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<b>let </b><font color="Maroon">Q1</font> be  <a href="msualg_6.html#V3" target="_self">invariant</a> <a href="msualg_4.html#NM4">ManySortedRelation</a> of <font color="Maroon">A</font>, <font color="Maroon">Q2</font> be  <a href="msualg_6.html#V3" target="_self">invariant</a> <a href="msualg_4.html#NM4">ManySortedRelation</a> of <font color="Maroon">A</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:51_1_1"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">R</font> <a href="pboole.html#R2">c=</a> <font color="Maroon">Q1</font>
 <b>and </b><br/><a NAME="E2:51_1_1"/><i><font color="Green">E34</font></i>: 
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">Q1</font> <a href="pboole.html#R2">c=</a> <font color="Olive">Q</font>
 <b>and </b><br/><a NAME="E3:51_1_1"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">R</font> <a href="pboole.html#R2">c=</a> <font color="Maroon">Q2</font>
 <b>and </b><br/><a NAME="E4:51_1_1"/><i><font color="Green">E46</font></i>: 
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">Q2</font> <a href="pboole.html#R2">c=</a> <font color="Olive">Q</font>
 ;<br/>

<b>thus </b><a NAME="E5:51_1_1"/>
( <font color="Maroon">Q1</font> <a href="pboole.html#R2">c=</a> <font color="Maroon">Q2</font> &amp; <font color="Maroon">Q2</font> <a href="pboole.html#R2">c=</a> <font color="Maroon">Q1</font> )
 <b>by </b><i><a class="txt" href="msualg_6.html#E2:51_1_1"><i><font color="Green">E34</font></i></a>, , , <a class="ref" href="msualg_6.html#T1" target="_self">Th1</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="pboole.html#D13">PBOOLE:def 13</a><br/>


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