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

<b>let </b><font color="Maroon" title="c1">CNS</font> be   <a href="clvect_1.html#NM5" title="CLVECT_1:NM.5">ComplexNormSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">RNS</font> be   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a>;<br/><b>let </b><font color="Maroon" title="c3">f</font> be   <a href="struct_0.html#NM10" title="STRUCT_0:NM.10">PartFunc</a> of <font color="Maroon" title="c1">CNS</font>,<font color="Maroon" title="c2">RNS</font>;<br/><b>let </b><font color="Maroon" title="c4">Y</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">CNS</font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:139"/><i><font color="Green" title="E104">A1</font></i>: 
<font color="Maroon" title="c4">Y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>and </b><br/><a NAME="E2:139"/><i><font color="Green" title="E105">A2</font></i>: 
<font color="Maroon" title="c4">Y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f</font>
 <b>and </b><br/><a NAME="E3:139"/><i><font color="Green" title="E106">A3</font></i>: 
<font color="Maroon" title="c4">Y</font> is <a href="ncfcont1.html#V1" title="NCFCONT1:attr.1">compact</a>
 <b>and </b><br/><a NAME="E4:139"/><i><font color="Green" title="E107">A4</font></i>: 
<font color="Maroon" title="c3">f</font> <a href="ncfcont1.html#R8" title="NCFCONT1:pred.8">is_continuous_on</a> <font color="Maroon" title="c4">Y</font>
 ;<br/>

<i><font color="Green" title="E108">A5</font></i>:  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c4">Y</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c4">Y</font>
<b>by </b><i><a class="ref" href="relat_1.html#T90" title="RELAT_1:th.90">RELAT_1:90</a></i>
<br/>.= 
<font color="Maroon" title="c4">Y</font>
<b>by </b><i><a class="txt" href="ncfcont1.html#E2:139"><i><font color="Green" title="E105">A2</font></i></a>, <a class="ref" href="xboole_1.html#T28" title="XBOOLE_1:th.28">XBOOLE_1:28</a></i>
;<br/>
<a NAME="E6:139"/>
<font color="Maroon" title="c3">f</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c4">Y</font> <a href="ncfcont1.html#R8" title="NCFCONT1:pred.8">is_continuous_on</a> <font color="Maroon" title="c4">Y</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="139_2"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:139_2"/>
<font color="Maroon" title="c4">Y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c4">Y</font></span>)</span>
 <b>by </b><i><a class="txt" href="ncfcont1.html#E5:139"><i><font color="Green" title="E108">A5</font></i></a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="ncfcont1.html#D22" target="_self" title="NCFCONT1:def.22">NCFCONT1:def 22</a><br/>

<b>let </b><font color="Maroon" title="c5">r</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">CNS</font>;<br/>

<b>assume </b><a NAME="E2:139_2"/>
<font color="Maroon" title="c5">r</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">Y</font>
 ;<br/>

<a NAME="E3:139_2"/><b>then </b>
<font color="Maroon" title="c3">f</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c4">Y</font> <a href="ncfcont1.html#R2" title="NCFCONT1:pred.2">is_continuous_in</a> <font color="Maroon" title="c5">r</font>
 
<b>by </b><i><a class="txt" href="ncfcont1.html#E4:139"><i><font color="Green" title="E107">A4</font></i></a>, <a class="ref" href="ncfcont1.html#D22" target="_self" title="NCFCONT1:def.22">Def22</a></i>;<br/>
<b>hence </b><a NAME="E4:139_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c4">Y</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c4">Y</font> <a href="ncfcont1.html#R2" title="NCFCONT1:pred.2">is_continuous_in</a> <font color="Maroon" title="c5">r</font>
 <b>by </b><i><a class="ref" href="relat_1.html#T101" title="RELAT_1:th.101">RELAT_1:101</a></i>;<br/>


