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<span class="kw">let </span><font color="Maroon" title="c1">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">A</font>, <font color="Olive" title="b2">B</font> being   <a href="prob_1.html#NM2" title="PROB_1:NM.2">SetSequence</a> of <font color="Maroon" title="c1">X</font><br/>  for <font color="Olive" title="b3">C</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>  st (  for <font color="Olive" title="b4">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <font color="Olive" title="b2">B</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b4">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">C</font> <a href="subset_1.html#K5" title="SUBSET_1:func.5">\+\</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">A</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b4">n</font></span>)</span> ) holds <br/><font color="Olive" title="b3">C</font> <a href="subset_1.html#K5" title="SUBSET_1:func.5">\+\</a> <span class="p1">(<span class="default"><a href="kurato_0.html#K3" title="KURATO_0:func.3">lim_inf</a> <font color="Olive" title="b1">A</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="kurato_0.html#K4" title="KURATO_0:func.4">lim_sup</a> <font color="Olive" title="b2">B</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">A</font>, <font color="Maroon" title="c3">B</font> be   <a href="prob_1.html#NM2" title="PROB_1:NM.2">SetSequence</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">C</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>  st (  for <font color="Olive" title="b2">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <font color="Maroon" title="c3">B</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">C</font> <a href="subset_1.html#K5" title="SUBSET_1:func.5">\+\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">n</font></span>)</span> ) holds <br/><font color="Olive" title="b1">C</font> <a href="subset_1.html#K5" title="SUBSET_1:func.5">\+\</a> <span class="p1">(<span class="default"><a href="kurato_0.html#K3" title="KURATO_0:func.3">lim_inf</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="kurato_0.html#K4" title="KURATO_0:func.4">lim_sup</a> <font color="Maroon" title="c3">B</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">C</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( (  for <font color="Olive" title="b1">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <font color="Maroon" title="c3">B</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">C</font> <a href="subset_1.html#K5" title="SUBSET_1:func.5">\+\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">n</font></span>)</span> ) implies <font color="Maroon" title="c4">C</font> <a href="subset_1.html#K5" title="SUBSET_1:func.5">\+\</a> <span class="p1">(<span class="default"><a href="kurato_0.html#K3" title="KURATO_0:func.3">lim_inf</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="kurato_0.html#K4" title="KURATO_0:func.4">lim_sup</a> <font color="Maroon" title="c3">B</font> )</span><br/>





<span class="kw">assume </span><a NAME="E1:20"/><span class="lab"><font color="Green" title="E10">A1</font></span>: 
 for <font color="Olive" title="b1">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <font color="Maroon" title="c3">B</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">C</font> <a href="subset_1.html#K5" title="SUBSET_1:func.5">\+\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">n</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">C</font> <a href="subset_1.html#K5" title="SUBSET_1:func.5">\+\</a> <span class="p1">(<span class="default"><a href="kurato_0.html#K3" title="KURATO_0:func.3">lim_inf</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="kurato_0.html#K4" title="KURATO_0:func.4">lim_sup</a> <font color="Maroon" title="c3">B</font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c5">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">C</font> <a href="subset_1.html#K5" title="SUBSET_1:func.5">\+\</a> <span class="p1">(<span class="default"><a href="kurato_0.html#K3" title="KURATO_0:func.3">lim_inf</a> <font color="Maroon" title="c2">A</font></span>)</span> or <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="kurato_0.html#K4" title="KURATO_0:func.4">lim_sup</a> <font color="Maroon" title="c3">B</font> )</span><br/>

