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<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1">set</a> ] <b>means </b>( <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="funct_2.html#K1">Funcs</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>,<span class="p1">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <span class="p2">(<span class="default"><a href="card_3.html#K3">Union</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">U0</font></span>)</span></span>)</span> &amp; <font color="Maroon">a<sub>1</sub></font> is   <a href="msualg_2.html#NM1">MSSubset</a> of <font color="Maroon">U0</font> &amp; ( for <font color="Olive">B</font> being  <a href="msualg_2.html#NM1">MSSubset</a> of <font color="Maroon">U0</font>  st <font color="Olive">B</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a<sub>1</sub></font> holds <br/>( <font color="Olive">B</font> is <a href="msualg_2.html#V3" target="_self">opers_closed</a> &amp;  <a href="msualg_2.html#K2" target="_self">Constants</a> <font color="Maroon">U0</font> <a href="pboole.html#R2">c=</a> <font color="Olive">B</font> &amp; <font color="Maroon">A</font> <a href="pboole.html#R2">c=</a> <font color="Olive">B</font> ) ) );<br/>
<a NAME="E1:31_1_2"/>
for <font color="Olive">X1</font>, <font color="Olive">X2</font> being   <a href="hidden.html#M1">set</a>   st ( for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Olive">X1</font> iff <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">x</font>] ) ) &amp; ( for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Olive">X2</font> iff <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">x</font>] ) ) holds <br/><font color="Olive">X1</font> <a href="hidden.html#R1">=</a> <font color="Olive">X2</font>
 
<b>from </b><i><a class="ref" href="xboole_0.html#S3">XBOOLE_0:sch 3</a>();<br/></i>
<b>hence </b><a NAME="E2:31_1_2"/>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="hidden.html#M1">set</a>   st ( for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> iff ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="funct_2.html#K1">Funcs</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>,<span class="p1">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <span class="p2">(<span class="default"><a href="card_3.html#K3">Union</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">U0</font></span>)</span></span>)</span> &amp; <font color="Olive">x</font> is   <a href="msualg_2.html#NM1">MSSubset</a> of <font color="Maroon">U0</font> &amp; ( for <font color="Olive">B</font> being  <a href="msualg_2.html#NM1">MSSubset</a> of <font color="Maroon">U0</font>  st <font color="Olive">B</font> <a href="hidden.html#R1">=</a> <font color="Olive">x</font> holds <br/>( <font color="Olive">B</font> is <a href="msualg_2.html#V3" target="_self">opers_closed</a> &amp;  <a href="msualg_2.html#K2" target="_self">Constants</a> <font color="Maroon">U0</font> <a href="pboole.html#R2">c=</a> <font color="Olive">B</font> &amp; <font color="Maroon">A</font> <a href="pboole.html#R2">c=</a> <font color="Olive">B</font> ) ) ) ) ) &amp; ( for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>2</sub></font> iff ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="funct_2.html#K1">Funcs</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>,<span class="p1">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <span class="p2">(<span class="default"><a href="card_3.html#K3">Union</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">U0</font></span>)</span></span>)</span> &amp; <font color="Olive">x</font> is   <a href="msualg_2.html#NM1">MSSubset</a> of <font color="Maroon">U0</font> &amp; ( for <font color="Olive">B</font> being  <a href="msualg_2.html#NM1">MSSubset</a> of <font color="Maroon">U0</font>  st <font color="Olive">B</font> <a href="hidden.html#R1">=</a> <font color="Olive">x</font> holds <br/>( <font color="Olive">B</font> is <a href="msualg_2.html#V3" target="_self">opers_closed</a> &amp;  <a href="msualg_2.html#K2" target="_self">Constants</a> <font color="Maroon">U0</font> <a href="pboole.html#R2">c=</a> <font color="Olive">B</font> &amp; <font color="Maroon">A</font> <a href="pboole.html#R2">c=</a> <font color="Olive">B</font> ) ) ) ) ) holds <br/><font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font>
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