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<b>let </b><font color="Maroon">a</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="orders_3.html#D4">ORDERS_3:def 4</a><br/>

<b>assume </b><a NAME="E1:4_1_1"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="yellow21.html#K2" target="_self">POSETS</a> <font color="Maroon">W</font>
 ;<br/>

<a NAME="E2:4_1_1"/><b>then </b><i><font color="Green">E38</font></i>: 
( <font color="Maroon">a</font> is  <a href="orders_2.html#V1">strict</a> <a href="orders_2.html#NM1">Poset</a> &amp; the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="yellow21.html#K1" target="_self">as_1-sorted</a> </span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">W</font> )
 
<b>by </b><i/>;<br/>
<b>reconsider </b><font color="Maroon">a</font> = <font color="Maroon">a</font> as   <a href="orders_2.html#NM1">Poset</a> <b>by </b><i>, </i>;<br/>
<a NAME="E4:4_1_1"/>
( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="yellow21.html#K1" target="_self">as_1-sorted</a>  &amp; the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="yellow21.html#K1" target="_self">as_1-sorted</a> </span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  )
 
<b>by </b><i>, , <a class="ref" href="setfam_1.html#D9">SETFAM_1:def 9</a></i>;<br/>
<b>hence </b><a NAME="E5:4_1_1"/>
<font color="Maroon">a</font> is    <a href="orders_2.html#L1">RelStr</a> 
 <b>by </b><i><a class="ref" href="struct_0.html#D1">STRUCT_0:def 1</a></i>;<br/>


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