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

<span class="kw">let </span><font color="Maroon" title="c2">f</font> be   <a href="pscomp_1.html#NM1" title="PSCOMP_1:NM.1">RealMap</a> of <font color="Maroon" title="c1">T</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="c2">f</font> is  <a href="pscomp_1.html#V1" title="PSCOMP_1:attr.1">continuous</a>  implies ( <font color="Maroon" title="c2">f</font> is  <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a>  &amp; <font color="Maroon" title="c2">f</font> is  <a href="measure6.html#V5" title="MEASURE6:attr.5">with_max</a>  &amp; <font color="Maroon" title="c2">f</font> is  <a href="measure6.html#V6" title="MEASURE6:attr.6">with_min</a>  ) )</span><br/>

<span class="kw">assume </span><a NAME="E1:30_1_1"/><span class="lab"><font color="Green" title="E15">A1</font></span>: 
<font color="Maroon" title="c2">f</font> is  <a href="pscomp_1.html#V1" title="PSCOMP_1:attr.1">continuous</a> 
 ; <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="c2">f</font> is  <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a>  &amp; <font color="Maroon" title="c2">f</font> is  <a href="measure6.html#V5" title="MEASURE6:attr.5">with_max</a>  &amp; <font color="Maroon" title="c2">f</font> is  <a href="measure6.html#V6" title="MEASURE6:attr.6">with_min</a>  )</span><br/>

<span class="kw">hence </span><a NAME="E2:30_1_1"/>
<font color="Maroon" title="c2">f</font> is  <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pscomp_1.html#D4" target="_self" title="PSCOMP_1:def.4">Def27</a></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="c2">f</font> is  <a href="measure6.html#V5" title="MEASURE6:attr.5">with_max</a>  &amp; <font color="Maroon" title="c2">f</font> is  <a href="measure6.html#V6" title="MEASURE6:attr.6">with_min</a>  )</span><br/>

<a NAME="E3:30_1_1"/><span class="lab"><font color="Green" title="E16">A2</font></span>: 
 for <font color="Olive" title="b1">f</font> being   <a href="pscomp_1.html#NM1" title="PSCOMP_1:NM.1">RealMap</a> of <font color="Maroon" title="c1">T</font>  st <font color="Olive" title="b1">f</font> is  <a href="pscomp_1.html#V1" title="PSCOMP_1:attr.1">continuous</a>  holds <br/><font color="Olive" title="b1">f</font> is  <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pscomp_1.html#D4" target="_self" title="PSCOMP_1:def.4">Def27</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:30_1_1"/>
<font color="Maroon" title="c2">f</font> is  <a href="measure6.html#V5" title="MEASURE6:attr.5">with_max</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:30_1_1"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="ref" href="pscomp_1.html#T15" target="_self" title="PSCOMP_1:th.15">Th61</a></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="c2">f</font> is  <a href="measure6.html#V6" title="MEASURE6:attr.6">with_min</a> </span><br/>

<a NAME="E5:30_1_1"/>
 for <font color="Olive" title="b1">f</font> being   <a href="pscomp_1.html#NM1" title="PSCOMP_1:NM.1">RealMap</a> of <font color="Maroon" title="c1">T</font>  st <font color="Olive" title="b1">f</font> is  <a href="pscomp_1.html#V1" title="PSCOMP_1:attr.1">continuous</a>  holds <br/><font color="Olive" title="b1">f</font> is  <a href="measure6.html#V5" title="MEASURE6:attr.5">with_max</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:30_1_1"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="ref" href="pscomp_1.html#T15" target="_self" title="PSCOMP_1:th.15">Th61</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:30_1_1"/>
<font color="Maroon" title="c2">f</font> is  <a href="measure6.html#V6" title="MEASURE6:attr.6">with_min</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:30_1_1"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="ref" href="pscomp_1.html#T14" target="_self" title="PSCOMP_1:th.14">Th60</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>
