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

<b>let </b><font color="Maroon" title="c1">T</font>, <font color="Maroon" title="c2">S</font> be   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">f</font> being  <a href="struct_0.html#NM10" title="STRUCT_0:NM.10">PartFunc</a> of <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c1">T</font>  st  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Olive" title="b1">f</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>  &amp;  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Olive" title="b1">f</font> is <a href="nfcont_1.html#V1" title="NFCONT_1:attr.1">compact</a> &amp; <font color="Olive" title="b1">f</font> <a href="nfcont_1.html#R3" title="NFCONT_1:pred.3">is_continuous_on</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Olive" title="b1">f</font> holds <br/> ex <font color="Olive" title="b2">x1</font>, <font color="Olive" title="b3">x2</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">S</font> st <br/>( <font color="Olive" title="b2">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> <font color="Olive" title="b1">f</font> &amp; <font color="Olive" title="b3">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> <font color="Olive" title="b1">f</font> &amp; <span class="p1"><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">||.</a><span class="default"><font color="Olive" title="b1">f</font></span><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">.||</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b2">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="nfcont_1.html#K1" title="NFCONT_1:func.1">||.</a><span class="default"><font color="Olive" title="b1">f</font></span><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">.||</a></span></span>)</span> &amp; <span class="p1"><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">||.</a><span class="default"><font color="Olive" title="b1">f</font></span><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">.||</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b3">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="nfcont_1.html#K1" title="NFCONT_1:func.1">||.</a><span class="default"><font color="Olive" title="b1">f</font></span><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">.||</a></span></span>)</span> )</span><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="c2">S</font>,<font color="Maroon" title="c1">T</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f</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>  &amp;  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f</font> is <a href="nfcont_1.html#V1" title="NFCONT_1:attr.1">compact</a> &amp; <font color="Maroon" title="c3">f</font> <a href="nfcont_1.html#R3" title="NFCONT_1:pred.3">is_continuous_on</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f</font> implies  ex <font color="Olive" title="b1">x1</font>, <font color="Olive" title="b2">x2</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">S</font> st <br/>( <font color="Olive" title="b1">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> <font color="Maroon" title="c3">f</font> &amp; <font color="Olive" title="b2">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> <font color="Maroon" title="c3">f</font> &amp; <span class="p1"><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">.||</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b1">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="nfcont_1.html#K1" title="NFCONT_1:func.1">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">.||</a></span></span>)</span> &amp; <span class="p1"><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">.||</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b2">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="nfcont_1.html#K1" title="NFCONT_1:func.1">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">.||</a></span></span>)</span> ) )</span><br/>





<b>assume </b><b>that </b><br/><a NAME="E1:52"/><i><font color="Green" title="E41">A1</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#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="E2:52"/><i><font color="Green" title="E42">A2</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f</font> is <a href="nfcont_1.html#V1" title="NFCONT_1:attr.1">compact</a>
 <b>and </b><br/><a NAME="E3:52"/><i><font color="Green" title="E43">A3</font></i>: 
<font color="Maroon" title="c3">f</font> <a href="nfcont_1.html#R3" title="NFCONT_1:pred.3">is_continuous_on</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">x1</font>, <font color="Olive" title="b2">x2</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">S</font> st <br/>( <font color="Olive" title="b1">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> <font color="Maroon" title="c3">f</font> &amp; <font color="Olive" title="b2">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> <font color="Maroon" title="c3">f</font> &amp; <span class="p1"><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">.||</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b1">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="nfcont_1.html#K1" title="NFCONT_1:func.1">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">.||</a></span></span>)</span> &amp; <span class="p1"><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">.||</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b2">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="nfcont_1.html#K1" title="NFCONT_1:func.1">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">.||</a></span></span>)</span> )</span><br/>

<a NAME="E4:52"/><i><font color="Green" title="E44">A4</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1"><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">.||</a></span> is <a href="nfcont_1.html#V1" title="NFCONT_1:attr.1">compact</a>
 
<b>by </b><i><a class="txt" href="nfcont_1.html#E2:52"><i><font color="Green" title="E42">A2</font></i></a>, <a class="ref" href="nfcont_1.html#D2" target="_self" title="NFCONT_1:def.2">Def2</a></i>;<br/>
<a NAME="E5:52"/><i><font color="Green" title="E45">A5</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="nfcont_1.html#K1" title="NFCONT_1:func.1">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">.||</a></span>
 
<b>by </b><i><a class="ref" href="nfcont_1.html#D2" target="_self" title="NFCONT_1:def.2">Def2</a></i>;<br/>
<a NAME="E6:52"/><b>then </b><i><font color="Green" title="E46">A6</font></i>: 
<span class="p1"><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">.||</a></span> <a href="nfcont_1.html#R4" title="NFCONT_1:pred.4">is_continuous_on</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1"><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">.||</a></span>
 
