<?xml version="1.0"?>
<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/>

<b>thus </b><a NAME="E1:6"/>
( <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> implies <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>  )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:6_1"/>
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</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="tarski.html#R1">c=</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_0.html#D13">YELLOW_0:def 13</a><br/>

<b>hence </b><a NAME="E2:6_1"/>
( the <a href="struct_0.html#U1">carrier</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="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</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> &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="tarski.html#R1">c=</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> )
 <b>by </b><i><a class="ref" href="waybel10.html#T1" target="_self">Th1</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_0.html#D13">YELLOW_0:def 13</a><br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E2:6"/>
( <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>  implies <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> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:6_2"/>
( the <a href="struct_0.html#U1">carrier</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="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</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> &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="tarski.html#R1">c=</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> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_0.html#D13">YELLOW_0:def 13</a><br/>

<b>hence </b><a NAME="E2:6_2"/>
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</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="tarski.html#R1">c=</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font> )
 <b>by </b><i><a class="ref" href="waybel10.html#T1" target="_self">Th1</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_0.html#D13">YELLOW_0:def 13</a><br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E3:6"/>
( <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> implies <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>  )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:6_3"/>
( the <a href="struct_0.html#U1">carrier</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="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</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="tarski.html#R1">c=</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_0.html#D13">YELLOW_0:def 13</a><br/>

<b>hence </b><a NAME="E2:6_3"/>
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</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> &amp; the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</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> )
 <b>by </b><i><a class="ref" href="waybel10.html#T1" target="_self">Th1</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_0.html#D13">YELLOW_0:def 13</a><br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E4:6"/>
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</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> &amp; the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</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> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_0.html#D13">YELLOW_0:def 13</a><br/>

<b>hence </b><a NAME="E5:6"/>
( the <a href="struct_0.html#U1">carrier</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="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</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="tarski.html#R1">c=</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font> )
 <b>by </b><i><a class="ref" href="waybel10.html#T1" target="_self">Th1</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_0.html#D13">YELLOW_0:def 13</a><br/>


</div>
