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<b>let </b><font color="Maroon">T</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">A</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">N</font> be   <a href="waybel_0.html#NM2">net</a> of <font color="Maroon">T</font>;<br/>





<b>given </b><font color="Maroon">i</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">N</font><b> such that </b><a NAME="E1:27"/><i><font color="Green">E31</font></i>: 
for <font color="Olive">j</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">N</font>  st <font color="Maroon">i</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Olive">j</font> holds <br/><font color="Maroon">N</font> <a href="waybel_0.html#K2">.</a> <font color="Olive">j</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</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">S</font> be    <a href="yellow_6.html#M2">subnet</a> of <font color="Maroon">N</font>;<br/>

<b>consider </b><font color="Maroon">f</font> being   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">S</font>,<font color="Maroon">N</font><b> such that </b><br/><a NAME="E3:27"/><i><font color="Green">E36</font></i>: 
the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">S</font> <a href="hidden.html#R1">=</a> the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">N</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">f</font>
 <b>and </b><br/><a NAME="E4:27"/><i><font color="Green">E37</font></i>: 
for <font color="Olive">m</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">N</font>  ex <font color="Olive">n</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font> st <br/>for <font color="Olive">p</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font>  st <font color="Olive">n</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Olive">p</font> holds <br/><font color="Olive">m</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">f</font> <a href="yellow_6.html#K3">.</a> <font color="Olive">p</font>
 <b>by </b><i><a class="ref" href="yellow_6.html#D12">YELLOW_6:def 12</a></i>;<br/>
<b>consider </b><font color="Maroon">n</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font><b> such that </b><br/><a NAME="E6:27"/><i><font color="Green">E40</font></i>: 
for <font color="Olive">p</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font>  st <font color="Maroon">n</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Olive">p</font> holds <br/><font color="Maroon">i</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">f</font> <a href="yellow_6.html#K3">.</a> <font color="Olive">p</font>
 <b>by </b><i/>;<br/>
<b>take </b>
<font color="Maroon">n</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">p</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font>;<br/>

<b>assume </b><a NAME="E7:27"/>
<font color="Maroon">n</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">p</font>
 ;<br/>

<a NAME="E8:27"/><b>then </b>
<font color="Maroon">i</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">f</font> <a href="yellow_6.html#K3">.</a> <font color="Maroon">p</font>
 
<b>by </b><i/>;<br/>
<a NAME="E9:27"/><b>then </b><i><font color="Green">E49</font></i>: 
<font color="Maroon">N</font> <a href="waybel_0.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="yellow_6.html#K3">.</a> <font color="Maroon">p</font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 
<b>by </b><i/>;<br/>
<a NAME="E10:27"/>
<font color="Maroon">S</font> <a href="waybel_0.html#K2">.</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">N</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="yellow_6.html#K3">.</a> <font color="Maroon">p</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="funct_2.html#T21">FUNCT_2:21</a></i>;<br/>
<b>hence </b><a NAME="E11:27"/>
<font color="Maroon">S</font> <a href="waybel_0.html#K2">.</a> <font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 <b>by </b><i/>;<br/>


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