<b>by </b><i><a class="txt" href="nfcont_1.html#E3:52"><i><font color="Green" title="E43">A3</font></i></a>, <a class="ref" href="nfcont_1.html#T35" target="_self" title="NFCONT_1:th.35">Th35</a></i>;<br/>
<a NAME="E7:52"/><i><font color="Green" title="E47">A7</font></i>: 
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p1"><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">.||</a></span> <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>by </b><i><a class="txt" href="nfcont_1.html#E1:52"><i><font color="Green" title="E41">A1</font></i></a>, <a class="txt" href="nfcont_1.html#E5:52"><i><font color="Green" title="E45">A5</font></i></a>, <a class="ref" href="relat_1.html#T65" title="RELAT_1:th.65">RELAT_1:65</a></i>;<br/>
<a NAME="E8:52"/>
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p1"><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">.||</a></span> is <a href="rcomp_1.html#V1" title="RCOMP_1:attr.1">compact</a>
 
<b>by </b><i><a class="txt" href="nfcont_1.html#E4:52"><i><font color="Green" title="E44">A4</font></i></a>, <a class="txt" href="nfcont_1.html#E6:52"><i><font color="Green" title="E46">A6</font></i></a>, <a class="ref" href="nfcont_1.html#T38" target="_self" title="NFCONT_1:th.38">Th38</a></i>;<br/>
<a NAME="E9:52"/><b>then </b><i><font color="Green" title="E48">A8</font></i>: 
(  <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="nfcont_1.html#K1" title="NFCONT_1:func.1">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">.||</a></span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p1"><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">.||</a></span> &amp;  <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="nfcont_1.html#K1" title="NFCONT_1:func.1">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">.||</a></span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p1"><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">.||</a></span> )
 
<b>by </b><i><a class="txt" href="nfcont_1.html#E7:52"><i><font color="Green" title="E47">A7</font></i></a>, <a class="ref" href="rcomp_1.html#T32" title="RCOMP_1:th.32">RCOMP_1:32</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c4">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S</font><b> such that </b><br/><a NAME="E11:52"/><i><font color="Green" title="E49">A9</font></i>: 
( <font color="Maroon" title="c4">x</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="nfcont_1.html#K1" title="NFCONT_1:func.1">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">.||</a></span> &amp;  <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="nfcont_1.html#K1" title="NFCONT_1:func.1">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">.||</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">.||</a></span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c4">x</font> )
 <b>by </b><i><a class="ref" href="partfun1.html#T26" title="PARTFUN1:th.26">PARTFUN1:26</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c5">y</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S</font><b> such that </b><br/><a NAME="E13:52"/><i><font color="Green" title="E50">A10</font></i>: 
( <font color="Maroon" title="c5">y</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="nfcont_1.html#K1" title="NFCONT_1:func.1">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">.||</a></span> &amp;  <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="nfcont_1.html#K1" title="NFCONT_1:func.1">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">.||</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">.||</a></span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c5">y</font> )
 <b>by </b><i><a class="txt" href="nfcont_1.html#E9:52"><i><font color="Green" title="E48">A8</font></i></a>, <a class="ref" href="partfun1.html#T26" title="PARTFUN1:th.26">PARTFUN1:26</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c4">x</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">x2</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">S</font> st <br/>( <font color="Maroon" title="c4">x</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> <font color="Maroon" title="c3">f</font> &amp; <font color="Olive" title="b1">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> <font color="Maroon" title="c3">f</font> &amp; <span class="p1"><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">.||</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c4">x</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="nfcont_1.html#K1" title="NFCONT_1:func.1">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">.||</a></span></span>)</span> &amp; <span class="p1"><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">.||</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b1">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="nfcont_1.html#K1" title="NFCONT_1:func.1">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">.||</a></span></span>)</span> )</span><br/>

<b>take </b>
<font color="Maroon" title="c5">y</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">x</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> <font color="Maroon" title="c3">f</font> &amp; <font color="Maroon" title="c5">y</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> <font color="Maroon" title="c3">f</font> &amp; <span class="p1"><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">.||</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c4">x</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="nfcont_1.html#K1" title="NFCONT_1:func.1">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">.||</a></span></span>)</span> &amp; <span class="p1"><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">.||</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c5">y</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="nfcont_1.html#K1" title="NFCONT_1:func.1">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">.||</a></span></span>)</span> )</span><br/>

<b>thus </b><a NAME="E14:52"/>
( <font color="Maroon" title="c4">x</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> <font color="Maroon" title="c3">f</font> &amp; <font color="Maroon" title="c5">y</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> <font color="Maroon" title="c3">f</font> &amp; <span class="p1"><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">.||</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c4">x</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="nfcont_1.html#K1" title="NFCONT_1:func.1">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">.||</a></span></span>)</span> &amp; <span class="p1"><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">.||</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c5">y</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="nfcont_1.html#K1" title="NFCONT_1:func.1">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">.||</a></span></span>)</span> )
 <b>by </b><i><a class="txt" href="nfcont_1.html#E11:52"><i><font color="Green" title="E49">A9</font></i></a>, <a class="txt" href="nfcont_1.html#E13:52"><i><font color="Green" title="E50">A10</font></i></a>, <a class="ref" href="nfcont_1.html#D2" target="_self" title="NFCONT_1:def.2">Def2</a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</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>
