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<b>consider </b><font color="Maroon" title="c1">A</font> being  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>
<b>consider </b><font color="Maroon" title="c2">a</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">A</font>;<br/>
<b>reconsider </b><font color="Maroon" title="c3">w</font> = <span class="p1">(<span class="default"><a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c2">a</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="partfun1.html#K4" title="PARTFUN1:func.4">PFuncs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> </span>)</span>,<font color="Maroon" title="c1">A</font> <b>by </b><i><a class="ref" href="unialg_1.html#T3" target="_self" title="UNIALG_1:th.3">Th3</a></i>;<br/>
<b>set </b><font color="Maroon" title="c4">U1</font> =  <a href="unialg_1.html#G1" title="UNIALG_1:aggr.1">UAStr</a>(# <font color="Maroon" title="c1">A</font>,<span class="p1"><a href="unialg_1.html#K1" title="UNIALG_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c3">w</font></span><a href="unialg_1.html#K1" title="UNIALG_1:func.1">*&gt;</a></span> #);<br/>
<b>take </b>
 <a href="unialg_1.html#G1" title="UNIALG_1:aggr.1">UAStr</a>(# <font color="Maroon" title="c1">A</font>,<span class="p1"><a href="unialg_1.html#K1" title="UNIALG_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c3">w</font></span><a href="unialg_1.html#K1" title="UNIALG_1:func.1">*&gt;</a></span> #)
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="unialg_1.html#G1" title="UNIALG_1:aggr.1">UAStr</a>(# <font color="Maroon" title="c1">A</font>,<span class="p1"><a href="unialg_1.html#K1" title="UNIALG_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c3">w</font></span><a href="unialg_1.html#K1" title="UNIALG_1:func.1">*&gt;</a></span> #) is <a href="unialg_1.html#V7" title="UNIALG_1:attr.7">quasi_total</a> &amp;  <a href="unialg_1.html#G1" title="UNIALG_1:aggr.1">UAStr</a>(# <font color="Maroon" title="c1">A</font>,<span class="p1"><a href="unialg_1.html#K1" title="UNIALG_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c3">w</font></span><a href="unialg_1.html#K1" title="UNIALG_1:func.1">*&gt;</a></span> #) is <a href="unialg_1.html#V6" title="UNIALG_1:attr.6">partial</a> &amp;  <a href="unialg_1.html#G1" title="UNIALG_1:aggr.1">UAStr</a>(# <font color="Maroon" title="c1">A</font>,<span class="p1"><a href="unialg_1.html#K1" title="UNIALG_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c3">w</font></span><a href="unialg_1.html#K1" title="UNIALG_1:func.1">*&gt;</a></span> #) is <a href="unialg_1.html#V8" title="UNIALG_1:attr.8">non-empty</a> &amp;  <a href="unialg_1.html#G1" title="UNIALG_1:aggr.1">UAStr</a>(# <font color="Maroon" title="c1">A</font>,<span class="p1"><a href="unialg_1.html#K1" title="UNIALG_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c3">w</font></span><a href="unialg_1.html#K1" title="UNIALG_1:func.1">*&gt;</a></span> #) is <a href="unialg_1.html#V3" title="UNIALG_1:attr.3">strict</a> &amp; not  <a href="unialg_1.html#G1" title="UNIALG_1:aggr.1">UAStr</a>(# <font color="Maroon" title="c1">A</font>,<span class="p1"><a href="unialg_1.html#K1" title="UNIALG_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c3">w</font></span><a href="unialg_1.html#K1" title="UNIALG_1:func.1">*&gt;</a></span> #) is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> )</span><br/>

<a NAME="E4:21_1_1"/><i><font color="Green" title="E10">A1</font></i>: 