</div><b>end;</b></div>
<b>then consider </b><font color="Maroon" title="c5">x1</font>, <font color="Maroon" title="c6">x2</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">CNS</font><b> such that </b><br/><a NAME="E8:139"/><i><font color="Green" title="E109">A6</font></i>: 
( <font color="Maroon" title="c5">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c4">Y</font></span>)</span> &amp; <font color="Maroon" title="c6">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c4">Y</font></span>)</span> &amp; <span class="p1"><a href="ncfcont1.html#K2" title="NCFCONT1:func.2">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c4">Y</font></span>)</span></span><a href="ncfcont1.html#K2" title="NCFCONT1:func.2">.||</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c5">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="seq_4.html#K4" title="SEQ_4:func.4">upper_bound</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p2"><a href="ncfcont1.html#K2" title="NCFCONT1:func.2">||.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c4">Y</font></span>)</span></span><a href="ncfcont1.html#K2" title="NCFCONT1:func.2">.||</a></span></span>)</span> &amp; <span class="p1"><a href="ncfcont1.html#K2" title="NCFCONT1:func.2">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c4">Y</font></span>)</span></span><a href="ncfcont1.html#K2" title="NCFCONT1:func.2">.||</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">x2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="seq_4.html#K5" title="SEQ_4:func.5">lower_bound</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p2"><a href="ncfcont1.html#K2" title="NCFCONT1:func.2">||.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c4">Y</font></span>)</span></span><a href="ncfcont1.html#K2" title="NCFCONT1:func.2">.||</a></span></span>)</span> )
 <b>by </b><i><a class="txt" href="ncfcont1.html#E1:139"><i><font color="Green" title="E104">A1</font></i></a>, <a class="txt" href="ncfcont1.html#E3:139"><i><font color="Green" title="E106">A3</font></i></a>, <a class="txt" href="ncfcont1.html#E5:139"><i><font color="Green" title="E108">A5</font></i></a>, <a class="ref" href="ncfcont1.html#T109" target="_self" title="NCFCONT1:th.109">Th109</a></i>;<br/>
<a NAME="E9:139"/><i><font color="Green" title="E110">A7</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1"><a href="ncfcont1.html#K2" title="NCFCONT1:func.2">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="ncfcont1.html#K2" title="NCFCONT1:func.2">.||</a></span>
 
<b>by </b><i><a class="ref" href="ncfcont1.html#D3" target="_self" title="NCFCONT1:def.3">Def3</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c5">x1</font>
;<br/>

<b>take </b>
<font color="Maroon" title="c6">x2</font>
;<br/>

<b>thus </b><a NAME="E10:139"/>
( <font color="Maroon" title="c5">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">Y</font> &amp; <font color="Maroon" title="c6">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">Y</font> )
 <b>by </b><i><a class="txt" href="ncfcont1.html#E5:139"><i><font color="Green" title="E108">A5</font></i></a>, <a class="txt" href="ncfcont1.html#E8:139"><i><font color="Green" title="E109">A6</font></i></a></i>;<br/>

<a NAME="E11:139"/><i><font color="Green" title="E111">A8</font></i>: 
( <font color="Maroon" title="c5">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1"><a href="ncfcont1.html#K2" title="NCFCONT1:func.2">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c4">Y</font></span>)</span></span><a href="ncfcont1.html#K2" title="NCFCONT1:func.2">.||</a></span> &amp; <font color="Maroon" title="c6">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1"><a href="ncfcont1.html#K2" title="NCFCONT1:func.2">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c4">Y</font></span>)</span></span><a href="ncfcont1.html#K2" title="NCFCONT1:func.2">.||</a></span> )
 
