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<b>let </b><font color="Maroon">S</font> be  <a href="osalg_1.html#V8">monotone</a> <a href="osalg_1.html#V10">regular</a> <a href="osalg_4.html#V2">locally_directed</a> <a href="osalg_1.html#NM3">OrderSortedSign</a>;<br/><b>let </b><font color="Maroon">X</font> be  <a href="relat_1.html#V2">V5</a> <a href="struct_0.html#NM8">ManySortedSet</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/>





<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:95_1"/>
<font color="Maroon">x</font> is    <a href="osafree.html#M2" target="_self">MinTerm</a> of <font color="Maroon">S</font>,<font color="Maroon">X</font>
 ;<br/><b>then reconsider </b><font color="Maroon">t</font> = <font color="Maroon">x</font> as    <a href="osafree.html#M2" target="_self">MinTerm</a> of <font color="Maroon">S</font>,<font color="Maroon">X</font> ;<br/><a NAME="E3:95_1"/>
<span class="p1">(<span class="default"><a href="osafree.html#K29" target="_self">PTMin</a> <font color="Maroon">X</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font>
 <b>by </b><i/>;<br/><a NAME="E4:95_1"/><b>then </b>
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="osafree.html#K29" target="_self">PTMin</a> <font color="Maroon">X</font></span>)</span>
 <b>by </b><i><a class="ref" href="funct_2.html#T6">FUNCT_2:6</a></i>;<br/><b>hence </b><a NAME="E5:95_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="osafree.html#K30" target="_self">MinTerms</a> <font color="Maroon">X</font>
 ;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:95"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="osafree.html#K30" target="_self">MinTerms</a> <font color="Maroon">X</font>
 ;<br/>

<a NAME="E3:95"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="osafree.html#K29" target="_self">PTMin</a> <font color="Maroon">X</font></span>)</span>
 
;<br/>
<b>then consider </b><font color="Maroon">y</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E5:95"/><i><font color="Green">E34</font></i>: 
( <font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="osafree.html#K29" target="_self">PTMin</a> <font color="Maroon">X</font></span>)</span> &amp; <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="osafree.html#K29" target="_self">PTMin</a> <font color="Maroon">X</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<b>reconsider </b><font color="Maroon">t</font> = <font color="Maroon">y</font> as    <a href="dtconstr.html#M1">Element</a> of  <a href="dtconstr.html#K4">TS</a> <span class="p1">(<span class="default"><a href="osafree.html#K2" target="_self">DTConOSA</a> <font color="Maroon">X</font></span>)</span> <b>by </b><i/>;<br/>
<a NAME="E7:95"/>
<span class="p1">(<span class="default"><a href="osafree.html#K29" target="_self">PTMin</a> <font color="Maroon">X</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">t</font> is    <a href="dtconstr.html#M1">Element</a> of  <a href="dtconstr.html#K4">TS</a> <span class="p1">(<span class="default"><a href="osafree.html#K2" target="_self">DTConOSA</a> <font color="Maroon">X</font></span>)</span>
 
;<br/>
<b>then reconsider </b><font color="Maroon">tx</font> = <font color="Maroon">x</font> as    <a href="dtconstr.html#M1">Element</a> of  <a href="dtconstr.html#K4">TS</a> <span class="p1">(<span class="default"><a href="osafree.html#K2" target="_self">DTConOSA</a> <font color="Maroon">X</font></span>)</span> <b>by </b><i/>;<br/>
<a NAME="E9:95"/>
<span class="p1">(<span class="default"><a href="osafree.html#K29" target="_self">PTMin</a> <font color="Maroon">X</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">tx</font> <a href="hidden.html#R1">=</a> <font color="Maroon">tx</font>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E10:95"/>
<font color="Maroon">x</font> is    <a href="osafree.html#M2" target="_self">MinTerm</a> of <font color="Maroon">S</font>,<font color="Maroon">X</font>
 <b>by </b><i/>;<br/>


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