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<b>let </b><font color="Maroon">A</font> be  <a href="waybel_0.html#V6">strict</a>  <a href="waybel_0.html#L1">NetStr</a> of <font color="Maroon">L</font>, <font color="Maroon">B</font> be  <a href="waybel_0.html#V6">strict</a>  <a href="waybel_0.html#L1">NetStr</a> of <font color="Maroon">L</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:32_1_2"/><i><font color="Green">E34</font></i>: 
(  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">A</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">N</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">N</font> #) &amp; ( for <font color="Olive">i</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">A</font>  ex <font color="Olive">y</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> st <br/>( <font color="Olive">y</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_1.html#K1">.</a> <font color="Olive">i</font> &amp; the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> <a href="lattice3.html#K11">"/\"</a> <font color="Olive">y</font> ) ) )
 <b>and </b><br/><a NAME="E2:32_1_2"/><i><font color="Green">E35</font></i>: 
(  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">B</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">B</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">N</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">N</font> #) &amp; ( for <font color="Olive">i</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">B</font>  ex <font color="Olive">y</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> st <br/>( <font color="Olive">y</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_1.html#K1">.</a> <font color="Olive">i</font> &amp; the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">B</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> <a href="lattice3.html#K11">"/\"</a> <font color="Olive">y</font> ) ) )
 ;<br/>

<b>reconsider </b><font color="Maroon">C</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font> as  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a>  <b>by </b><i/>;<br/>
<b>reconsider </b><font color="Maroon">f1</font> = the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">A</font>, <font color="Maroon">f2</font> = the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">B</font> as   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">C</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font> <b>by </b><i>, </i>;<br/>
<a NAME="E5:32_1_2"/>
for <font color="Olive">c</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C</font> holds  <font color="Maroon">f1</font> <a href="funct_2.html#K3">.</a> <font color="Olive">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> <a href="funct_2.html#K3">.</a> <font color="Olive">c</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="32_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C</font>;<br/>

<b>consider </b><font color="Maroon">ya</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font><b> such that </b><br/><a NAME="E2:32_1_2_1"/><i><font color="Green">E36</font></i>: 
( <font color="Maroon">ya</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_1.html#K1">.</a> <font color="Maroon">c</font> &amp; <font color="Maroon">f1</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> <a href="lattice3.html#K11">"/\"</a> <font color="Maroon">ya</font> )
 <b>by </b><i/>;<br/>
<b>consider </b><font color="Maroon">yb</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font><b> such that </b><br/><a NAME="E4:32_1_2_1"/><i><font color="Green">E56</font></i>: 
( <font color="Maroon">yb</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_1.html#K1">.</a> <font color="Maroon">c</font> &amp; <font color="Maroon">f2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> <a href="lattice3.html#K11">"/\"</a> <font color="Maroon">yb</font> )
 <b>by </b><i>, </i>;<br/>
<b>thus </b><a NAME="E5:32_1_2_1"/>
<font color="Maroon">f1</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c</font>
 <b>by </b><i>, </i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E6:32_1_2"/>
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B</font>
 <b>by </b><i>, , <a class="ref" href="funct_2.html#T113">FUNCT_2:113</a></i>;<br/>


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