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<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be    <a href="orders_2.html#L1">RelStr</a> ;<br/>

<a NAME="E1:7"/><i><font color="Green">E4</font></i>: 
( <span class="p1">(<span class="default">the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font> <a href="wellord1.html#K2">|_2</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="relat_1.html#K4">~</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font> <a href="relset_1.html#K6">~</a> </span>)</span> <a href="wellord1.html#K2">|_2</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> &amp; <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">c<sub>1</sub></font> <a href="relset_1.html#K6">~</a> </span>)</span> <a href="wellord1.html#K2">|_2</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="relat_1.html#K4">~</a>  <a href="hidden.html#R1">=</a> <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">c<sub>1</sub></font> <a href="relset_1.html#K6">~</a> </span>)</span> <a href="relset_1.html#K6">~</a> </span>)</span> <a href="wellord1.html#K2">|_2</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="orders_1.html#T193">ORDERS_1:193</a></i>;<br/>
<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:7_1"/>
<font color="Maroon">c<sub>2</sub></font> is  <a href="yellow_0.html#V4">full</a>  <a href="yellow_0.html#M1">SubRelStr</a> of <font color="Maroon">c<sub>1</sub></font>
 ;<br/><a NAME="E2:7_1"/><b>then </b>
( <font color="Maroon">c<sub>2</sub></font> <a href="yellow_7.html#NK1" target="_self">opp</a>  is    <a href="yellow_0.html#M1">SubRelStr</a> of <font color="Maroon">c<sub>1</sub></font> <a href="yellow_7.html#NK1" target="_self">opp</a>  &amp; the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font> <a href="wellord1.html#K2">|_2</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="ref" href="waybel10.html#T3" target="_self">Th3</a>, <a class="ref" href="yellow_0.html#D14">YELLOW_0:def 14</a></i>;<br/><b>hence </b><a NAME="E3:7_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="yellow_7.html#NK1" target="_self">opp</a>  is  <a href="yellow_0.html#V4">full</a>  <a href="yellow_0.html#M1">SubRelStr</a> of <font color="Maroon">c<sub>1</sub></font> <a href="yellow_7.html#NK1" target="_self">opp</a> 
 <b>by </b><i><a class="txt" href="waybel10.html#E1:7"><i><font color="Green">E4</font></i></a>, <a class="ref" href="yellow_0.html#D14">YELLOW_0:def 14</a></i>;<br/></div>
<b>end;</b></div>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:7_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="yellow_7.html#NK1" target="_self">opp</a>  is  <a href="yellow_0.html#V4">full</a>  <a href="yellow_0.html#M1">SubRelStr</a> of <font color="Maroon">c<sub>1</sub></font> <a href="yellow_7.html#NK1" target="_self">opp</a> 
 ;<br/><a NAME="E2:7_2"/><b>then </b>
( <font color="Maroon">c<sub>2</sub></font> is    <a href="yellow_0.html#M1">SubRelStr</a> of <font color="Maroon">c<sub>1</sub></font> &amp; the <a href="orders_2.html#U1">InternalRel</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="yellow_7.html#NK1" target="_self">opp</a> </span>)</span> <a href="hidden.html#R1">=</a> the <a href="orders_2.html#U1">InternalRel</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="yellow_7.html#NK1" target="_self">opp</a> </span>)</span> <a href="wellord1.html#K2">|_2</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="ref" href="waybel10.html#T3" target="_self">Th3</a>, <a class="ref" href="yellow_0.html#D14">YELLOW_0:def 14</a></i>;<br/><b>hence </b><a NAME="E3:7_2"/>
<font color="Maroon">c<sub>2</sub></font> is  <a href="yellow_0.html#V4">full</a>  <a href="yellow_0.html#M1">SubRelStr</a> of <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="waybel10.html#E1:7"><i><font color="Green">E4</font></i></a>, <a class="ref" href="yellow_0.html#D14">YELLOW_0:def 14</a></i>;<br/></div>
<b>end;</b></div>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:7_3"/>
<font color="Maroon">c<sub>2</sub></font> <a href="yellow_7.html#NK1" target="_self">opp</a>  is  <a href="yellow_0.html#V4">full</a>  <a href="yellow_0.html#M1">SubRelStr</a> of <font color="Maroon">c<sub>1</sub></font>
 ;<br/><a NAME="E2:7_3"/><b>then </b>
( <font color="Maroon">c<sub>2</sub></font> is    <a href="yellow_0.html#M1">SubRelStr</a> of <font color="Maroon">c<sub>1</sub></font> <a href="yellow_7.html#NK1" target="_self">opp</a>  &amp; the <a href="orders_2.html#U1">InternalRel</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="yellow_7.html#NK1" target="_self">opp</a> </span>)</span> <a href="hidden.html#R1">=</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font> <a href="wellord1.html#K2">|_2</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="ref" href="waybel10.html#T3" target="_self">Th3</a>, <a class="ref" href="yellow_0.html#D14">YELLOW_0:def 14</a></i>;<br/><b>hence </b><a NAME="E3:7_3"/>
<font color="Maroon">c<sub>2</sub></font> is  <a href="yellow_0.html#V4">full</a>  <a href="yellow_0.html#M1">SubRelStr</a> of <font color="Maroon">c<sub>1</sub></font> <a href="yellow_7.html#NK1" target="_self">opp</a> 
 <b>by </b><i><a class="txt" href="waybel10.html#E1:7"><i><font color="Green">E4</font></i></a>, <a class="ref" href="yellow_0.html#D14">YELLOW_0:def 14</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E5:7"/>
<font color="Maroon">c<sub>2</sub></font> is  <a href="yellow_0.html#V4">full</a>  <a href="yellow_0.html#M1">SubRelStr</a> of <font color="Maroon">c<sub>1</sub></font> <a href="yellow_7.html#NK1" target="_self">opp</a> 
 ;<br/>

<a NAME="E6:7"/><b>then </b>
( <font color="Maroon">c<sub>2</sub></font> <a href="yellow_7.html#NK1" target="_self">opp</a>  is    <a href="yellow_0.html#M1">SubRelStr</a> of <font color="Maroon">c<sub>1</sub></font> &amp; the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> the <a href="orders_2.html#U1">InternalRel</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="yellow_7.html#NK1" target="_self">opp</a> </span>)</span> <a href="wellord1.html#K2">|_2</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="waybel10.html#T3" target="_self">Th3</a>, <a class="ref" href="yellow_0.html#D14">YELLOW_0:def 14</a></i>;<br/>
<b>hence </b><a NAME="E7:7"/>
<font color="Maroon">c<sub>2</sub></font> <a href="yellow_7.html#NK1" target="_self">opp</a>  is  <a href="yellow_0.html#V4">full</a>  <a href="yellow_0.html#M1">SubRelStr</a> of <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="waybel10.html#E1:7"><i><font color="Green">E4</font></i></a>, <a class="ref" href="yellow_0.html#D14">YELLOW_0:def 14</a></i>;<br/>


</div>
