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<span class="kw">let </span><font color="Maroon" title="c1">R1</font>, <font color="Maroon" title="c2">R2</font> be    <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="neckla_2.html#K1" title="NECKLA_2:func.1">union_of</a> <font color="Maroon" title="c1">R1</font>,<font color="Maroon" title="c2">R2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="neckla_2.html#K1" title="NECKLA_2:func.1">union_of</a> <font color="Maroon" title="c2">R2</font>,<font color="Maroon" title="c1">R1</font> &amp;  <a href="neckla_2.html#K2" title="NECKLA_2:func.2">sum_of</a> <font color="Maroon" title="c1">R1</font>,<font color="Maroon" title="c2">R2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="neckla_2.html#K2" title="NECKLA_2:func.2">sum_of</a> <font color="Maroon" title="c2">R2</font>,<font color="Maroon" title="c1">R1</font> )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c3">U1</font> =  <a href="neckla_2.html#K1" title="NECKLA_2:func.1">union_of</a> <font color="Maroon" title="c1">R1</font>,<font color="Maroon" title="c2">R2</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">S1</font> =  <a href="neckla_2.html#K2" title="NECKLA_2:func.2">sum_of</a> <font color="Maroon" title="c1">R1</font>,<font color="Maroon" title="c2">R2</font>;<br/>
<a NAME="E1:18"/><span class="lab"><font color="Green" title="E7">A1</font></span>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="neckla_2.html#K2" title="NECKLA_2:func.2">sum_of</a> <font color="Maroon" title="c1">R1</font>,<font color="Maroon" title="c2">R2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">R2</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">R1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="neckla_2.html#D3" title="NECKLA_2:def.3">NECKLA_2:def 3</a></span>;<br/>
<span class="lab"><font color="Green" title="E8">A2</font></span>: the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><a href="neckla_2.html#K2" title="NECKLA_2:func.2">sum_of</a> <font color="Maroon" title="c1">R1</font>,<font color="Maroon" title="c2">R2</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">R1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c2">R2</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">R1</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">R2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">R2</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">R1</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="neckla_2.html#D3" title="NECKLA_2:def.3">NECKLA_2:def 3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c2">R2</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">R1</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">R2</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">R1</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">R1</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">R2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T4" title="XBOOLE_1:th.4">XBOOLE_1:4</a></span>
;<br/>
<a NAME="E3:18"/>
( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="neckla_2.html#K1" title="NECKLA_2:func.1">union_of</a> <font color="Maroon" title="c1">R1</font>,<font color="Maroon" title="c2">R2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">R2</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">R1</font> &amp; the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><a href="neckla_2.html#K1" title="NECKLA_2:func.1">union_of</a> <font color="Maroon" title="c1">R1</font>,<font color="Maroon" title="c2">R2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c2">R2</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">R1</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="neckla_2.html#D2" title="NECKLA_2:def.2">NECKLA_2:def 2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:18"/>
(  <a href="neckla_2.html#K1" title="NECKLA_2:func.1">union_of</a> <font color="Maroon" title="c1">R1</font>,<font color="Maroon" title="c2">R2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="neckla_2.html#K1" title="NECKLA_2:func.1">union_of</a> <font color="Maroon" title="c2">R2</font>,<font color="Maroon" title="c1">R1</font> &amp;  <a href="neckla_2.html#K2" title="NECKLA_2:func.2">sum_of</a> <font color="Maroon" title="c1">R1</font>,<font color="Maroon" title="c2">R2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="neckla_2.html#K2" title="NECKLA_2:func.2">sum_of</a> <font color="Maroon" title="c2">R2</font>,<font color="Maroon" title="c1">R1</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:18"><span class="lab"><font color="Green" title="E7">A1</font></span></a>, <a class="txt" href="#E2:18"><span class="lab"><font color="Green" title="E8">A2</font></span></a>, <a class="ref" href="neckla_2.html#D2" title="NECKLA_2:def.2">NECKLA_2:def 2</a>, <a class="ref" href="neckla_2.html#D3" title="NECKLA_2:def.3">NECKLA_2:def 3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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