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<b>let </b><font color="Maroon">R1</font> be    <a href="orders_2.html#L1">RelStr</a> , <font color="Maroon">R2</font> be    <a href="orders_2.html#L1">RelStr</a> ;<br/>

<b>set </b><font color="Maroon">U1</font> =  <a href="neckla_2.html#K1">union_of</a> <font color="Maroon">R1</font>,<font color="Maroon">R2</font>;<br/>
<b>set </b><font color="Maroon">S1</font> =  <a href="neckla_2.html#K2">sum_of</a> <font color="Maroon">R1</font>,<font color="Maroon">R2</font>;<br/>
<a NAME="E1:18"/><i><font color="Green">E31</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="neckla_2.html#K1">union_of</a> <font color="Maroon">R1</font>,<font color="Maroon">R2</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R2</font> <a href="xboole_0.html#K2">\/</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R1</font>
 
<b>by </b><i><a class="ref" href="neckla_2.html#D2">NECKLA_2:def 2</a></i>;<br/>
<a NAME="E2:18"/><i><font color="Green">E34</font></i>: 
the <a href="orders_2.html#U1">InternalRel</a> of <span class="p1">(<span class="default"><a href="neckla_2.html#K1">union_of</a> <font color="Maroon">R1</font>,<font color="Maroon">R2</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">R2</font> <a href="xboole_0.html#K2">\/</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">R1</font>
 
<b>by </b><i><a class="ref" href="neckla_2.html#D2">NECKLA_2:def 2</a></i>;<br/>
<a NAME="E3:18"/><i><font color="Green">E35</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="neckla_2.html#K2">sum_of</a> <font color="Maroon">R1</font>,<font color="Maroon">R2</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R2</font> <a href="xboole_0.html#K2">\/</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R1</font>
 
<b>by </b><i><a class="ref" href="neckla_2.html#D3">NECKLA_2:def 3</a></i>;<br/>
the <a href="orders_2.html#U1">InternalRel</a> of <span class="p1">(<span class="default"><a href="neckla_2.html#K2">sum_of</a> <font color="Maroon">R1</font>,<font color="Maroon">R2</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">R1</font> <a href="xboole_0.html#K2">\/</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">R2</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R1</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R2</font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R2</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R1</font></span><a href="zfmisc_1.html#K2">:]</a></span>
<b>by </b><i><a class="ref" href="neckla_2.html#D3">NECKLA_2:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">R2</font> <a href="xboole_0.html#K2">\/</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">R1</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R2</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R1</font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R1</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R2</font></span><a href="zfmisc_1.html#K2">:]</a></span>
<b>by </b><i><a class="ref" href="xboole_1.html#T4">XBOOLE_1:4</a></i>
;<br/>
<b>hence </b><a NAME="E5:18"/>
(  <a href="neckla_2.html#K1">union_of</a> <font color="Maroon">R1</font>,<font color="Maroon">R2</font> <a href="hidden.html#R1">=</a>  <a href="neckla_2.html#K1">union_of</a> <font color="Maroon">R2</font>,<font color="Maroon">R1</font> &amp;  <a href="neckla_2.html#K2">sum_of</a> <font color="Maroon">R1</font>,<font color="Maroon">R2</font> <a href="hidden.html#R1">=</a>  <a href="neckla_2.html#K2">sum_of</a> <font color="Maroon">R2</font>,<font color="Maroon">R1</font> )
 <b>by </b><i>, , , <a class="ref" href="neckla_2.html#D2">NECKLA_2:def 2</a>, <a class="ref" href="neckla_2.html#D3">NECKLA_2:def 3</a></i>;<br/>


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