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<b>let </b><font color="Maroon" title="c1">S</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> non <a href="msualg_1.html#V2" title="MSUALG_1:attr.2">void</a>  <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> ;<br/><b>let </b><font color="Maroon" title="c2">V</font> be  <a href="relat_1.html#V2" title="RELAT_1:attr.2">V5</a>  <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font>;<br/><b>let </b><font color="Maroon" title="c3">t</font> be   <a href="msaterm.html#NM1" title="MSATERM:NM.1">Term</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">V</font>;<br/><b>let </b><font color="Maroon" title="c4">o</font> be   <a href="msualg_1.html#NM2" title="MSUALG_1:NM.2">OperSymbol</a> of <font color="Maroon" title="c1">S</font>;<br/>







<b>assume </b><a NAME="E1:28"/><i><font color="Green" title="E16">A1</font></i>: 
<font color="Maroon" title="c3">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">o</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 ;<br/>

<b>set </b><font color="Maroon" title="c5">X</font> = <font color="Maroon" title="c2">V</font>;<br/>
<b>set </b><font color="Maroon" title="c6">G</font> =  <a href="msafree.html#K5" title="MSAFREE:func.5">DTConMSA</a> <font color="Maroon" title="c2">V</font>;<br/>
<b>reconsider </b><font color="Maroon" title="c7">t</font> = <font color="Maroon" title="c3">t</font> as    <a href="dtconstr.html#M1" title="DTCONSTR:mode.1">Element</a> of  <a href="dtconstr.html#K4" title="DTCONSTR:func.4">TS</a> <span class="p1">(<span class="default"><a href="msafree.html#K5" title="MSAFREE:func.5">DTConMSA</a> <font color="Maroon" title="c2">V</font></span>)</span> ;<br/>
<a NAME="E3:28"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">o</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msaterm.html#K2" title="MSATERM:func.2">Sym</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c2">V</font>
 
<b>by </b><i><a class="ref" href="msafree.html#D11" title="MSAFREE:def.11">MSAFREE:def 11</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c8">p</font> being    <a href="trees_4.html#M1" title="TREES_4:mode.1">FinSequence</a> of  <a href="dtconstr.html#K4" title="DTCONSTR:func.4">TS</a> <span class="p1">(<span class="default"><a href="msafree.html#K5" title="MSAFREE:func.5">DTConMSA</a> <font color="Maroon" title="c2">V</font></span>)</span><b> such that </b><br/><a NAME="E5:28"/><i><font color="Green" title="E17">A2</font></i>: 
( <font color="Maroon" title="c7">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="msaterm.html#K2" title="MSATERM:func.2">Sym</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c2">V</font></span>)</span> <a href="trees_4.html#K12" title="TREES_4:func.12">-tree</a> <font color="Maroon" title="c8">p</font> &amp;  <a href="msaterm.html#K2" title="MSATERM:func.2">Sym</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c2">V</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a>  <a href="dtconstr.html#K1" title="DTCONSTR:func.1">roots</a> <font color="Maroon" title="c8">p</font> )
 <b>by </b><i><a class="txt" href="msaterm.html#E1:28"><i><font color="Green" title="E16">A1</font></i></a>, <a class="ref" href="dtconstr.html#T10" title="DTCONSTR:th.10">DTCONSTR:10</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c9">a</font> = <font color="Maroon" title="c8">p</font> as    <a href="trees_4.html#M1" title="TREES_4:mode.1">FinSequence</a> of <font color="Maroon" title="c1">S</font> <a href="msaterm.html#K1" title="MSATERM:func.1">-Terms</a> <font color="Maroon" title="c2">V</font> ;<br/>
<a NAME="E7:28"/>
<font color="Maroon" title="c9">a</font> is    <a href="dtconstr.html#M2" title="DTCONSTR:mode.2">SubtreeSeq</a> of  <a href="msaterm.html#K2" title="MSATERM:func.2">Sym</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c2">V</font>
 
<b>by </b><i><a class="txt" href="msaterm.html#E5:28"><i><font color="Green" title="E17">A2</font></i></a>, <a class="ref" href="dtconstr.html#D9" title="DTCONSTR:def.9">DTCONSTR:def 9</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c10">a</font> = <font color="Maroon" title="c9">a</font> as    <a href="msaterm.html#M1" title="MSATERM:mode.1">ArgumentSeq</a> of  <a href="msaterm.html#K2" title="MSATERM:func.2">Sym</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c2">V</font> <b>by </b><i><a class="ref" href="msaterm.html#D2" target="_self" title="MSATERM:def.2">Def2</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c10">a</font>
;<br/>

<b>thus </b><a NAME="E9:28"/>
<font color="Maroon" title="c3">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">o</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="trees_4.html#K4" title="TREES_4:func.4">-tree</a> <font color="Maroon" title="c10">a</font>
 <b>by </b><i><a class="txt" href="msaterm.html#E5:28"><i><font color="Green" title="E17">A2</font></i></a>, <a class="ref" href="msafree.html#D11" title="MSAFREE:def.11">MSAFREE:def 11</a></i>;<br/>


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