<b>by </b><i><a class="txt" href="ncfcont1.html#E8:139"><i><font color="Green" title="E109">A6</font></i></a>, <a class="ref" href="ncfcont1.html#D3" target="_self" title="NCFCONT1:def.3">Def3</a></i>;<br/>
<b>then </b><i><font color="Green" title="E112">A9</font></i>: <span class="p1"><a href="ncfcont1.html#K2" title="NCFCONT1:func.2">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c4">Y</font></span>)</span></span><a href="ncfcont1.html#K2" title="NCFCONT1:func.2">.||</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c5">x1</font> = 
<span class="p1"><a href="ncfcont1.html#K2" title="NCFCONT1:func.2">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c4">Y</font></span>)</span></span><a href="ncfcont1.html#K2" title="NCFCONT1:func.2">.||</a></span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c5">x1</font>
<b>by </b><i><a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></i>
<br/>.= 
<span class="p1"><a href="normsp_1.html#K1" title="NORMSP_1:func.1">||.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c4">Y</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c5">x1</font></span>)</span></span><a href="normsp_1.html#K1" title="NORMSP_1:func.1">.||</a></span>
<b>by </b><i><a class="txt" href="ncfcont1.html#E11:139"><i><font color="Green" title="E111">A8</font></i></a>, <a class="ref" href="ncfcont1.html#D3" target="_self" title="NCFCONT1:def.3">Def3</a></i>
<br/>.= 
<span class="p1"><a href="normsp_1.html#K1" title="NORMSP_1:func.1">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c5">x1</font></span>)</span></span><a href="normsp_1.html#K1" title="NORMSP_1:func.1">.||</a></span>
<b>by </b><i><a class="txt" href="ncfcont1.html#E8:139"><i><font color="Green" title="E109">A6</font></i></a>, <a class="ref" href="partfun2.html#T32" title="PARTFUN2:th.32">PARTFUN2:32</a></i>
<br/>.= 
<span class="p1"><a href="ncfcont1.html#K2" title="NCFCONT1:func.2">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="ncfcont1.html#K2" title="NCFCONT1:func.2">.||</a></span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c5">x1</font>
<b>by </b><i><a class="txt" href="ncfcont1.html#E2:139"><i><font color="Green" title="E105">A2</font></i></a>, <a class="txt" href="ncfcont1.html#E5:139"><i><font color="Green" title="E108">A5</font></i></a>, <a class="txt" href="ncfcont1.html#E8:139"><i><font color="Green" title="E109">A6</font></i></a>, <a class="txt" href="ncfcont1.html#E9:139"><i><font color="Green" title="E110">A7</font></i></a>, <a class="ref" href="ncfcont1.html#D3" target="_self" title="NCFCONT1:def.3">Def3</a></i>
<br/>.= 
<span class="p1"><a href="ncfcont1.html#K2" title="NCFCONT1:func.2">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="ncfcont1.html#K2" title="NCFCONT1:func.2">.||</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c5">x1</font>
<b>by </b><i><a class="txt" href="ncfcont1.html#E2:139"><i><font color="Green" title="E105">A2</font></i></a>, <a class="txt" href="ncfcont1.html#E5:139"><i><font color="Green" title="E108">A5</font></i></a>, <a class="txt" href="ncfcont1.html#E8:139"><i><font color="Green" title="E109">A6</font></i></a>, <a class="txt" href="ncfcont1.html#E9:139"><i><font color="Green" title="E110">A7</font></i></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></i>
;<br/>
<i><font color="Green" title="E113">A10</font></i>: <span class="p1"><a href="ncfcont1.html#K2" title="NCFCONT1:func.2">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c4">Y</font></span>)</span></span><a href="ncfcont1.html#K2" title="NCFCONT1:func.2">.||</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">x2</font> = 
<span class="p1"><a href="ncfcont1.html#K2" title="NCFCONT1:func.2">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c4">Y</font></span>)</span></span><a href="ncfcont1.html#K2" title="NCFCONT1:func.2">.||</a></span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c6">x2</font>
<b>by </b><i><a class="txt" href="ncfcont1.html#E11:139"><i><font color="Green" title="E111">A8</font></i></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></i>
<br/>.= 
<span class="p1"><a href="normsp_1.html#K1" title="NORMSP_1:func.1">||.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c4">Y</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">x2</font></span>)</span></span><a href="normsp_1.html#K1" title="NORMSP_1:func.1">.||</a></span>
<b>by </b><i><a class="txt" href="ncfcont1.html#E11:139"><i><font color="Green" title="E111">A8</font></i></a>, <a class="ref" href="ncfcont1.html#D3" target="_self" title="NCFCONT1:def.3">Def3</a></i>
<br/>.= 
