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<b>consider </b><font color="Maroon">A</font> being  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/>
<b>consider </b><font color="Maroon">a</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">A</font>;<br/>
<b>reconsider </b><font color="Maroon">w</font> = <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K6">&lt;*&gt;</a> <font color="Maroon">A</font></span>)</span></span><a href="tarski.html#K1">}</a></span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">a</font> as    <a href="subset_1.html#M1">Element</a> of  <a href="partfun1.html#K4">PFuncs</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="finseq_1.html#K13">*</a> </span>)</span>,<font color="Maroon">A</font> <b>by </b><i/>;<br/>
<b>set </b><font color="Maroon">U1</font> =  <a href="unialg_1.html#G1" target="_self">UAStr</a>(# <font color="Maroon">A</font>,<span class="p1"><a href="unialg_1.html#K1" target="_self">&lt;*</a><span class="default"><font color="Maroon">w</font></span><a href="unialg_1.html#K1" target="_self">*&gt;</a></span> #);<br/>
<b>take </b>
 <a href="unialg_1.html#G1" target="_self">UAStr</a>(# <font color="Maroon">A</font>,<span class="p1"><a href="unialg_1.html#K1" target="_self">&lt;*</a><span class="default"><font color="Maroon">w</font></span><a href="unialg_1.html#K1" target="_self">*&gt;</a></span> #)
;<br/>

<a NAME="E4:16_1_1"/><i><font color="Green">E28</font></i>: 
( the <a href="unialg_1.html#U1" target="_self">charact</a> of <a href="unialg_1.html#G1" target="_self">UAStr</a>(# <font color="Maroon">A</font>,<span class="p1"><a href="unialg_1.html#K1" target="_self">&lt;*</a><span class="default"><font color="Maroon">w</font></span><a href="unialg_1.html#K1" target="_self">*&gt;</a></span> #) is <a href="unialg_1.html#V5" target="_self">quasi_total</a> &amp; the <a href="unialg_1.html#U1" target="_self">charact</a> of <a href="unialg_1.html#G1" target="_self">UAStr</a>(# <font color="Maroon">A</font>,<span class="p1"><a href="unialg_1.html#K1" target="_self">&lt;*</a><span class="default"><font color="Maroon">w</font></span><a href="unialg_1.html#K1" target="_self">*&gt;</a></span> #) is <a href="unialg_1.html#V4" target="_self">homogeneous</a> &amp; the <a href="unialg_1.html#U1" target="_self">charact</a> of <a href="unialg_1.html#G1" target="_self">UAStr</a>(# <font color="Maroon">A</font>,<span class="p1"><a href="unialg_1.html#K1" target="_self">&lt;*</a><span class="default"><font color="Maroon">w</font></span><a href="unialg_1.html#K1" target="_self">*&gt;</a></span> #) is <a href="relat_1.html#V2">non-empty</a> )
 
<b>by </b><i/>;<br/>
<a NAME="E5:16_1_1"/>
the <a href="unialg_1.html#U1" target="_self">charact</a> of <a href="unialg_1.html#G1" target="_self">UAStr</a>(# <font color="Maroon">A</font>,<span class="p1"><a href="unialg_1.html#K1" target="_self">&lt;*</a><span class="default"><font color="Maroon">w</font></span><a href="unialg_1.html#K1" target="_self">*&gt;</a></span> #) <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_1_1_1"/><i><font color="Green">E29</font></i>: 
the <a href="unialg_1.html#U1" target="_self">charact</a> of <a href="unialg_1.html#G1" target="_self">UAStr</a>(# <font color="Maroon">A</font>,<span class="p1"><a href="unialg_1.html#K1" target="_self">&lt;*</a><span class="default"><font color="Maroon">w</font></span><a href="unialg_1.html#K1" target="_self">*&gt;</a></span> #) <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<a NAME="E2:16_1_1_1"/>
 <a href="finseq_1.html#K3">len</a> the <a href="unialg_1.html#U1" target="_self">charact</a> of <a href="unialg_1.html#G1" target="_self">UAStr</a>(# <font color="Maroon">A</font>,<span class="p1"><a href="unialg_1.html#K1" target="_self">&lt;*</a><span class="default"><font color="Maroon">w</font></span><a href="unialg_1.html#K1" target="_self">*&gt;</a></span> #) <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i><a class="ref" href="finseq_1.html#T56">FINSEQ_1:56</a></i>;<br/>
<b>hence </b><a NAME="E3:16_1_1_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="finseq_1.html#T25">FINSEQ_1:25</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E6:16_1_1"/>
(  <a href="unialg_1.html#G1" target="_self">UAStr</a>(# <font color="Maroon">A</font>,<span class="p1"><a href="unialg_1.html#K1" target="_self">&lt;*</a><span class="default"><font color="Maroon">w</font></span><a href="unialg_1.html#K1" target="_self">*&gt;</a></span> #) is <a href="unialg_1.html#V7" target="_self">quasi_total</a> &amp;  <a href="unialg_1.html#G1" target="_self">UAStr</a>(# <font color="Maroon">A</font>,<span class="p1"><a href="unialg_1.html#K1" target="_self">&lt;*</a><span class="default"><font color="Maroon">w</font></span><a href="unialg_1.html#K1" target="_self">*&gt;</a></span> #) is <a href="unialg_1.html#V6" target="_self">partial</a> &amp;  <a href="unialg_1.html#G1" target="_self">UAStr</a>(# <font color="Maroon">A</font>,<span class="p1"><a href="unialg_1.html#K1" target="_self">&lt;*</a><span class="default"><font color="Maroon">w</font></span><a href="unialg_1.html#K1" target="_self">*&gt;</a></span> #) is <a href="unialg_1.html#V8" target="_self">non-empty</a> &amp;  <a href="unialg_1.html#G1" target="_self">UAStr</a>(# <font color="Maroon">A</font>,<span class="p1"><a href="unialg_1.html#K1" target="_self">&lt;*</a><span class="default"><font color="Maroon">w</font></span><a href="unialg_1.html#K1" target="_self">*&gt;</a></span> #) is <a href="unialg_1.html#V3" target="_self">strict</a> &amp; not  <a href="unialg_1.html#G1" target="_self">UAStr</a>(# <font color="Maroon">A</font>,<span class="p1"><a href="unialg_1.html#K1" target="_self">&lt;*</a><span class="default"><font color="Maroon">w</font></span><a href="unialg_1.html#K1" target="_self">*&gt;</a></span> #) is <a href="struct_0.html#V3">empty</a> )
 <b>by </b><i>, , , </i>;<br/>


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