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

<b>let </b><font color="Maroon">S</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">A</font> be  <a href="msualg_1.html#V5">non-empty</a>  <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">V</font> be    <a href="msaterm.html#M4" target="_self">Variables</a> of <font color="Maroon">A</font>;<br/><b>let </b><font color="Maroon">t</font> be   <a href="msaterm.html#NM3">c-Term</a> of <font color="Maroon">A</font>,<font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">f</font> be    <a href="pboole.html#M3">ManySortedFunction</a> of <font color="Maroon">V</font>,the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font>;<br/>









<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1">set</a> ] <b>means </b> ex <font color="Olive">t</font> being  <a href="msaterm.html#NM3">c-Term</a> of <font color="Maroon">A</font>,<font color="Maroon">V</font> ex <font color="Olive">vt</font> being <a href="finset_1.html#V1">finite</a> <a href="trees_2.html#NM4">DecoratedTree</a> st <br/>( <font color="Olive">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a<sub>1</sub></font> &amp; <font color="Olive">vt</font> <a href="msaterm.html#R1" target="_self">is_an_evaluation_of</a> <font color="Olive">t</font>,<font color="Maroon">f</font> );<br/>
<a NAME="E1:64"/><i><font color="Green">E26</font></i>: 
for <font color="Olive">s</font> being  <a href="msualg_1.html#NM1">SortSymbol</a> of <font color="Maroon">S</font><br/> for <font color="Olive">x</font> being   <a href="subset_1.html#M1">Element</a> of the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Olive">s</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">x</font>,<font color="Olive">s</font></span><a href="tarski.html#K4">]</a></span>]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="64_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">s</font> be   <a href="msualg_1.html#NM1">SortSymbol</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">x</font> be    <a href="subset_1.html#M1">Element</a> of the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">s</font>;<br/>



<b>reconsider </b><font color="Maroon">t</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">x</font>,<font color="Maroon">s</font></span><a href="tarski.html#K4">]</a></span> as   <a href="msaterm.html#NM3">c-Term</a> of <font color="Maroon">A</font>,<font color="Maroon">V</font> <b>by </b><i/>;<br/>
<b>take </b>
<font color="Maroon">t</font>
;<br/>

<b>take </b>
 <a href="trees_4.html#K2">root-tree</a> <font color="Maroon">x</font>
;<br/>

<b>thus </b><a NAME="E2:64_1"/>
<font color="Maroon">t</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">x</font>,<font color="Maroon">s</font></span><a href="tarski.html#K4">]</a></span>
 ;<br/>

<b>thus </b><a NAME="E3:64_1"/>
 <a href="trees_4.html#K2">root-tree</a> <font color="Maroon">x</font> <a href="msaterm.html#R1" target="_self">is_an_evaluation_of</a> <font color="Maroon">t</font>,<font color="Maroon">f</font>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<a NAME="E2:64"/><i><font color="Green">E27</font></i>: 
for <font color="Olive">s</font> being  <a href="msualg_1.html#NM1">SortSymbol</a> of <font color="Maroon">S</font><br/> for <font color="Olive">v</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">V</font> <a href="funct_1.html#K1">.</a> <font color="Olive">s</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">v</font>,<font color="Olive">s</font></span><a href="tarski.html#K4">]</a></span>]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="64_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">s</font> be   <a href="msualg_1.html#NM1">SortSymbol</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">x</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">V</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">s</font>;<br/>



<b>reconsider </b><font color="Maroon">t</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">x</font>,<font color="Maroon">s</font></span><a href="tarski.html#K4">]</a></span> as   <a href="msaterm.html#NM3">c-Term</a> of <font color="Maroon">A</font>,<font color="Maroon">V</font> <b>by </b><i/>;<br/>
<b>take </b>
<font color="Maroon">t</font>
;<br/>

<b>take </b>
 <a href="trees_4.html#K2">root-tree</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="msualg_3.html#K1">.</a> <font color="Maroon">s</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font></span>)</span>
;<br/>

<b>thus </b><a NAME="E2:64_2"/>
<font color="Maroon">t</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">x</font>,<font color="Maroon">s</font></span><a href="tarski.html#K4">]</a></span>
 ;<br/>

