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<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="funct_1.html#NM1">Function</a>,  <a href="msualg_1.html#NM1">SortSymbol</a> of <font color="Maroon">S</font>,  <a href="msualg_1.html#NM1">SortSymbol</a> of <font color="Maroon">S</font>] <b>means </b>(  <a href="msualg_6.html#K3" target="_self">TranslationRel</a> <font color="Maroon">S</font> <a href="rewrite1.html#R1">reduces</a> <font color="Maroon">a<sub>2</sub></font>,<font color="Maroon">a<sub>3</sub></font> &amp; <font color="Maroon">a<sub>1</sub></font> is    <a href="msualg_6.html#M2" target="_self">Translation</a> of <font color="Maroon">A</font>,<font color="Maroon">a<sub>2</sub></font>,<font color="Maroon">a<sub>3</sub></font> );<br/>
<b>defpred </b><font color="Maroon">S<sub>2</sub></font>[  <a href="msualg_1.html#NM1">SortSymbol</a> of <font color="Maroon">S</font>,   <a href="hidden.html#M1">set</a> ,   <a href="hidden.html#M1">set</a> ] <b>means </b> ex <font color="Olive">s'</font> being  <a href="msualg_1.html#NM1">SortSymbol</a> of <font color="Maroon">S</font> ex <font color="Olive">f</font> being  <a href="funct_2.html#NM1">Function</a> of the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Olive">s'</font>,the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">a<sub>1</sub></font> ex <font color="Olive">x</font>, <font color="Olive">y</font> being  <a href="msualg_6.html#NM1">Element</a> of <font color="Maroon">A</font>,<font color="Olive">s'</font> st <br/>( <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">f</font>,<font color="Olive">s'</font>,<font color="Maroon">a<sub>1</sub></font>] &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">x</font>,<font color="Olive">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">R</font> <a href="msualg_4.html#K1">.</a> <font color="Olive">s'</font> &amp; <font color="Maroon">a<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">x</font> &amp; <font color="Maroon">a<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">y</font> );<br/>
<b>consider </b><font color="Maroon">Q</font> being   <a href="msualg_4.html#NM3">ManySortedRelation</a> of the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font><b> such that </b><br/><a NAME="E2:51_1_2"/><i><font color="Green">E55</font></i>: 
for <font color="Olive">s</font> being  <a href="msualg_1.html#NM1">SortSymbol</a> of <font color="Maroon">S</font><br/> for <font color="Olive">a</font>, <font color="Olive">b</font> being  <a href="msualg_6.html#NM1">Element</a> of <font color="Maroon">A</font>,<font color="Olive">s</font> holds <br/> ( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">a</font>,<font color="Olive">b</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">Q</font> <a href="msualg_4.html#K1">.</a> <font color="Olive">s</font> iff <font color="Maroon">S<sub>2</sub></font>[<font color="Olive">s</font>,<font color="Olive">a</font>,<font color="Olive">b</font>] )
 <b>from </b><i><a class="ref" href="msualg_6.html#S2" target="_self">MSUALG_6:sch 2</a>();<br/></i>
<b>reconsider </b><font color="Maroon">R</font> = <font color="Maroon">R</font>, <font color="Maroon">Q</font> = <font color="Maroon">Q</font> as   <a href="msualg_4.html#NM4">ManySortedRelation</a> of <font color="Maroon">A</font> ;<br/>
<b>reconsider </b><font color="Maroon">Q</font> = <font color="Maroon">Q</font> as  <a href="msualg_6.html#V3" target="_self">invariant</a> <a href="msualg_4.html#NM4">ManySortedRelation</a> of <font color="Maroon">A</font> <b>by </b><i>, </i>;<br/>
<b>take </b>
<font color="Maroon">Q</font>
;<br/>

<b>thus </b><a NAME="E5:51_1_2"/>
( <font color="Maroon">R</font> <a href="pboole.html#R2">c=</a> <font color="Maroon">Q</font> &amp; ( for <font color="Olive">Q</font> being <a href="msualg_6.html#V3" target="_self">invariant</a> <a href="msualg_4.html#NM4">ManySortedRelation</a> of <font color="Maroon">A</font>  st <font color="Maroon">R</font> <a href="pboole.html#R2">c=</a> <font color="Olive">Q</font> holds <br/><font color="Maroon">Q</font> <a href="pboole.html#R2">c=</a> <font color="Olive">Q</font> ) )
 <b>by </b><i>, </i>;<br/>


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