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<b>let </b><font color="Maroon">S</font> be  non <a href="struct_0.html#V3">empty</a> <a href="orders_2.html#NM1">Poset</a>;<br/><b>let </b><font color="Maroon">w1</font> be    <a href="finseq_2.html#M2">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font> <a href="finseq_2.html#K3">*</a> , <font color="Maroon">w2</font> be    <a href="finseq_2.html#M2">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font> <a href="finseq_2.html#K3">*</a> ;<br/>



<b>assume </b><a NAME="E1:26"/><i><font color="Green">E24</font></i>: 
( <font color="Maroon">w1</font> <a href="osalg_1.html#R2" target="_self">&lt;=</a> <font color="Maroon">w2</font> &amp; <font color="Maroon">w2</font> <a href="osalg_1.html#R2" target="_self">&lt;=</a> <font color="Maroon">w1</font> )
 ;<br/>

<a NAME="E2:26"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">w1</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">w2</font>
 
<b>by </b><i/>;<br/>
<a NAME="E3:26"/><b>then </b><i><font color="Green">E40</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <font color="Maroon">w1</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">w2</font>
 
<b>by </b><i><a class="ref" href="finseq_3.html#T31">FINSEQ_3:31</a></i>;<br/>
<a NAME="E4:26"/>
for <font color="Olive">i</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">w1</font> holds <br/><font color="Maroon">w1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">w2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">i</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:26_1"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">w1</font>
 ;<br/>

<b>reconsider </b><font color="Maroon">s3</font> = <font color="Maroon">w1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>, <font color="Maroon">s4</font> = <font color="Maroon">w2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font> <b>by </b><i>, , <a class="ref" href="partfun1.html#T27">PARTFUN1:27</a></i>;<br/>
<a NAME="E3:26_1"/>
( <font color="Maroon">s3</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">s4</font> &amp; <font color="Maroon">s4</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">s3</font> )
 
<b>by </b><i>, , , </i>;<br/>
<b>hence </b><a NAME="E4:26_1"/>
<font color="Maroon">w1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">w2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
 <b>by </b><i><a class="ref" href="orders_2.html#T25">ORDERS_2:25</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E5:26"/>
<font color="Maroon">w1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">w2</font>
 <b>by </b><i>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>


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