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<span class="kw">consider </span><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/>
<span class="kw">consider </span><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/>
<span class="kw">reconsider </span><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> <span class="kw">by</span> <span class="lab"><a class="ref" href="unialg_1.html#T3" target="_self" title="UNIALG_1:th.3">Th3</a></span>;<br/>
<span class="kw">set </span><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/>
<span class="kw">take </span>
 <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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="E4:23_1_1"/><span class="lab"><font color="Green" title="E10">A1</font></span>: 
( 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>  &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> #) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="unialg_1.html#T4" target="_self" title="UNIALG_1:th.4">Th4</a></span>;<br/>
<a NAME="E5:23_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> #) 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>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="unialg_1.html#T4" target="_self" title="UNIALG_1:th.4">Th4</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:23_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>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:23_1_1"><span class="lab"><font color="Green" title="E10">A1</font></span></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></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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