<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">p</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="limfunc1.html#K2" title="LIMFUNC1:func.2">left_closed_halfline</a> <font color="Maroon" title="c1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">p</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="limfunc1.html#NK2" title="LIMFUNC1:NK.2">left_open_halfline</a> <font color="Maroon" title="c1">p</font></span>)</span></span><br/>

<b>thus </b><a NAME="E1:13"/>
 <a href="limfunc1.html#K2" title="LIMFUNC1:func.2">left_closed_halfline</a> <font color="Maroon" title="c1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">p</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="limfunc1.html#NK2" title="LIMFUNC1:NK.2">left_open_halfline</a> <font color="Maroon" title="c1">p</font></span>)</span>
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">p</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="limfunc1.html#NK2" title="LIMFUNC1:NK.2">left_open_halfline</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="limfunc1.html#K2" title="LIMFUNC1:func.2">left_closed_halfline</a> <font color="Maroon" title="c1">p</font></span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="limfunc1.html#K2" title="LIMFUNC1:func.2">left_closed_halfline</a> <font color="Maroon" title="c1">p</font> or <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">p</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="limfunc1.html#NK2" title="LIMFUNC1:NK.2">left_open_halfline</a> <font color="Maroon" title="c1">p</font></span>)</span> )</span><br/>

<b>assume </b><a NAME="E1:13_1"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="limfunc1.html#K2" title="LIMFUNC1:func.2">left_closed_halfline</a> <font color="Maroon" title="c1">p</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">p</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="limfunc1.html#NK2" title="LIMFUNC1:NK.2">left_open_halfline</a> <font color="Maroon" title="c1">p</font></span>)</span></span><br/>

<a NAME="E2:13_1"/><b>then </b>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">g1</font> where <font color="Olive" title="b1">g1</font> is   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> : <font color="Olive" title="b1">g1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">p</font> </span>}</span> 
 
<b>by </b><i><a class="ref" href="limfunc1.html#T153" title="LIMFUNC1:th.153">LIMFUNC1:153</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c3">g1</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><b> such that </b><br/><a NAME="E4:13_1"/><i><font color="Green" title="E11">A1</font></i>: 
( <font color="Maroon" title="c3">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> &amp; <font color="Maroon" title="c3">g1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">p</font> )
 ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:13_1_1_1"/>
( <font color="Maroon" title="c3">g1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">p</font> or <font color="Maroon" title="c3">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">p</font> )
 </span><b>by </b><i><a class="txt" href="fcont_3.html#E4:13_1"><i><font color="Green" title="E11">A1</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_1_1_1_1"><b>suppose </b></a><a NAME="E1:13_1_1_1_1"/>
<font color="Maroon" title="c3">g1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">p</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">p</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="limfunc1.html#NK2" title="LIMFUNC1:NK.2">left_open_halfline</a> <font color="Maroon" title="c1">p</font></span>)</span></span><br/><div class="add"><a NAME="E2:13_1_1_1_1"/><b>then </b>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">g2</font> where <font color="Olive" title="b1">g2</font> is   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> : <font color="Olive" title="b1">g2</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">p</font> </span>}</span> 
 <b>by </b><i><a class="txt" href="fcont_3.html#E4:13_1"><i><font color="Green" title="E11">A1</font></i></a></i>;<br/><a NAME="E3:13_1_1_1_1"/><b>then </b>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="limfunc1.html#NK2" title="LIMFUNC1:NK.2">left_open_halfline</a> <font color="Maroon" title="c1">p</font>
 <b>by </b><i><a class="ref" href="limfunc1.html#T151" title="LIMFUNC1:th.151">LIMFUNC1:151</a></i>;<br/><b>hence </b><a NAME="E4:13_1_1_1_1"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">p</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="limfunc1.html#NK2" title="LIMFUNC1:NK.2">left_open_halfline</a> <font color="Maroon" title="c1">p</font></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_1_1_1_2"><b>suppose </b></a><a NAME="E1:13_1_1_1_2"/>
<font color="Maroon" title="c3">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">p</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">p</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="limfunc1.html#NK2" title="LIMFUNC1:NK.2">left_open_halfline</a> <font color="Maroon" title="c1">p</font></span>)</span></span><br/><div class="add"><a NAME="E2:13_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">p</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="fcont_3.html#E4:13_1"><i><font color="Green" title="E11">A1</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E3:13_1_1_1_2"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">p</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="limfunc1.html#NK2" title="LIMFUNC1:NK.2">left_open_halfline</a> <font color="Maroon" title="c1">p</font></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E6:13_1"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">p</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="limfunc1.html#NK2" title="LIMFUNC1:NK.2">left_open_halfline</a> <font color="Maroon" title="c1">p</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>