( the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <a href="unialg_1.html#G1" title="UNIALG_1:aggr.1">UAStr</a>(# <font color="Maroon" title="c1">A</font>,<span class="p1"><a href="unialg_1.html#K1" title="UNIALG_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c3">w</font></span><a href="unialg_1.html#K1" title="UNIALG_1:func.1">*&gt;</a></span> #) is <a href="unialg_1.html#V5" title="UNIALG_1:attr.5">quasi_total</a> &amp; the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <a href="unialg_1.html#G1" title="UNIALG_1:aggr.1">UAStr</a>(# <font color="Maroon" title="c1">A</font>,<span class="p1"><a href="unialg_1.html#K1" title="UNIALG_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c3">w</font></span><a href="unialg_1.html#K1" title="UNIALG_1:func.1">*&gt;</a></span> #) is <a href="unialg_1.html#V4" title="UNIALG_1:attr.4">homogeneous</a> &amp; the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <a href="unialg_1.html#G1" title="UNIALG_1:aggr.1">UAStr</a>(# <font color="Maroon" title="c1">A</font>,<span class="p1"><a href="unialg_1.html#K1" title="UNIALG_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c3">w</font></span><a href="unialg_1.html#K1" title="UNIALG_1:func.1">*&gt;</a></span> #) is <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a> )
 
<b>by </b><i><a class="ref" href="unialg_1.html#T4" target="_self" title="UNIALG_1:th.4">Th4</a></i>;<br/>
<a NAME="E5:21_1_1"/>
the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <a href="unialg_1.html#G1" title="UNIALG_1:aggr.1">UAStr</a>(# <font color="Maroon" title="c1">A</font>,<span class="p1"><a href="unialg_1.html#K1" title="UNIALG_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c3">w</font></span><a href="unialg_1.html#K1" title="UNIALG_1:func.1">*&gt;</a></span> #) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<b>by </b><i><a class="ref" href="finseq_1.html#T56" title="FINSEQ_1:th.56">FINSEQ_1:56</a>, <a class="ref" href="card_1.html#T47" title="CARD_1:th.47">CARD_1:47</a></i>;<br/>
<b>hence </b><a NAME="E6:21_1_1"/>
(  <a href="unialg_1.html#G1" title="UNIALG_1:aggr.1">UAStr</a>(# <font color="Maroon" title="c1">A</font>,<span class="p1"><a href="unialg_1.html#K1" title="UNIALG_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c3">w</font></span><a href="unialg_1.html#K1" title="UNIALG_1:func.1">*&gt;</a></span> #) is <a href="unialg_1.html#V7" title="UNIALG_1:attr.7">quasi_total</a> &amp;  <a href="unialg_1.html#G1" title="UNIALG_1:aggr.1">UAStr</a>(# <font color="Maroon" title="c1">A</font>,<span class="p1"><a href="unialg_1.html#K1" title="UNIALG_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c3">w</font></span><a href="unialg_1.html#K1" title="UNIALG_1:func.1">*&gt;</a></span> #) is <a href="unialg_1.html#V6" title="UNIALG_1:attr.6">partial</a> &amp;  <a href="unialg_1.html#G1" title="UNIALG_1:aggr.1">UAStr</a>(# <font color="Maroon" title="c1">A</font>,<span class="p1"><a href="unialg_1.html#K1" title="UNIALG_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c3">w</font></span><a href="unialg_1.html#K1" title="UNIALG_1:func.1">*&gt;</a></span> #) is <a href="unialg_1.html#V8" title="UNIALG_1:attr.8">non-empty</a> &amp;  <a href="unialg_1.html#G1" title="UNIALG_1:aggr.1">UAStr</a>(# <font color="Maroon" title="c1">A</font>,<span class="p1"><a href="unialg_1.html#K1" title="UNIALG_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c3">w</font></span><a href="unialg_1.html#K1" title="UNIALG_1:func.1">*&gt;</a></span> #) is <a href="unialg_1.html#V3" title="UNIALG_1:attr.3">strict</a> &amp; not  <a href="unialg_1.html#G1" title="UNIALG_1:aggr.1">UAStr</a>(# <font color="Maroon" title="c1">A</font>,<span class="p1"><a href="unialg_1.html#K1" title="UNIALG_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c3">w</font></span><a href="unialg_1.html#K1" title="UNIALG_1:func.1">*&gt;</a></span> #) is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> )
 <b>by </b><i><a class="txt" href="unialg_1.html#E4:21_1_1"><i><font color="Green" title="E10">A1</font></i></a>, <a class="ref" href="unialg_1.html#D7" target="_self" title="UNIALG_1:def.7">Def7</a>, <a class="ref" href="unialg_1.html#D8" target="_self" title="UNIALG_1:def.8">Def8</a>, <a class="ref" href="unialg_1.html#D9" target="_self" title="UNIALG_1:def.9">Def9</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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