<b>thus </b><a NAME="E3:64_2"/>
 <a href="trees_4.html#K2">root-tree</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="msualg_3.html#K1">.</a> <font color="Maroon">s</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font></span>)</span> <a href="msaterm.html#R1" target="_self">is_an_evaluation_of</a> <font color="Maroon">t</font>,<font color="Maroon">f</font>
 <b>by </b><i><a class="ref" href="msaterm.html#D1" target="_self">Def1</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:64"/><i><font color="Green">E28</font></i>: 
for <font color="Olive">o</font> being  <a href="msualg_1.html#NM2">OperSymbol</a> of <font color="Maroon">S</font><br/> for <font color="Olive">p</font> being  <a href="msaterm.html#NM4">ArgumentSeq</a> of <font color="Olive">o</font>,<font color="Maroon">A</font>,<font color="Maroon">V</font>  st ( for <font color="Olive">t</font> being  <a href="msaterm.html#NM3">c-Term</a> of <font color="Maroon">A</font>,<font color="Maroon">V</font>  st <font color="Olive">t</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Olive">p</font> holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive">t</font>] ) holds <br/><font color="Maroon">S<sub>1</sub></font>[<span class="p1">(<span class="default"><a href="msaterm.html#K2" target="_self">Sym</a> <font color="Olive">o</font>,<span class="p2">(<span class="default">the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font> <a href="pboole.html#K2">\/</a> <font color="Maroon">V</font></span>)</span></span>)</span> <a href="msaterm.html#K6" target="_self">-tree</a> <font color="Olive">p</font>]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="64_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">o</font> be   <a href="msualg_1.html#NM2">OperSymbol</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">p</font> be   <a href="msaterm.html#NM4">ArgumentSeq</a> of <font color="Maroon">o</font>,<font color="Maroon">A</font>,<font color="Maroon">V</font>;<br/>



<b>assume </b><a NAME="E1:64_3"/><i><font color="Green">E45</font></i>: 
for <font color="Olive">t</font> being  <a href="msaterm.html#NM3">c-Term</a> of <font color="Maroon">A</font>,<font color="Maroon">V</font>  st <font color="Olive">t</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">p</font> holds <br/> ex <font color="Olive">u</font> being  <a href="msaterm.html#NM3">c-Term</a> of <font color="Maroon">A</font>,<font color="Maroon">V</font> ex <font color="Olive">vt</font> being <a href="finset_1.html#V1">finite</a> <a href="trees_2.html#NM4">DecoratedTree</a> st <br/>( <font color="Olive">u</font> <a href="hidden.html#R1">=</a> <font color="Olive">t</font> &amp; <font color="Olive">vt</font> <a href="msaterm.html#R1" target="_self">is_an_evaluation_of</a> <font color="Olive">u</font>,<font color="Maroon">f</font> )
 ;<br/>

<a NAME="E2:64_3"/><i><font color="Green">E51</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<b>defpred </b><font color="Maroon">S<sub>2</sub></font>[   <a href="hidden.html#M1">set</a> ,   <a href="hidden.html#M1">set</a> ] <b>means </b> ex <font color="Olive">t</font> being  <a href="msaterm.html#NM3">c-Term</a> of <font color="Maroon">A</font>,<font color="Maroon">V</font> ex <font color="Olive">vt</font> being <a href="finset_1.html#V1">finite</a> <a href="trees_2.html#NM4">DecoratedTree</a> st <br/>( <font color="Maroon">a<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">vt</font> &amp; <font color="Olive">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">a<sub>1</sub></font> &amp; <font color="Olive">vt</font> <a href="msaterm.html#R1" target="_self">is_an_evaluation_of</a> <font color="Olive">t</font>,<font color="Maroon">f</font> );<br/>
<a NAME="E3:64_3"/><i><font color="Green">E52</font></i>: 
for <font color="Olive">e</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">e</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">p</font> holds <br/> ex <font color="Olive">u</font> being   <a href="hidden.html#M1">set</a>  st <font color="Maroon">S<sub>2</sub></font>[<font color="Olive">e</font>,<font color="Olive">u</font>]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="64_3_1"><b>proof </b></a><div class="add">

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

<b>assume </b><a NAME="E1:64_3_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">p</font>
 ;<br/>

