERM:12</a></i>;<br/>
<b>let </b><font color="Maroon">c<sub>14</sub></font>, <font color="Maroon">c<sub>15</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a><br/>

<b>assume </b><a NAME="E15:55"/><i><font color="Green">E39</font></i>: 
( <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>12</sub></font> )
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>16</sub></font> = <font color="Maroon">c<sub>14</sub></font>, <font color="Maroon">c<sub>17</sub></font> = <font color="Maroon">c<sub>15</sub></font> as   <a href="msaterm.html#NM1">Term</a> of <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#K7">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <b>by </b><i><a class="txt" href="instalg1.html#E13:55"><i><font color="Green">E37</font></i></a>, <a class="txt" href="instalg1.html#E14:55"><i><font color="Green">E38</font></i></a></i>;<br/>
<a NAME="E17:55"/>
( <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">c<sub>16</sub></font>] &amp;  <a href="msaterm.html#K7">the_sort_of</a> <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font> &amp;  <a href="msaterm.html#K7">the_sort_of</a> <font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font> )
 
<b>by </b><i><a class="txt" href="instalg1.html#E9:55"><i><font color="Green">E35</font></i></a>, <a class="txt" href="instalg1.html#E13:55"><i><font color="Green">E37</font></i></a>, <a class="txt" href="instalg1.html#E15:55"><i><font color="Green">E39</font></i></a>, <a class="ref" href="msaterm.html#D5">MSATERM:def 5</a></i>;<br/>
<b>hence </b><a NAME="E18:55"/>
(  not <font color="Maroon">c<sub>12</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>12</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font> or <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>15</sub></font> )
 <b>by </b><i><a class="txt" href="instalg1.html#E12:55"><i><font color="Green">E36</font></i></a></i>;<br/>


</div>
