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<b>let </b><font color="Maroon" title="c1">S</font> be  non <a href="msualg_1.html#V2" title="MSUALG_1:attr.2">void</a> <a href="catalg_1.html#NM1" title="CATALG_1:NM.1">Signature</a>;<br/><b>let </b><font color="Maroon" title="c2">X</font> be  <a href="relat_1.html#V3" title="RELAT_1:attr.3">V4</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="msafree3.html#NM1" title="MSAFREE3:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="msafree3.html#K1" title="MSAFREE3:func.1">Free</a> <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">X</font></span>)</span>;<br/><b>let </b><font color="Maroon" title="c4">p</font> be    <a href="trees_1.html#M1" title="TREES_1:mode.1">Element</a> of  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c3">t</font>;<br/>







<b>set </b><font color="Maroon" title="c5">Y</font> = <font color="Maroon" title="c2">X</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <span class="p1">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default">0</span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span>;<br/>
<a NAME="E1:45"/><i><font color="Green" title="E33">A1</font></i>: 
the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p1">(<span class="default"><a href="msafree3.html#K1" title="MSAFREE3:func.1">Free</a> <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">X</font></span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c1">S</font> <a href="msafree3.html#K5" title="MSAFREE3:func.5">-Terms</a> <font color="Maroon" title="c2">X</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <span class="p2">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default">0</span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="msafree3.html#T25" target="_self" title="MSAFREE3:th.25">Th25</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">t</font> = <font color="Maroon" title="c3">t</font> as   <a href="msaterm.html#NM1" title="MSATERM:NM.1">Term</a> of <font color="Maroon" title="c1">S</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <span class="p2">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default">0</span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span></span>)</span> <b>by </b><i><a class="ref" href="msafree3.html#T9" target="_self" title="MSAFREE3:th.9">Th9</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c7">p</font> = <font color="Maroon" title="c4">p</font> as    <a href="trees_1.html#M1" title="TREES_1:mode.1">Element</a> of  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c6">t</font> ;<br/>
<a NAME="E4:45"/><i><font color="Green" title="E34">A2</font></i>: 
 <a href="msafree3.html#K4" title="MSAFREE3:func.4">variables_in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">t</font> <a href="msaterm.html#K8" title="MSATERM:func.8">|</a> <font color="Maroon" title="c7">p</font></span>)</span> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a>  <a href="msafree3.html#K4" title="MSAFREE3:func.4">variables_in</a> <font color="Maroon" title="c6">t</font>
 
<b>by </b><i><a class="ref" href="msafree3.html#T33" target="_self" title="MSAFREE3:th.33">Th33</a></i>;<br/>
<a NAME="E5:45"/><i><font color="Green" title="E35">A3</font></i>: 
(  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">S</font> <a href="msafree3.html#K5" title="MSAFREE3:func.5">-Terms</a> <font color="Maroon" title="c2">X</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <span class="p3">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default">0</span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font> &amp; <font color="Maroon" title="c6">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_3.html#K3" title="CARD_3:func.3">Union</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p1">(<span class="default"><a href="msafree3.html#K1" title="MSAFREE3:func.1">Free</a> <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">X</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="pboole.html#D3" title="PBOOLE:def.3">PBOOLE:def 3</a></i>;<br/>
<a NAME="E6:45"/><b>then </b>
 ex <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font> &amp; <font color="Maroon" title="c6">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">S</font> <a href="msafree3.html#K5" title="MSAFREE3:func.5">-Terms</a> <font color="Maroon" title="c2">X</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <span class="p3">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default">0</span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> )
 
<b>by </b><i><a class="txt" href="msafree3.html#E1:45"><i><font color="Green" title="E33">A1</font></i></a>, <a class="ref" href="card_5.html#T10" title="CARD_5:th.10">CARD_5:10</a></i>;<br/>
<a NAME="E7:45"/><b>then </b>
 <a href="msafree3.html#K4" title="MSAFREE3:func.4">variables_in</a> <font color="Maroon" title="c6">t</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c2">X</font>
 
<b>by </b><i><a class="ref" href="msafree3.html#T18" target="_self" title="MSAFREE3:th.18">Th18</a></i>;<br/>
<a NAME="E8:45"/><b>then </b>
 <a href="msafree3.html#K4" title="MSAFREE3:func.4">variables_in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">t</font> <a href="msaterm.html#K8" title="MSATERM:func.8">|</a> <font color="Maroon" title="c7">p</font></span>)</span> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c2">X</font>
 
<b>by </b><i><a class="txt" href="msafree3.html#E4:45"><i><font color="Green" title="E34">A2</font></i></a>, <a class="ref" href="pboole.html#T15" title="PBOOLE:th.15">PBOOLE:15</a></i>;<br/>
<a NAME="E9:45"/><b>then </b>
<font color="Maroon" title="c6">t</font> <a href="msaterm.html#K8" title="MSATERM:func.8">|</a> <font color="Maroon" title="c7">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">q</font> where <font color="Olive" title="b1">q</font> is   <a href="msaterm.html#NM1" title="MSATERM:NM.1">Term</a> of <font color="Maroon" title="c1">S</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <span class="p2">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default">0</span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span></span>)</span> : (  <a href="msaterm.html#K7" title="MSATERM:func.7">the_sort_of</a> <font color="Olive" title="b1">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msaterm.html#K7" title="MSATERM:func.7">the_sort_of</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">t</font> <a href="msaterm.html#K8" title="MSATERM:func.8">|</a> <font color="Maroon" title="c7">p</font></span>)</span> &amp;  <a href="msafree3.html#K4" title="MSAFREE3:func.4">variables_in</a> <font color="Olive" title="b1">q</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c2">X</font> ) </span>}</span> 
 
;<br/>
<a NAME="E10:45"/><b>then </b>
<font color="Maroon" title="c6">t</font> <a href="msaterm.html#K8" title="MSATERM:func.8">|</a> <font color="Maroon" title="c7">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">S</font> <a href="msafree3.html#K5" title="MSAFREE3:func.5">-Terms</a> <font color="Maroon" title="c2">X</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <span class="p3">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default">0</span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="msaterm.html#K7" title="MSATERM:func.7">the_sort_of</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">t</font> <a href="msaterm.html#K8" title="MSATERM:func.8">|</a> <font color="Maroon" title="c7">p</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="msafree3.html#D6" target="_self" title="MSAFREE3:def.6">Def6</a></i>;<br/>
<b>hence </b><a NAME="E11:45"/>
<font color="Maroon" title="c3">t</font> <a href="trees_2.html#K5" title="TREES_2:func.5">|</a> <font color="Maroon" title="c4">p</font> is   <a href="msafree3.html#NM1" title="MSAFREE3:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="msafree3.html#K1" title="MSAFREE3:func.1">Free</a> <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">X</font></span>)</span>
 <b>by </b><i><a class="txt" href="msafree3.html#E1:45"><i><font color="Green" title="E33">A1</font></i></a>, <a class="txt" href="msafree3.html#E5:45"><i><font color="Green" title="E35">A3</font></i></a>, <a class="ref" href="card_5.html#T10" title="CARD_5:th.10">CARD_5:10</a></i>;<br/>


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