<a NAME="E2:64_3_1"/><b>then </b><i><font color="Green">E53</font></i>: 
( <font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">p</font> &amp;  <a href="relat_1.html#K2">rng</a> <font color="Maroon">p</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">S</font> <a href="msaterm.html#K1" target="_self">-Terms</a> <span class="p1">(<span class="default">the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font> <a href="pboole.html#K2">\/</a> <font color="Maroon">V</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">t</font> = <font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> as   <a href="msaterm.html#NM3">c-Term</a> of <font color="Maroon">A</font>,<font color="Maroon">V</font> ;<br/>
<a NAME="E4:64_3_1"/>
 ex <font color="Olive">u</font> being  <a href="msaterm.html#NM3">c-Term</a> of <font color="Maroon">A</font>,<font color="Maroon">V</font> ex <font color="Olive">vt</font> being <a href="finset_1.html#V1">finite</a> <a href="trees_2.html#NM4">DecoratedTree</a> st <br/>( <font color="Olive">u</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> &amp; <font color="Olive">vt</font> <a href="msaterm.html#R1" target="_self">is_an_evaluation_of</a> <font color="Olive">u</font>,<font color="Maroon">f</font> )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E5:64_3_1"/>
 ex <font color="Olive">y</font> being   <a href="hidden.html#M1">set</a>  ex <font color="Olive">t</font> being  <a href="msaterm.html#NM3">c-Term</a> of <font color="Maroon">A</font>,<font color="Maroon">V</font> ex <font color="Olive">vt</font> being <a href="finset_1.html#V1">finite</a> <a href="trees_2.html#NM4">DecoratedTree</a> st <br/>( <font color="Olive">y</font> <a href="hidden.html#R1">=</a> <font color="Olive">vt</font> &amp; <font color="Olive">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> &amp; <font color="Olive">vt</font> <a href="msaterm.html#R1" target="_self">is_an_evaluation_of</a> <font color="Olive">t</font>,<font color="Maroon">f</font> )
 ;<br/>


</div><b>end;</b></div>
<b>consider </b><font color="Maroon">q</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E5:64_3"/><i><font color="Green">E54</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">q</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">p</font> &amp; ( for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">p</font> holds <br/><font color="Maroon">S<sub>2</sub></font>[<font color="Olive">x</font>,<font color="Maroon">q</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font>] ) )
 <b>from </b><i><a class="ref" href="zfrefle1.html#S1">ZFREFLE1:sch 1</a>(<a class="txt" href="msaterm.html#E6"><i><font color="Green">Lemma46</font></i></a>);<br/></i>
<b>reconsider </b><font color="Maroon">q</font> = <font color="Maroon">q</font> as   <a href="finseq_1.html#NM1">FinSequence</a> <b>by </b><i><a class="txt" href="msaterm.html#E1:64_3"><i><font color="Green">E45</font></i></a>, , <a class="ref" href="finseq_1.html#D2">FINSEQ_1:def 2</a></i>;<br/>
<a NAME="E7:64_3"/><i><font color="Green">E62</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">q</font>
 
