<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">A</font> be    <a href="unialg_1.html#L1">UAStr</a> ;<br/>

<b>assume </b><a NAME="E1:6_1_1"/><i><font color="Green">E29</font></i>: 
( the <a href="unialg_1.html#U1">charact</a> of <font color="Maroon">A</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; the <a href="unialg_1.html#U1">charact</a> of <font color="Maroon">A</font> is <a href="relat_1.html#V2">non-empty</a> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="unialg_1.html#D9">UNIALG_1:def 9</a><br/>

<b>then reconsider </b><font color="Maroon">f</font> = the <a href="unialg_1.html#U1">charact</a> of <font color="Maroon">A</font> as  non <a href="xboole_0.html#V1">empty</a> <a href="funct_1.html#NM1">Function</a> ;<br/>
<b>consider </b><font color="Maroon">x</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font>;<br/>
<b>reconsider </b><font color="Maroon">y</font> = <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> as  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a>  <b>by </b><i>, <a class="ref" href="funct_1.html#D15">FUNCT_1:def 15</a></i>;<br/>
<a NAME="E5:6_1_1"/><i><font color="Green">E36</font></i>: 
( <font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">f</font> &amp;  <a href="relat_1.html#K2">rng</a> <font color="Maroon">f</font> <a href="tarski.html#R1">c=</a>  <a href="partfun1.html#K4">PFuncs</a> <span class="p1">(<span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font> <a href="finseq_2.html#K3">*</a> </span>)</span>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E6:6_1_1"/><b>then </b><i><font color="Green">E37</font></i>: 
<font color="Maroon">y</font> is   <a href="partfun1.html#NM1">PartFunc</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font> <a href="finseq_2.html#K3">*</a> ,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font>
 
<b>by </b><i><a class="ref" href="partfun1.html#T121">PARTFUN1:121</a></i>;<br/>
<b>reconsider </b><font color="Maroon">y</font> = <font color="Maroon">y</font> as  non <a href="xboole_0.html#V1">empty</a> <a href="funct_1.html#NM1">Function</a> <b>by </b><i>, <a class="ref" href="partfun1.html#T121">PARTFUN1:121</a></i>;<br/>
<b>consider </b><font color="Maroon">z</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="relat_1.html#K2">rng</a> <font color="Maroon">y</font>;<br/>
<a NAME="E9:6_1_1"/>
( <font color="Maroon">z</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">y</font> &amp;  <a href="relat_1.html#K2">rng</a> <font color="Maroon">y</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font> )
 
<b>by </b><i>, <a class="ref" href="relset_1.html#T12">RELSET_1:12</a></i>;<br/>
<b>hence </b><a NAME="E10:6_1_1"/>
not the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font> is <a href="xboole_0.html#V1">empty</a>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="struct_0.html#D1">STRUCT_0:def 1</a><br/>


</div>
