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<span class="kw">thus </span><a NAME="E1:28_1_1"/>
 ex <font color="Olive" title="b1">Un</font> being  <a href="nagata_1.html#NM1" title="NAGATA_1:NM.1">FamilySequence</a> of <font color="Maroon" title="c1">T</font> st <font color="Olive" title="b1">Un</font> is  <a href="nagata_1.html#V3" title="NAGATA_1:attr.3">sigma_locally_finite</a> 
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">consider </span><font color="Maroon" title="c2">Un</font> being   <a href="nagata_1.html#NM1" title="NAGATA_1:NM.1">FamilySequence</a> of <font color="Maroon" title="c1">T</font><span class="kw"> such that </span><br/><a NAME="E2:28_1_1_1"/><span class="lab"><font color="Green" title="E15">A1</font></span>: 
<font color="Maroon" title="c2">Un</font> is  <a href="nagata_1.html#V2" title="NAGATA_1:attr.2">sigma_discrete</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="nagata_1.html#E18"><span class="lab"><font color="Green" title="E12">Lm5</font></span></a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c2">Un</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">Un</font> is  <a href="nagata_1.html#V3" title="NAGATA_1:attr.3">sigma_locally_finite</a> </span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1_1_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c3">n</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">Un</font> <a href="nagata_1.html#K1" title="NAGATA_1:func.1">.</a> <font color="Maroon" title="c3">n</font> is  <a href="pcomps_1.html#V1" title="PCOMPS_1:attr.1">locally_finite</a> </span><br/><a NAME="E1:28_1_1_1_1"/>
<font color="Maroon" title="c2">Un</font> <a href="nagata_1.html#K1" title="NAGATA_1:func.1">.</a> <font color="Maroon" title="c3">n</font> is  <a href="nagata_1.html#V1" title="NAGATA_1:attr.1">discrete</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:28_1_1_1"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="ref" href="nagata_1.html#D2" target="_self" title="NAGATA_1:def.2">Def2</a></span>;<br/><span class="kw">hence </span><a NAME="E2:28_1_1_1_1"/>
<font color="Maroon" title="c2">Un</font> <a href="nagata_1.html#K1" title="NAGATA_1:func.1">.</a> <font color="Maroon" title="c3">n</font> is  <a href="pcomps_1.html#V1" title="PCOMPS_1:attr.1">locally_finite</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nagata_1.html#T11" target="_self" title="NAGATA_1:th.11">Th11</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/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E4:28_1_1_1"/>
<font color="Maroon" title="c2">Un</font> is  <a href="nagata_1.html#V3" title="NAGATA_1:attr.3">sigma_locally_finite</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nagata_1.html#D3" target="_self" title="NAGATA_1:def.3">Def3</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/>


</div><span class="kw">end;</span></div>


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