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<b>let </b><font color="Maroon">L1</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="struct_0.html#L1">1-sorted</a> , <font color="Maroon">L2</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="struct_0.html#L1">1-sorted</a> ;<br/><b>let </b><font color="Maroon">N1</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="waybel_0.html#L1">NetStr</a> of <font color="Maroon">L1</font>;<br/><b>let </b><font color="Maroon">N2</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="waybel_0.html#L1">NetStr</a> of <font color="Maroon">L2</font>;<br/>





<b>assume </b><a NAME="E1:14"/><i><font color="Green">E46</font></i>: 
(  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">N1</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">N1</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">N2</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">N2</font> #) &amp; the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">N1</font> <a href="funct_2.html#R1">=</a> the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">N2</font> )
 ;<br/>

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

<b>given </b><font color="Maroon">i1</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">N1</font><b> such that </b><a NAME="E2:14"/><i><font color="Green">E47</font></i>: 
for <font color="Olive">j</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">N1</font>  st <font color="Maroon">i1</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Olive">j</font> holds <br/><font color="Maroon">N1</font> <a href="waybel_0.html#K2">.</a> <font color="Olive">j</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_0.html#D11">WAYBEL_0:def 11</a><br/>

<b>reconsider </b><font color="Maroon">i2</font> = <font color="Maroon">i1</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">N2</font> <b>by </b><i/>;<br/>
<b>take </b>
<font color="Maroon">i2</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_0.html#D11">WAYBEL_0:def 11</a><br/>

<b>let </b><font color="Maroon">j2</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">N2</font>;<br/>

<b>reconsider </b><font color="Maroon">j1</font> = <font color="Maroon">j2</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">N1</font> <b>by </b><i/>;<br/>
<b>assume </b><a NAME="E5:14"/>
<font color="Maroon">i2</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">j2</font>
 ;<br/>

<a NAME="E6:14"/><b>then </b>
<font color="Maroon">i1</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">j1</font>
 
<b>by </b><i>, <a class="ref" href="yellow_0.html#T1">YELLOW_0:1</a></i>;<br/>
<a NAME="E7:14"/><b>then </b>
<font color="Maroon">N1</font> <a href="waybel_0.html#K2">.</a> <font color="Maroon">j1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 
<b>by </b><i/>;<br/>
<a NAME="E8:14"/><b>then </b>
the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">N2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">j2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E9:14"/>
<font color="Maroon">N2</font> <a href="waybel_0.html#K2">.</a> <font color="Maroon">j2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 ;<br/>


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