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<div class="add">

<b>let </b><font color="Maroon">R1</font> be  <a href="lfuzzy_0.html#V1" target="_self">real</a>  <a href="orders_2.html#L1">RelStr</a> , <font color="Maroon">R2</font> be  <a href="lfuzzy_0.html#V1" target="_self">real</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/>

<b>assume </b><a NAME="E1:7"/><i><font color="Green">E41</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R1</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R2</font>
 ;<br/>

<b>set </b><font color="Maroon">X</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R1</font>;<br/>
<a NAME="E2:7"/>
the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">R1</font> <a href="hidden.html#R1">=</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">R2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">a</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">b</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="relat_1.html#D2">RELAT_1:def 2</a><br/>

<a NAME="E1:7_1"/><i><font color="Green">E42</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R1</font> <a href="tarski.html#R1">c=</a>  <a href="numbers.html#K1">REAL</a> 
 
<b>by </b><i/>;<br/>
<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:7_1_1"/><i><font color="Green">E48</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">R1</font>
 ;<br/><a NAME="E2:7_1_1"/><b>then </b><i><font color="Green">E52</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R1</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R1</font> )
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/><b>then reconsider </b><font color="Maroon">a'</font> = <font color="Maroon">a</font>, <font color="Maroon">b'</font> = <font color="Maroon">b</font> as    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K1">REAL</a>  <b>by </b><i/>;<br/><a NAME="E4:7_1_1"/>
<font color="Maroon">a'</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">b'</font>
 <b>by </b><i>, , </i>;<br/><b>hence </b><a NAME="E5:7_1_1"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">R2</font>
 <b>by </b><i>, , </i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E3:7_1"/><i><font color="Green">E55</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">R2</font>
 ;<br/>

<a NAME="E4:7_1"/><b>then </b><i><font color="Green">E56</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R1</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R1</font> )
 
<b>by </b><i>, <a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">a'</font> = <font color="Maroon">a</font>, <font color="Maroon">b'</font> = <font color="Maroon">b</font> as    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K1">REAL</a>  <b>by </b><i/>;<br/>
<a NAME="E6:7_1"/>
<font color="Maroon">a'</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">b'</font>
 
<b>by </b><i>, , , </i>;<br/>
<b>hence </b><a NAME="E7:7_1"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">R1</font>
 <b>by </b><i>, </i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:7"/>
 <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R1</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">R1</font> #) <a href="hidden.html#R1">=</a>  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R2</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">R2</font> #)
 <b>by </b><i/>;<br/>


</div>
