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<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font>] <b>means </b><font color="Maroon">a<sub>1</sub></font> <a href="gcd_1.html#R3" target="_self">is_associated_to</a> <font color="Maroon">a</font>;<br/>
<a NAME="E1:32_1_2"/>
for <font color="Olive">X1</font>, <font color="Olive">X2</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">R</font>  st ( for <font color="Olive">y</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font> holds <br/> ( <font color="Olive">y</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">y</font>] ) ) &amp; ( for <font color="Olive">y</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font> holds <br/> ( <font color="Olive">y</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">y</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="subset_1.html#S2">SUBSET_1:sch 2</a>();<br/></i>
<b>hence </b><a NAME="E2:32_1_2"/>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">R</font>  st ( for <font color="Olive">b</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font> holds <br/> ( <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> iff <font color="Olive">b</font> <a href="gcd_1.html#R3" target="_self">is_associated_to</a> <font color="Maroon">a</font> ) ) &amp; ( for <font color="Olive">b</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font> holds <br/> ( <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>2</sub></font> iff <font color="Olive">b</font> <a href="gcd_1.html#R3" target="_self">is_associated_to</a> <font color="Maroon">a</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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