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<b>let </b><font color="Maroon" title="c1">X1</font>, <font color="Maroon" title="c2">X2</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="neckla_2.html#K3" title="NECKLA_2:func.3">fin_RelStr</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:13_1_2"/><i><font color="Green" title="E8">A25</font></i>: 
for <font color="Olive" title="b1">R</font> being <a href="orders_2.html#V1" title="ORDERS_2:attr.1">strict</a>  <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a>   st not the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">R</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">R</font> is <a href="realset1.html#V1" title="REALSET1:attr.1">trivial</a> &amp; the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">R</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="classes2.html#K13" title="CLASSES2:func.13">FinSETS</a>  holds <br/><font color="Olive" title="b1">R</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X1</font>
 <b>and </b><br/><a NAME="E2:13_1_2"/><i><font color="Green" title="E9">A26</font></i>: 
for <font color="Olive" title="b1">H1</font>, <font color="Olive" title="b2">H2</font> being <a href="orders_2.html#V1" title="ORDERS_2:attr.1">strict</a>  <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a>   st the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">H1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b2">H2</font> &amp; <font color="Olive" title="b1">H1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X1</font> &amp; <font color="Olive" title="b2">H2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X1</font> holds <br/>(  <a href="neckla_2.html#K1" title="NECKLA_2:func.1">union_of</a> <font color="Olive" title="b1">H1</font>,<font color="Olive" title="b2">H2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X1</font> &amp;  <a href="neckla_2.html#K2" title="NECKLA_2:func.2">sum_of</a> <font color="Olive" title="b1">H1</font>,<font color="Olive" title="b2">H2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X1</font> )
 <b>and </b><br/><a NAME="E3:13_1_2"/><i><font color="Green" title="E10">A27</font></i>: 
for <font color="Olive" title="b1">M</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="neckla_2.html#K3" title="NECKLA_2:func.3">fin_RelStr</a>   st ( for <font color="Olive" title="b2">R</font> being <a href="orders_2.html#V1" title="ORDERS_2:attr.1">strict</a>  <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a>   st not the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b2">R</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b2">R</font> is <a href="realset1.html#V1" title="REALSET1:attr.1">trivial</a> &amp; the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b2">R</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="classes2.html#K13" title="CLASSES2:func.13">FinSETS</a>  holds <br/><font color="Olive" title="b2">R</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> ) &amp; ( for <font color="Olive" title="b2">H1</font>, <font color="Olive" title="b3">H2</font> being <a href="orders_2.html#V1" title="ORDERS_2:attr.1">strict</a>  <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a>   st the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b2">H1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b3">H2</font> &amp; <font color="Olive" title="b2">H1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> &amp; <font color="Olive" title="b3">H2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> holds <br/>(  <a href="neckla_2.html#K1" title="NECKLA_2:func.1">union_of</a> <font color="Olive" title="b2">H1</font>,<font color="Olive" title="b3">H2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> &amp;  <a href="neckla_2.html#K2" title="NECKLA_2:func.2">sum_of</a> <font color="Olive" title="b2">H1</font>,<font color="Olive" title="b3">H2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> ) ) holds <br/><font color="Maroon" title="c1">X1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">M</font>
 <b>and </b><br/><a NAME="E4:13_1_2"/><i><font color="Green" title="E11">A28</font></i>: 
for <font color="Olive" title="b1">R</font> being <a href="orders_2.html#V1" title="ORDERS_2:attr.1">strict</a>  <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a>   st not the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">R</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">R</font> is <a href="realset1.html#V1" title="REALSET1:attr.1">trivial</a> &amp; the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">R</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="classes2.html#K13" title="CLASSES2:func.13">FinSETS</a>  holds <br/><font color="Olive" title="b1">R</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X2</font>
 <b>and </b><br/><a NAME="E5:13_1_2"/><i><font color="Green" title="E12">A29</font></i>: 
for <font color="Olive" title="b1">H1</font>, <font color="Olive" title="b2">H2</font> being <a href="orders_2.html#V1" title="ORDERS_2:attr.1">strict</a>  <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a>   st the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">H1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b2">H2</font> &amp; <font color="Olive" title="b1">H1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X2</font> &amp; <font color="Olive" title="b2">H2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X2</font> holds <br/>(  <a href="neckla_2.html#K1" title="NECKLA_2:func.1">union_of</a> <font color="Olive" title="b1">H1</font>,<font color="Olive" title="b2">H2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X2</font> &amp;  <a href="neckla_2.html#K2" title="NECKLA_2:func.2">sum_of</a> <font color="Olive" title="b1">H1</font>,<font color="Olive" title="b2">H2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X2</font> )
 <b>and </b><br/><a NAME="E6:13_1_2"/><i><font color="Green" title="E13">A30</font></i>: 
for <font color="Olive" title="b1">M</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="neckla_2.html#K3" title="NECKLA_2:func.3">fin_RelStr</a>   st ( for <font color="Olive" title="b2">R</font> being <a href="orders_2.html#V1" title="ORDERS_2:attr.1">strict</a>  <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a>   st not the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b2">R</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b2">R</font> is <a href="realset1.html#V1" title="REALSET1:attr.1">trivial</a> &amp; the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b2">R</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="classes2.html#K13" title="CLASSES2:func.13">FinSETS</a>  holds <br/><font color="Olive" title="b2">R</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> ) &amp; ( for <font color="Olive" title="b2">H1</font>, <font color="Olive" title="b3">H2</font> being <a href="orders_2.html#V1" title="ORDERS_2:attr.1">strict</a>  <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a>   st the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b2">H1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b3">H2</font> &amp; <font color="Olive" title="b2">H1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> &amp; <font color="Olive" title="b3">H2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> holds <br/>(  <a href="neckla_2.html#K1" title="NECKLA_2:func.1">union_of</a> <font color="Olive" title="b2">H1</font>,<font color="Olive" title="b3">H2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> &amp;  <a href="neckla_2.html#K2" title="NECKLA_2:func.2">sum_of</a> <font color="Olive" title="b2">H1</font>,<font color="Olive" title="b3">H2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> ) ) holds <br/><font color="Maroon" title="c2">X2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">M</font>
 ;<br/>

<a NAME="E7:13_1_2"/>
( <font color="Maroon" title="c1">X1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">X2</font> &amp; <font color="Maroon" title="c2">X2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">X1</font> )
 
<b>by </b><i><a class="txt" href="neckla_2.html#E1:13_1_2"><i><font color="Green" title="E8">A25</font></i></a>, <a class="txt" href="neckla_2.html#E2:13_1_2"><i><font color="Green" title="E9">A26</font></i></a>, <a class="txt" href="neckla_2.html#E3:13_1_2"><i><font color="Green" title="E10">A27</font></i></a>, <a class="txt" href="neckla_2.html#E4:13_1_2"><i><font color="Green" title="E11">A28</font></i></a>, <a class="txt" href="neckla_2.html#E5:13_1_2"><i><font color="Green" title="E12">A29</font></i></a>, <a class="txt" href="neckla_2.html#E6:13_1_2"><i><font color="Green" title="E13">A30</font></i></a></i>;<br/>
<b>hence </b><a NAME="E8:13_1_2"/>
<font color="Maroon" title="c1">X1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">X2</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a></i>;<br/>


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