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<b>let </b><font color="Maroon">L1</font> be  non <a href="struct_0.html#V3">empty</a> <a href="orders_2.html#V2">reflexive</a> <a href="orders_2.html#V4">antisymmetric</a> <a href="waybel_0.html#V24">up-complete</a>  <a href="orders_2.html#L1">RelStr</a> , <font color="Maroon">L2</font> be  non <a href="struct_0.html#V3">empty</a> <a href="orders_2.html#V2">reflexive</a> <a href="orders_2.html#V4">antisymmetric</a> <a href="waybel_0.html#V24">up-complete</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/>

<b>assume </b><a NAME="E1:23"/><i><font color="Green">E31</font></i>: 
 <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L1</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">L1</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">L2</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">L2</font> #)
 ;<br/>

<b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L1</font>;<br/><b>let </b><font color="Maroon">y</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L2</font>;<br/>



<b>assume </b><a NAME="E2:23"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">z</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:23_1"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a>  <a href="waybel_8.html#K2" target="_self">compactbelow</a> <font color="Maroon">x</font>
 ;<br/><b>then reconsider </b><font color="Maroon">z1</font> = <font color="Maroon">z</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L1</font> ;<br/><b>reconsider </b><font color="Maroon">z2</font> = <font color="Maroon">z1</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L2</font> <b>by </b><i/>;<br/><a NAME="E4:23_1"/>
( <font color="Maroon">z1</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">x</font> &amp; <font color="Maroon">z1</font> is <a href="waybel_3.html#V1">compact</a> )
 <b>by </b><i>, </i>;<br/><a NAME="E5:23_1"/><b>then </b>
( <font color="Maroon">z2</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y</font> &amp; <font color="Maroon">z2</font> is <a href="waybel_3.html#V1">compact</a> )
 <b>by </b><i>, , , <a class="ref" href="yellow_0.html#T1">YELLOW_0:1</a></i>;<br/><b>hence </b><a NAME="E6:23_1"/>
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a>  <a href="waybel_8.html#K2" target="_self">compactbelow</a> <font color="Maroon">y</font>
 ;<br/></div><b>end;</b></div>
<a NAME="E4:23"/><b>then </b><i><font color="Green">E37</font></i>: 
 <a href="waybel_8.html#K2" target="_self">compactbelow</a> <font color="Maroon">x</font> <a href="tarski.html#R1">c=</a>  <a href="waybel_8.html#K2" target="_self">compactbelow</a> <font color="Maroon">y</font>
 
<b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">z</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:23_2"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a>  <a href="waybel_8.html#K2" target="_self">compactbelow</a> <font color="Maroon">y</font>
 ;<br/><b>then reconsider </b><font color="Maroon">z2</font> = <font color="Maroon">z</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L2</font> ;<br/><b>reconsider </b><font color="Maroon">z1</font> = <font color="Maroon">z2</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L1</font> <b>by </b><i/>;<br/><a NAME="E4:23_2"/>
( <font color="Maroon">z2</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y</font> &amp; <font color="Maroon">z2</font> is <a href="waybel_3.html#V1">compact</a> )
 <b>by </b><i>, </i>;<br/><a NAME="E5:23_2"/><b>then </b>
( <font color="Maroon">z1</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">x</font> &amp; <font color="Maroon">z1</font> is <a href="waybel_3.html#V1">compact</a> )
 <b>by </b><i>, , , <a class="ref" href="yellow_0.html#T1">YELLOW_0:1</a></i>;<br/><b>hence </b><a NAME="E6:23_2"/>
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a>  <a href="waybel_8.html#K2" target="_self">compactbelow</a> <font color="Maroon">x</font>
 ;<br/></div><b>end;</b></div>
<a NAME="E6:23"/><b>then </b>
 <a href="waybel_8.html#K2" target="_self">compactbelow</a> <font color="Maroon">y</font> <a href="tarski.html#R1">c=</a>  <a href="waybel_8.html#K2" target="_self">compactbelow</a> <font color="Maroon">x</font>
 
<b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<b>hence </b><a NAME="E7:23"/>
 <a href="waybel_8.html#K2" target="_self">compactbelow</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="waybel_8.html#K2" target="_self">compactbelow</a> <font color="Maroon">y</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>


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