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<b>let </b><font color="Maroon">A</font> be  <a href="unialg_1.html#V6">partial</a> <a href="unialg_1.html#V8">non-empty</a>  <a href="unialg_1.html#L1">UAStr</a> ;<br/><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">R</font> be   <a href="relset_1.html#NM3">Relation</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font>;<br/>





<b>consider </b><font color="Maroon">F</font> being    <a href="pboole.html#M1">ManySortedSet</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E2:41"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">R</font> <a href="pua2mss1.html#K8" target="_self">|^</a> <font color="Maroon">A</font>,<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
 <b>and </b><br/><a NAME="E3:41"/><i><font color="Green">E36</font></i>: 
( <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> 0 <a href="hidden.html#R1">=</a> <font color="Maroon">R</font> &amp; ( for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> <br/> for <font color="Olive">R</font> being  <a href="relset_1.html#NM3">Relation</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font>  st <font color="Olive">R</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> holds <br/><font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Olive">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">R</font> <a href="pua2mss1.html#K7" target="_self">|^</a> <font color="Maroon">A</font> ) )
 <b>by </b><i/>;<br/>
<a NAME="E4:41"/>
<font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="pua2mss1.html#K8" target="_self">|^</a> <font color="Maroon">A</font>,<font color="Maroon">i</font></span>)</span> <a href="pua2mss1.html#K7" target="_self">|^</a> <font color="Maroon">A</font>
 
<b>by </b><i>, <a class="txt" href="pua2mss1.html#E2"><i><font color="Green">Lemma25</font></i></a></i>;<br/>
<b>hence </b><a NAME="E5:41"/>
<font color="Maroon">R</font> <a href="pua2mss1.html#K8" target="_self">|^</a> <font color="Maroon">A</font>,<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="pua2mss1.html#K8" target="_self">|^</a> <font color="Maroon">A</font>,<font color="Maroon">i</font></span>)</span> <a href="pua2mss1.html#K7" target="_self">|^</a> <font color="Maroon">A</font>
 <b>by </b><i><a class="txt" href="pua2mss1.html#E2"><i><font color="Green">Lemma25</font></i></a>, </i>;<br/>


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