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

<b>let </b><font color="Maroon">T</font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">F</font> be    <a href="seqfunc.html#M1">Functional_Sequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font>, <a href="numbers.html#K1">REAL</a> ;<br/>



<b>assume </b><a NAME="E1:26"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">F</font> <a href="seqfunc.html#R3">is_unif_conv_on</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font> &amp; ( for <font color="Olive">i</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Maroon">F</font> <a href="seqfunc.html#K1">.</a> <font color="Olive">i</font> is  <a href="pre_topc.html#V5">continuous</a> <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">T</font>,<a href="topmetr.html#K3">R^1</a>  ) )
 ;<br/>

<a NAME="E2:26"/>
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font> <a href="seqfunc.html#R1">common_on_dom</a> <font color="Maroon">F</font> &amp; <font color="Maroon">F</font> <a href="seqfunc.html#R2">is_point_conv_on</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font> &amp; ( for <font color="Olive">r</font> being  <a href="real_1.html#NM1">Real</a>  st 0 <a href="xxreal_0.html#R1">&lt;</a> <font color="Olive">r</font> holds <br/> ex <font color="Olive">k</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  st <br/>for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <br/> for <font color="Olive">x</font> being  <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font>  st <font color="Olive">n</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Olive">k</font> &amp; <font color="Olive">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font> holds <br/> <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="seqfunc.html#K1">.</a> <font color="Olive">n</font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Olive">x</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="seqfunc.html#K11">lim</a> <font color="Maroon">F</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Olive">x</font></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Olive">r</font> ) )
 
<b>by </b><i>, <a class="ref" href="seqfunc.html#T44">SEQFUNC:44</a></i>;<br/>
<a NAME="E3:26"/><b>then </b><i><font color="Green">E38</font></i>: 
(  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="seqfunc.html#K11">lim</a> <font color="Maroon">F</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font> &amp; ( for <font color="Olive">x</font> being   <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font>  st <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="seqfunc.html#K11">lim</a> <font color="Maroon">F</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font></span>)</span> holds <br/><span class="p1">(<span class="default"><a href="seqfunc.html#K11">lim</a> <font color="Maroon">F</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a>  <a href="seq_2.html#K2">lim</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="seqfunc.html#K10">#</a> <font color="Olive">x</font></span>)</span> ) )
 