<b>let </b><font color="Maroon" title="c2">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">p</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="limfunc1.html#NK2" title="LIMFUNC1:NK.2">left_open_halfline</a> <font color="Maroon" title="c1">p</font></span>)</span> or <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="limfunc1.html#K2" title="LIMFUNC1:func.2">left_closed_halfline</a> <font color="Maroon" title="c1">p</font> )</span><br/>

<b>assume </b><a NAME="E2:13"/><i><font color="Green" title="E11">A2</font></i>: 
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">p</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="limfunc1.html#NK2" title="LIMFUNC1:NK.2">left_open_halfline</a> <font color="Maroon" title="c1">p</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="limfunc1.html#K2" title="LIMFUNC1:func.2">left_closed_halfline</a> <font color="Maroon" title="c1">p</font></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:13_2_1"/>
( <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">p</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> or <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="limfunc1.html#NK2" title="LIMFUNC1:NK.2">left_open_halfline</a> <font color="Maroon" title="c1">p</font> )
 </span><b>by </b><i><a class="txt" href="fcont_3.html#E2:13"><i><font color="Green" title="E11">A2</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_1_1"><b>suppose </b></a><a NAME="E1:13_2_1_1"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">p</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="limfunc1.html#K2" title="LIMFUNC1:func.2">left_closed_halfline</a> <font color="Maroon" title="c1">p</font></span><br/><div class="add"><a NAME="E2:13_2_1_1"/><b>then </b>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">p</font>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E3:13_2_1_1"/><b>then </b>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">g</font> where <font color="Olive" title="b1">g</font> is   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> : <font color="Olive" title="b1">g</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">p</font> </span>}</span> 
 ;<br/><b>hence </b><a NAME="E4:13_2_1_1"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="limfunc1.html#K2" title="LIMFUNC1:func.2">left_closed_halfline</a> <font color="Maroon" title="c1">p</font>
 <b>by </b><i><a class="ref" href="limfunc1.html#T153" title="LIMFUNC1:th.153">LIMFUNC1:153</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_1_2"><b>suppose </b></a><a NAME="E1:13_2_1_2"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="limfunc1.html#NK2" title="LIMFUNC1:NK.2">left_open_halfline</a> <font color="Maroon" title="c1">p</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="limfunc1.html#K2" title="LIMFUNC1:func.2">left_closed_halfline</a> <font color="Maroon" title="c1">p</font></span><br/><div class="add"><a NAME="E2:13_2_1_2"/><b>then </b>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">g</font> where <font color="Olive" title="b1">g</font> is   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> : <font color="Olive" title="b1">g</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">p</font> </span>}</span> 
 <b>by </b><i><a class="ref" href="limfunc1.html#T151" title="LIMFUNC1:th.151">LIMFUNC1:151</a></i>;<br/><b>then consider </b><font color="Maroon" title="c3">g1</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><b> such that </b><br/><a NAME="E4:13_2_1_2"/><i><font color="Green" title="E12">A3</font></i>: 
( <font color="Maroon" title="c3">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> &amp; <font color="Maroon" title="c3">g1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">p</font> )
 ;<br/><a NAME="E5:13_2_1_2"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">g2</font> where <font color="Olive" title="b1">g2</font> is   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> : <font color="Olive" title="b1">g2</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">p</font> </span>}</span> 
 <b>by </b><i><a class="txt" href="fcont_3.html#E4:13_2_1_2"><i><font color="Green" title="E12">A3</font></i></a></i>;<br/><b>hence </b><a NAME="E6:13_2_1_2"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="limfunc1.html#K2" title="LIMFUNC1:func.2">left_closed_halfline</a> <font color="Maroon" title="c1">p</font>
 <b>by </b><i><a class="ref" href="limfunc1.html#T153" title="LIMFUNC1:th.153">LIMFUNC1:153</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E4:13"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="limfunc1.html#K2" title="LIMFUNC1:func.2">left_closed_halfline</a> <font color="Maroon" title="c1">p</font>
 ; <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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