<b>by </b><i>, <a class="ref" href="finseq_3.html#T31">FINSEQ_3:31</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="64_3_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:64_3_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">q</font>
 ;<br/><a NAME="E2:64_3_2"/><b>then </b>
 ex <font color="Olive">t</font> being  <a href="msaterm.html#NM3">c-Term</a> of <font color="Maroon">A</font>,<font color="Maroon">V</font> ex <font color="Olive">vt</font> being <a href="finset_1.html#V1">finite</a> <a href="trees_2.html#NM4">DecoratedTree</a> st <br/>( <font color="Maroon">q</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Olive">vt</font> &amp; <font color="Olive">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> &amp; <font color="Olive">vt</font> <a href="msaterm.html#R1" target="_self">is_an_evaluation_of</a> <font color="Olive">t</font>,<font color="Maroon">f</font> )
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E3:64_3_2"/>
<font color="Maroon">q</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> is   <a href="trees_2.html#NM4">DecoratedTree</a>
 ;<br/></div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">q</font> = <font color="Maroon">q</font> as  <a href="trees_3.html#V6">DTree-yielding</a> <a href="finseq_1.html#NM1">FinSequence</a> <b>by </b><i><a class="ref" href="trees_3.html#T26">TREES_3:26</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="64_3_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">t</font> be   <a href="msaterm.html#NM3">c-Term</a> of <font color="Maroon">A</font>,<font color="Maroon">V</font>;<br/><b>assume </b><a NAME="E1:64_3_3"/>
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">p</font>
 ;<br/><a NAME="E2:64_3_3"/><b>then </b>
 ex <font color="Olive">t</font> being  <a href="msaterm.html#NM3">c-Term</a> of <font color="Maroon">A</font>,<font color="Maroon">V</font> ex <font color="Olive">vt</font> being <a href="finset_1.html#V1">finite</a> <a href="trees_2.html#NM4">DecoratedTree</a> st <br/>( <font color="Maroon">q</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Olive">vt</font> &amp; <font color="Olive">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> &amp; <font color="Olive">vt</font> <a href="msaterm.html#R1" target="_self">is_an_evaluation_of</a> <font color="Olive">t</font>,<font color="Maroon">f</font> )
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E3:64_3_3"/>
( <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> implies  ex <font color="Olive">vt</font> being <a href="finset_1.html#V1">finite</a> <a href="trees_2.html#NM4">DecoratedTree</a> st <br/>( <font color="Olive">vt</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> &amp; <font color="Olive">vt</font> <a href="msaterm.html#R1" target="_self">is_an_evaluation_of</a> <font color="Maroon">t</font>,<font color="Maroon">f</font> ) )
 ;<br/></div><b>end;</b></div>
<a NAME="E11:64_3"/><b>then </b>
 ex <font color="Olive">vt</font> being <a href="finset_1.html#V1">finite</a> <a href="trees_2.html#NM4">DecoratedTree</a> st <br/>( <font color="Olive">vt</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_1.html#K5">Den</a> <font color="Maroon">o</font>,<font color="Maroon">A</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><a href="trees_3.html#K16">roots</a> <font color="Maroon">q</font></span>)</span></span>)</span> <a href="trees_4.html#K4">-tree</a> <font color="Maroon">q</font> &amp; <font color="Olive">vt</font> <a href="msaterm.html#R1" target="_self">is_an_evaluation_of</a> <span class="p1">(<span class="default"><a href="msaterm.html#K2" target="_self">Sym</a> <font color="Maroon">o</font>,<span class="p2">(<span class="default">the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font> <a href="pboole.html#K2">\/</a> <font color="Maroon">V</font></span>)</span></span>)</span> <a href="msaterm.html#K6" target="_self">-tree</a> <font color="Maroon">p</font>,<font color="Maroon">f</font> )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E12:64_3"/>
<font color="Maroon">S<sub>1</sub></font>[<span class="p1">(<span class="default"><a href="msaterm.html#K2" target="_self">Sym</a> <font color="Maroon">o</font>,<span class="p2">(<span class="default">the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font> <a href="pboole.html#K2">\/</a> <font color="Maroon">V</font></span>)</span></span>)</span> <a href="msaterm.html#K6" target="_self">-tree</a> <font color="Maroon">p</font>]
 ;<br/>


</div><b>end;</b></div>
<a NAME="E4:64"/>
for <font color="Olive">t</font> being  <a href="msaterm.html#NM3">c-Term</a> of <font color="Maroon">A</font>,<font color="Maroon">V</font> holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">t</font>]
 
<b>from </b><i><a class="ref" href="msaterm.html#S2" target="_self">MSATERM:sch 2</a>(<a class="ref" href="msaterm.html#D2" target="_self">Def2</a>, , <a class="ref" href="msaterm.html#T1" target="_self">Th1</a>);<br/></i>
<a NAME="E5:64"/><b>then </b>
 ex <font color="Olive">u</font> being  <a href="msaterm.html#NM3">c-Term</a> of <font color="Maroon">A</font>,<font color="Maroon">V</font> ex <font color="Olive">vt</font> being <a href="finset_1.html#V1">finite</a> <a href="trees_2.html#NM4">DecoratedTree</a> st <br/>( <font color="Olive">u</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> &amp; <font color="Olive">vt</font> <a href="msaterm.html#R1" target="_self">is_an_evaluation_of</a> <font color="Olive">u</font>,<font color="Maroon">f</font> )
 
;<br/>
<b>hence </b><a NAME="E6:64"/>
 ex <font color="Olive">vt</font> being <a href="finset_1.html#V1">finite</a> <a href="trees_2.html#NM4">DecoratedTree</a> st <font color="Olive">vt</font> <a href="msaterm.html#R1" target="_self">is_an_evaluation_of</a> <font color="Maroon">t</font>,<font color="Maroon">f</font>
 ;<br/>


</div>