<b>by </b><i><a class="ref" href="seqfunc.html#D14">SEQFUNC:def 14</a></i>;<br/>
<b>reconsider </b><font color="Maroon">l</font> =  <a href="seqfunc.html#K11">lim</a> <font color="Maroon">F</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font> as   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">T</font>,<a href="topmetr.html#K3">R^1</a>  <b>by </b><i>, <a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a>, <a class="ref" href="topmetr.html#T24">TOPMETR:24</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">p</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">e</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>assume </b><a NAME="E1:26_1_1"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">e</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/><b>reconsider </b><font color="Maroon">e3</font> = <font color="Maroon">e</font> <a href="xcmplx_0.html#K7">/</a> 3 as   <a href="real_1.html#NM1">Real</a> <b>by </b><i><a class="ref" href="xreal_0.html#D1">XREAL_0:def 1</a></i>;<br/><a NAME="E3:26_1_1"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">e3</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T141">XREAL_1:141</a></i>;<br/><b>consider </b><font color="Maroon">k</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E5:26_1_1"/><i><font color="Green">E41</font></i>: 
for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <br/> for <font color="Olive">x</font> being  <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font>  st <font color="Olive">n</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">k</font> &amp; <font color="Olive">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font> holds <br/> <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="seqfunc.html#K1">.</a> <font color="Olive">n</font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Olive">x</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="seqfunc.html#K11">lim</a> <font color="Maroon">F</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Olive">x</font></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">e3</font>
 <b>by </b><i>, <a class="ref" href="seqfunc.html#T44">SEQFUNC:44</a>, </i>;<br/><b>reconsider </b><font color="Maroon">Fk</font> = <font color="Maroon">F</font> <a href="seqfunc.html#K1">.</a> <font color="Maroon">k</font> as  <a href="pre_topc.html#V5">continuous</a> <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">T</font>,<a href="topmetr.html#K3">R^1</a>  <b>by </b><i/>;<br/><a NAME="E7:26_1_1"/>
<font color="Maroon">Fk</font> <a href="tmap_1.html#R1">is_continuous_at</a> <font color="Maroon">p</font>
 <b>by </b><i><a class="ref" href="tmap_1.html#T49">TMAP_1:49</a></i>;<br/><b>then consider </b><font color="Maroon">H</font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font><b> such that </b><br/><a NAME="E9:26_1_1"/><i><font color="Green">E46</font></i>: 
( <font color="Maroon">H</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">H</font> &amp; ( for <font color="Olive">y</font> being  <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font>  st <font color="Olive">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">H</font> holds <br/> <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">Fk</font> <a href="seq_1.html#K2">.</a> <font color="Olive">y</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">Fk</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">e3</font> ) )
 <b>by </b><i>, </i>;<br/><b>take </b><font color="Maroon">H</font> = <font color="Maroon">H</font>;<br/><b>thus </b><a NAME="E10:26_1_1"/>
( <font color="Maroon">H</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">H</font> )
 <b>by </b><i/>;<br/><b>let </b><font color="Maroon">y</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font>;<br/><b>assume </b><a NAME="E11:26_1_1"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">H</font>
 ;<br/><a NAME="E12:26_1_1"/><i><font color="Green">E57</font></i>: 
 <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">Fk</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">y</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">Fk</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">e3</font>
 <b>by </b><i>, </i>;<br/><a NAME="E13:26_1_1"/>
(  <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">Fk</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">l</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">e3</font> &amp;  <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">Fk</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">y</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">l</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">e3</font> )
 <b>by </b><i/>;<br/><a NAME="E14:26_1_1"/><b>then </b><i><font color="Green">E60</font></i>: 
(  <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">Fk</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">l</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">e3</font> &amp;  <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">Fk</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">y</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">l</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">y</font></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">e3</font> )
 <b>by </b><i><a class="ref" href="complex1.html#T138">COMPLEX1:138</a></i>;<br/><a NAME="E15:26_1_1"/><i><font color="Green">E61</font></i>: 
 <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">Fk</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">l</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><font color="Maroon">Fk</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><font color="Maroon">l</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">y</font></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="complex1.html#K18">abs</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">Fk</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">l</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="complex1.html#K18">abs</a> <span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">Fk</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">y</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">l</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">y</font></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="complex1.html#T142">COMPLEX1:142</a></i>;<br/><a NAME="E16:26_1_1"/>
<span class="p1">(<span class="default"><a href="complex1.html#K18">abs</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">Fk</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">l</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="complex1.html#K18">abs</a> <span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">Fk</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">y</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">l</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">y</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">e3</font> <a href="real_1.html#K3">+</a> <font color="Maroon">e3</font>
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T10">XREAL_1:10</a></i>;<br/><a NAME="E17:26_1_1"/><b>then </b><i><font color="Green">E62</font></i>: 
 <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">Fk</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">l</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><font color="Maroon">Fk</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><font color="Maroon">l</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">y</font></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;</a> 2 <a href="real_1.html#K4">*</a> <font color="Maroon">e3</font>
 <b>by </b><i>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E18:26_1_1"/><i><font color="Green">E64</font></i>: 
 <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">Fk</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">y</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">Fk</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">Fk</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">l</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p5">(<span class="default"><font color="Maroon">Fk</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><font color="Maroon">l</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">y</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="complex1.html#K18">abs</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">Fk</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">y</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">Fk</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="complex1.html#K18">abs</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">Fk</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">l</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p5">(<span class="default"><font color="Maroon">Fk</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><font color="Maroon">l</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">y</font></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="complex1.html#T142">COMPLEX1:142</a></i>;<br/><a NAME="E19:26_1_1"/>
<span class="p1">(<span class="default"><a href="complex1.html#K18">abs</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">Fk</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">y</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">Fk</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="complex1.html#K18">abs</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">Fk</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">l</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p5">(<span class="default"><font color="Maroon">Fk</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><font color="Maroon">l</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">y</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">e3</font> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default">2 <a href="real_1.html#K4">*</a> <font color="Maroon">e3</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="xreal_1.html#T10">XREAL_1:10</a></i>;<br/><b>hence </b><a NAME="E20:26_1_1"/>
 <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">l</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">y</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">l</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">e</font>
 <b>by </b><i>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E2:26_1"/>
<font color="Maroon">l</font> <a href="tmap_1.html#R1">is_continuous_at</a> <font color="Maroon">p</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:26"/>
 <a href="seqfunc.html#K11">lim</a> <font color="Maroon">F</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font> is  <a href="pre_topc.html#V5">continuous</a> <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">T</font>,<a href="topmetr.html#K3">R^1</a> 
 <b>by </b><i><a class="ref" href="tmap_1.html#T49">TMAP_1:49</a></i>;<br/>


</div>