<span class="kw">assume </span><a NAME="E2:20"/><span class="lab"><font color="Green" title="E11">A2</font></span>: 
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">C</font> <a href="subset_1.html#K5" title="SUBSET_1:func.5">\+\</a> <span class="p1">(<span class="default"><a href="kurato_0.html#K3" title="KURATO_0:func.3">lim_inf</a> <font color="Maroon" title="c2">A</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="kurato_0.html#K4" title="KURATO_0:func.4">lim_sup</a> <font color="Maroon" title="c3">B</font></span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:20_1"/>
( ( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">C</font> &amp;  not <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="kurato_0.html#K3" title="KURATO_0:func.3">lim_inf</a> <font color="Maroon" title="c2">A</font> ) or (  not <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">C</font> &amp; <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="kurato_0.html#K3" title="KURATO_0:func.3">lim_inf</a> <font color="Maroon" title="c2">A</font> ) )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:20"><span class="lab"><font color="Green" title="E11">A2</font></span></a>, <a class="ref" href="xboole_0.html#T1" title="XBOOLE_0:th.1">XBOOLE_0:1</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_1_1"><span class="kw">suppose </span></a><a NAME="E1:20_1_1"/><span class="lab"><font color="Green" title="E12">A3</font></span>: 
( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">C</font> &amp;  not <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="kurato_0.html#K3" title="KURATO_0:func.3">lim_inf</a> <font color="Maroon" title="c2">A</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="kurato_0.html#K4" title="KURATO_0:func.4">lim_sup</a> <font color="Maroon" title="c3">B</font></span><br/><div class="add"><a NAME="E2:20_1_1"/>
 for <font color="Olive" title="b1">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   ex <font color="Olive" title="b2">k</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Olive" title="b2">k</font></span>)</span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c6">n</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">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="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">k</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Olive" title="b1">k</font></span>)</span></span><br/>

<span class="kw">consider </span><font color="Maroon" title="c7">k</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <span class="kw"> such that </span><br/><a NAME="E2:20_1_1_1"/><span class="lab"><font color="Green" title="E13">A4</font></span>: 
 not <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c7">k</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:20_1_1"><span class="lab"><font color="Green" title="E12">A3</font></span></a>, <a class="ref" href="kurato_0.html#T4" target="_self" title="KURATO_0:th.4">Th7</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c7">k</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c7">k</font></span>)</span></span><br/>

<a NAME="E3:20_1_1_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">C</font> <a href="subset_1.html#K5" title="SUBSET_1:func.5">\+\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c7">k</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:20_1_1"><span class="lab"><font color="Green" title="E12">A3</font></span></a>, <a class="txt" href="#E2:20_1_1_1"><span class="lab"><font color="Green" title="E13">A4</font></span></a>, <a class="ref" href="xboole_0.html#T1" title="XBOOLE_0:th.1">XBOOLE_0:1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:20_1_1_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c7">k</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:20"><span class="lab"><font color="Green" title="E10">A1</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E3:20_1_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="kurato_0.html#K4" title="KURATO_0:func.4">lim_sup</a> <font color="Maroon" title="c3">B</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="kurato_0.html#T5" target="_self" title="KURATO_0:th.5">Th8</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_1_2"><span class="kw">suppose </span></a><a NAME="E1:20_1_2"/><span class="lab"><font color="Green" title="E12">A5</font></span>: 
(  not <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">C</font> &amp; <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="kurato_0.html#K3" title="KURATO_0:func.3">lim_inf</a> <font color="Maroon" title="c2">A</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="kurato_0.html#K4" title="KURATO_0:func.4">lim_sup</a> <font color="Maroon" title="c3">B</font></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <span class="kw"> such that </span><br/><a NAME="E3:20_1_2"/><span class="lab"><font color="Green" title="E13">A6</font></span>: 
 for <font color="Olive" title="b1">k</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Olive" title="b1">k</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="kurato_0.html#T4" target="_self" title="KURATO_0:th.4">Th7</a></span>;<br/><a NAME="E4:20_1_2"/>
 for <font color="Olive" title="b1">m</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   ex <font color="Olive" title="b2">k</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Olive" title="b2">k</font></span>)</span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_2_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c7">m</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">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="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">k</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Olive" title="b1">k</font></span>)</span></span><br/>

<span class="kw">take </span><font color="Maroon" title="c8">k</font> = <font color="Maroon" title="c6">n</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c8">k</font></span>)</span></span><br/>

<a NAME="E1:20_1_2_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c8">k</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:20_1_2"><span class="lab"><font color="Green" title="E13">A6</font></span></a></span>;<br/>
<a NAME="E2:20_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">C</font> <a href="subset_1.html#K5" title="SUBSET_1:func.5">\+\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c8">k</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:20_1_2"><span class="lab"><font color="Green" title="E12">A5</font></span></a>, <a class="ref" href="xboole_0.html#T1" title="XBOOLE_0:th.1">XBOOLE_0:1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:20_1_2_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c8">k</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:20"><span class="lab"><font color="Green" title="E10">A1</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E5:20_1_2"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="kurato_0.html#K4" title="KURATO_0:func.4">lim_sup</a> <font color="Maroon" title="c3">B</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="kurato_0.html#T5" target="_self" title="KURATO_0:th.5">Th8</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div>
