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<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font>] <b>means </b>$1 <a href="gcd_1.html#R3" title="GCD_1:pred.3">is_associated_to</a> <font color="Maroon" title="c2">a</font>;<br/>
<b>let </b><font color="Maroon" title="c3">X1</font>, <font color="Maroon" title="c4">X2</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">R</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( for <font color="Olive" title="b1">b</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font> holds <br/> ( <font color="Olive" title="b1">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">X1</font> iff <font color="Olive" title="b1">b</font> <a href="gcd_1.html#R3" title="GCD_1:pred.3">is_associated_to</a> <font color="Maroon" title="c2">a</font> ) ) &amp; ( for <font color="Olive" title="b1">b</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font> holds <br/> ( <font color="Olive" title="b1">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">X2</font> iff <font color="Olive" title="b1">b</font> <a href="gcd_1.html#R3" title="GCD_1:pred.3">is_associated_to</a> <font color="Maroon" title="c2">a</font> ) ) implies <font color="Maroon" title="c3">X1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">X2</font> )</span><br/>

<b>assume </b><b>that </b><br/><a NAME="E1:32_1_2"/><i><font color="Green" title="E22">Z1</font></i>: 
for <font color="Olive" title="b1">y</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font> holds <br/> ( <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">X1</font> iff <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">y</font>] )
 <b>and </b><br/><a NAME="E2:32_1_2"/><i><font color="Green" title="E23">Z2</font></i>: 
for <font color="Olive" title="b1">y</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font> holds <br/> ( <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">X2</font> iff <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">y</font>] )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">X1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">X2</font></span><br/>

<b>thus </b><a NAME="E3:32_1_2"/>
<font color="Maroon" title="c3">X1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">X2</font>
 <b>from </b><i><a class="ref" href="subset_1.html#S2" title="SUBSET_1:sch.2">SUBSET_1:sch 2</a>(<a class="txt" href="gcd_1.html#E1:32_1_2"><i><font color="Green" title="E22">Z1</font></i></a>, <a class="txt" href="gcd_1.html#E2:32_1_2"><i><font color="Green" title="E23">Z2</font></i></a>);</i> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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