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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="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>set </b><font color="Maroon" title="c3">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/>
<b>consider </b><font color="Maroon" title="c4">A</font> being   <a href="msualg_2.html#NM1" title="MSUALG_2:NM.1">MSSubset</a> of <span class="p1">(<span class="default"><a href="msafree.html#K11" title="MSAFREE:func.11">FreeMSA</a> <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><b> such that </b><br/><a NAME="E2:52"/><i><font color="Green" title="E38">A1</font></i>: 
(  <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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c4">A</font> &amp; <font color="Maroon" title="c4">A</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <span class="p1">(<span class="default"><a href="msafree.html#K15" title="MSAFREE:func.15">Reverse</a> <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="equation.html#K1" title="EQUATION:func.1">""</a> <font color="Maroon" title="c2">X</font> )
 <b>by </b><i><a class="ref" href="msafree3.html#D2" target="_self" title="MSAFREE3:def.2">Def2</a></i>;<br/>
<b>thus </b><a NAME="E3:52"/>
 <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> is <a href="msualg_6.html#V1" title="MSUALG_6:attr.1">feasible</a>
 <b>by </b><i><a class="txt" href="msafree3.html#E2:52"><i><font color="Green" title="E38">A1</font></i></a></i>;<br/>

<a NAME="E4:52"/>
<font color="Maroon" title="c4">A</font> is    <a href="pboole.html#M4" title="PBOOLE:mode.4">ManySortedSubset</a> of  <a href="msafree.html#K13" title="MSAFREE:func.13">FreeGen</a> <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="txt" href="msafree3.html#E2:52"><i><font color="Green" title="E38">A1</font></i></a>, <a class="ref" href="equation.html#T9" title="EQUATION:th.9">EQUATION:9</a></i>;<br/>
<a NAME="E5:52"/><b>then </b>
<font color="Maroon" title="c4">A</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a>  <a href="msafree.html#K13" title="MSAFREE:func.13">FreeGen</a> <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="pboole.html#D23" title="PBOOLE:def.23">PBOOLE:def 23</a></i>;<br/>
<b>hence </b><a NAME="E6:52"/>
 <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> is <a href="msafree.html#V2" title="MSAFREE:attr.2">free</a>
 <b>by </b><i><a class="txt" href="msafree3.html#E2:52"><i><font color="Green" title="E38">A1</font></i></a>, <a class="ref" href="equation.html#T30" title="EQUATION:th.30">EQUATION:30</a></i>;<br/>


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