<span class="p1"><a href="normsp_1.html#K1" title="NORMSP_1:func.1">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">x2</font></span>)</span></span><a href="normsp_1.html#K1" title="NORMSP_1:func.1">.||</a></span>
<b>by </b><i><a class="txt" href="ncfcont1.html#E8:139"><i><font color="Green" title="E109">A6</font></i></a>, <a class="ref" href="partfun2.html#T32" title="PARTFUN2:th.32">PARTFUN2:32</a></i>
<br/>.= 
<span class="p1"><a href="ncfcont1.html#K2" title="NCFCONT1:func.2">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="ncfcont1.html#K2" title="NCFCONT1:func.2">.||</a></span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c6">x2</font>
<b>by </b><i><a class="txt" href="ncfcont1.html#E2:139"><i><font color="Green" title="E105">A2</font></i></a>, <a class="txt" href="ncfcont1.html#E5:139"><i><font color="Green" title="E108">A5</font></i></a>, <a class="txt" href="ncfcont1.html#E8:139"><i><font color="Green" title="E109">A6</font></i></a>, <a class="txt" href="ncfcont1.html#E9:139"><i><font color="Green" title="E110">A7</font></i></a>, <a class="ref" href="ncfcont1.html#D3" target="_self" title="NCFCONT1:def.3">Def3</a></i>
<br/>.= 
<span class="p1"><a href="ncfcont1.html#K2" title="NCFCONT1:func.2">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="ncfcont1.html#K2" title="NCFCONT1:func.2">.||</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">x2</font>
<b>by </b><i><a class="txt" href="ncfcont1.html#E2:139"><i><font color="Green" title="E105">A2</font></i></a>, <a class="txt" href="ncfcont1.html#E5:139"><i><font color="Green" title="E108">A5</font></i></a>, <a class="txt" href="ncfcont1.html#E8:139"><i><font color="Green" title="E109">A6</font></i></a>, <a class="txt" href="ncfcont1.html#E9:139"><i><font color="Green" title="E110">A7</font></i></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></i>
;<br/>
<span class="p1"><a href="ncfcont1.html#K2" title="NCFCONT1:func.2">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="ncfcont1.html#K2" title="NCFCONT1:func.2">.||</a></span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c4">Y</font> = 
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p1">(<span class="default"><span class="p2"><a href="ncfcont1.html#K2" title="NCFCONT1:func.2">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="ncfcont1.html#K2" title="NCFCONT1:func.2">.||</a></span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c4">Y</font></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T148" title="RELAT_1:th.148">RELAT_1:148</a></i>
<br/>.= 
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p1"><a href="ncfcont1.html#K2" title="NCFCONT1:func.2">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c4">Y</font></span>)</span></span><a href="ncfcont1.html#K2" title="NCFCONT1:func.2">.||</a></span>
<b>by </b><i><a class="ref" href="ncfcont1.html#T112" target="_self" title="NCFCONT1:th.112">Th112</a></i>
;<br/>
<b>hence </b><a NAME="E15:139"/>
( <span class="p1"><a href="ncfcont1.html#K2" title="NCFCONT1:func.2">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="ncfcont1.html#K2" title="NCFCONT1:func.2">.||</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c5">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="seq_4.html#K4" title="SEQ_4:func.4">upper_bound</a> <span class="p1">(<span class="default"><span class="p2"><a href="ncfcont1.html#K2" title="NCFCONT1:func.2">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="ncfcont1.html#K2" title="NCFCONT1:func.2">.||</a></span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c4">Y</font></span>)</span> &amp; <span class="p1"><a href="ncfcont1.html#K2" title="NCFCONT1:func.2">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="ncfcont1.html#K2" title="NCFCONT1:func.2">.||</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">x2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="seq_4.html#K5" title="SEQ_4:func.5">lower_bound</a> <span class="p1">(<span class="default"><span class="p2"><a href="ncfcont1.html#K2" title="NCFCONT1:func.2">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="ncfcont1.html#K2" title="NCFCONT1:func.2">.||</a></span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c4">Y</font></span>)</span> )
 <b>by </b><i><a class="txt" href="ncfcont1.html#E8:139"><i><font color="Green" title="E109">A6</font></i></a>, <a class="txt" href="ncfcont1.html#E12:139"><i><font color="Green" title="E112">A9</font></i></a>, <a class="txt" href="ncfcont1.html#E13:139"><i><font color="Green" title="E113">A10</font></i></a></i>;<br/>


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