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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="subset_1.html#NM2">Subset</a> of <a href="neckla_2.html#K3" target="_self">fin_RelStr</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:13_1_2"/><i><font color="Green">E8</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being <a href="orders_2.html#V1">strict</a>  <a href="orders_2.html#L1">RelStr</a>  st not the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">b<sub>1</sub></font> is <a href="xboole_0.html#V1">empty</a> &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">b<sub>1</sub></font> is <a href="realset1.html#V1">trivial</a> &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="classes2.html#K13">FinSETS</a>  holds <br/><font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E2:13_1_2"/><i><font color="Green">E9</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being <a href="orders_2.html#V1">strict</a>  <a href="orders_2.html#L1">RelStr</a>  st the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">b<sub>1</sub></font> <a href="xboole_0.html#R1">misses</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">b<sub>2</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> holds <br/>(  <a href="neckla_2.html#K1" target="_self">union_of</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="neckla_2.html#K2" target="_self">sum_of</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> )
 <b>and </b><br/><a NAME="E3:13_1_2"/><i><font color="Green">E10</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="subset_1.html#NM2">Subset</a> of <a href="neckla_2.html#K3" target="_self">fin_RelStr</a>  st ( for <font color="Olive">b<sub>2</sub></font> being <a href="orders_2.html#V1">strict</a>  <a href="orders_2.html#L1">RelStr</a>  st not the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">b<sub>2</sub></font> is <a href="xboole_0.html#V1">empty</a> &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">b<sub>2</sub></font> is <a href="realset1.html#V1">trivial</a> &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="classes2.html#K13">FinSETS</a>  holds <br/><font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> ) &amp; ( for <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being <a href="orders_2.html#V1">strict</a>  <a href="orders_2.html#L1">RelStr</a>  st the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">b<sub>2</sub></font> <a href="xboole_0.html#R1">misses</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">b<sub>3</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> holds <br/>(  <a href="neckla_2.html#K1" target="_self">union_of</a> <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> &amp;  <a href="neckla_2.html#K2" target="_self">sum_of</a> <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> ) ) holds <br/><font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>1</sub></font>
 <b>and </b><br/><a NAME="E4:13_1_2"/><i><font color="Green">E11</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being <a href="orders_2.html#V1">strict</a>  <a href="orders_2.html#L1">RelStr</a>  st not the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">b<sub>1</sub></font> is <a href="xboole_0.html#V1">empty</a> &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">b<sub>1</sub></font> is <a href="realset1.html#V1">trivial</a> &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="classes2.html#K13">FinSETS</a>  holds <br/><font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 <b>and </b><br/><a NAME="E5:13_1_2"/><i><font color="Green">E12</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being <a href="orders_2.html#V1">strict</a>  <a href="orders_2.html#L1">RelStr</a>  st the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">b<sub>1</sub></font> <a href="xboole_0.html#R1">misses</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">b<sub>2</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> holds <br/>(  <a href="neckla_2.html#K1" target="_self">union_of</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="neckla_2.html#K2" target="_self">sum_of</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>and </b><br/><a NAME="E6:13_1_2"/><i><font color="Green">E13</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="subset_1.html#NM2">Subset</a> of <a href="neckla_2.html#K3" target="_self">fin_RelStr</a>  st ( for <font color="Olive">b<sub>2</sub></font> being <a href="orders_2.html#V1">strict</a>  <a href="orders_2.html#L1">RelStr</a>  st not the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">b<sub>2</sub></font> is <a href="xboole_0.html#V1">empty</a> &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">b<sub>2</sub></font> is <a href="realset1.html#V1">trivial</a> &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="classes2.html#K13">FinSETS</a>  holds <br/><font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> ) &amp; ( for <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being <a href="orders_2.html#V1">strict</a>  <a href="orders_2.html#L1">RelStr</a>  st the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">b<sub>2</sub></font> <a href="xboole_0.html#R1">misses</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">b<sub>3</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> holds <br/>(  <a href="neckla_2.html#K1" target="_self">union_of</a> <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> &amp;  <a href="neckla_2.html#K2" target="_self">sum_of</a> <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> ) ) holds <br/><font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>1</sub></font>
 ;<br/>

<a NAME="E7:13_1_2"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="txt" href="neckla_2.html#E1:13_1_2"><i><font color="Green">E8</font></i></a>, <a class="txt" href="neckla_2.html#E2:13_1_2"><i><font color="Green">E9</font></i></a>, <a class="txt" href="neckla_2.html#E3:13_1_2"><i><font color="Green">E10</font></i></a>, <a class="txt" href="neckla_2.html#E4:13_1_2"><i><font color="Green">E11</font></i></a>, <a class="txt" href="neckla_2.html#E5:13_1_2"><i><font color="Green">E12</font></i></a>, <a class="txt" href="neckla_2.html#E6:13_1_2"><i><font color="Green">E13</font></i></a></i>;<br/>
<b>hence </b><a NAME="E8:13_1_2"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>


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