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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">A</font> be  <a href="msualg_1.html#V5" title="MSUALG_1:attr.5">non-empty</a>  <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c1">S</font>;<br/><b>let </b><font color="Maroon" title="c3">V</font> be    <a href="msaterm.html#M4" title="MSATERM:mode.4">Variables</a> of <font color="Maroon" title="c2">A</font>;<br/><b>let </b><font color="Maroon" title="c4">f</font> be    <a href="pboole.html#M3" title="PBOOLE:mode.3">ManySortedFunction</a> of <font color="Maroon" title="c3">V</font>,the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c2">A</font>;<br/><b>let </b><font color="Maroon" title="c5">t</font> be   <a href="msaterm.html#NM3" title="MSATERM:NM.3">c-Term</a> of <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">V</font>;<br/><b>let </b><font color="Maroon" title="c6">vt</font> be  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="trees_2.html#NM4" title="TREES_2:NM.4">DecoratedTree</a>;<br/>











<b>assume </b><a NAME="E1:69"/><i><font color="Green" title="E45">A1</font></i>: 
<font color="Maroon" title="c6">vt</font> <a href="msaterm.html#R1" title="MSATERM:pred.1">is_an_evaluation_of</a> <font color="Maroon" title="c5">t</font>,<font color="Maroon" title="c4">f</font>
 ;<br/>

<b>let </b><font color="Maroon" title="c7">p</font> be   <a href="trees_4.html#NM1" title="TREES_4:NM.1">Node</a> of <font color="Maroon" title="c5">t</font>;<br/>

<b>reconsider </b><font color="Maroon" title="c8">n</font> = <font color="Maroon" title="c7">p</font> as   <a href="trees_4.html#NM1" title="TREES_4:NM.1">Node</a> of <font color="Maroon" title="c6">vt</font> <b>by </b><i><a class="txt" href="msaterm.html#E1:69"><i><font color="Green" title="E45">A1</font></i></a>, <a class="ref" href="msaterm.html#D9" target="_self" title="MSATERM:def.9">Def9</a></i>;<br/>
<a NAME="E3:69"/>
<font color="Maroon" title="c6">vt</font> <a href="trees_2.html#K5" title="TREES_2:func.5">|</a> <font color="Maroon" title="c8">n</font> <a href="msaterm.html#R1" title="MSATERM:pred.1">is_an_evaluation_of</a> <font color="Maroon" title="c5">t</font> <a href="msaterm.html#K8" title="MSATERM:func.8">|</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c4">f</font>
 
<b>by </b><i><a class="txt" href="msaterm.html#E1:69"><i><font color="Green" title="E45">A1</font></i></a>, <a class="ref" href="msaterm.html#T34" target="_self" title="MSATERM:th.34">Th34</a></i>;<br/>
<a NAME="E4:69"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon" title="c5">t</font> <a href="msaterm.html#K8" title="MSATERM:func.8">|</a> <font color="Maroon" title="c7">p</font></span>)</span> <a href="msaterm.html#K9" title="MSATERM:func.9">@</a> <font color="Maroon" title="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">vt</font> <a href="trees_2.html#K5" title="TREES_2:func.5">|</a> <font color="Maroon" title="c8">n</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="lang1.html#K2" title="LANG1:func.2">&lt;*&gt;</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span>)</span> &amp; <font color="Maroon" title="c8">n</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">n</font> &amp;  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c6">vt</font></span>)</span> <a href="trees_1.html#K4" title="TREES_1:func.4">|</a> <font color="Maroon" title="c7">p</font> )
 
<b>by </b><i><a class="ref" href="msaterm.html#T39" target="_self" title="MSATERM:th.39">Th39</a>, <a class="ref" href="finseq_1.html#T47" title="FINSEQ_1:th.47">FINSEQ_1:47</a>, <a class="ref" href="trees_1.html#T47" title="TREES_1:th.47">TREES_1:47</a></i>;<br/>
<b>hence </b><a NAME="E5:69"/>
<font color="Maroon" title="c6">vt</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">t</font> <a href="msaterm.html#K8" title="MSATERM:func.8">|</a> <font color="Maroon" title="c7">p</font></span>)</span> <a href="msaterm.html#K9" title="MSATERM:func.9">@</a> <font color="Maroon" title="c4">f</font>
 <b>by </b><i><a class="ref" href="trees_2.html#D11" title="TREES_2:def.11">TREES_2:def 11</a></i>;<br/>


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