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<b>let </b><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>;<br/>

<b>assume </b><a NAME="E1:100_1_1"/><i><font color="Green" title="E58">A1</font></i>: 
<font color="Maroon" title="c2">f</font> is <a href="pscomp_1.html#V9" title="PSCOMP_1:attr.9">continuous</a>
 ;<br/>

<b>hence </b><a NAME="E2:100_1_1"/>
<font color="Maroon" title="c2">f</font> is <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a>
 <b>by </b><i><a class="ref" href="pscomp_1.html#D27" target="_self" title="PSCOMP_1:def.27">Def27</a></i>;<br/>

<a NAME="E3:100_1_1"/><i><font color="Green" title="E59">A2</font></i>: 
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#V9" title="PSCOMP_1:attr.9">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>
 
<b>by </b><i><a class="ref" href="pscomp_1.html#D27" target="_self" title="PSCOMP_1:def.27">Def27</a></i>;<br/>
<a NAME="E4:100_1_1"/><b>then </b><i><font color="Green" title="E60">A3</font></i>: 
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#V9" title="PSCOMP_1:attr.9">continuous</a> holds <br/><font color="Olive" title="b1">f</font> is <a href="pscomp_1.html#V7" title="PSCOMP_1:attr.7">with_max</a>
 
<b>by </b><i><a class="ref" href="pscomp_1.html#T61" target="_self" title="PSCOMP_1:th.61">Th61</a></i>;<br/>
<b>thus </b><a NAME="E5:100_1_1"/>
<font color="Maroon" title="c2">f</font> is <a href="pscomp_1.html#V7" title="PSCOMP_1:attr.7">with_max</a>
 <b>by </b><i><a class="txt" href="pscomp_1.html#E1:100_1_1"><i><font color="Green" title="E58">A1</font></i></a>, <a class="txt" href="pscomp_1.html#E3:100_1_1"><i><font color="Green" title="E59">A2</font></i></a>, <a class="ref" href="pscomp_1.html#T61" target="_self" title="PSCOMP_1:th.61">Th61</a></i>;<br/>

<b>thus </b><a NAME="E6:100_1_1"/>
<font color="Maroon" title="c2">f</font> is <a href="pscomp_1.html#V8" title="PSCOMP_1:attr.8">with_min</a>
 <b>by </b><i><a class="txt" href="pscomp_1.html#E1:100_1_1"><i><font color="Green" title="E58">A1</font></i></a>, <a class="txt" href="pscomp_1.html#E4:100_1_1"><i><font color="Green" title="E60">A3</font></i></a>, <a class="ref" href="pscomp_1.html#T60" target="_self" title="PSCOMP_1:th.60">Th60</a></i>;<br/>


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