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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:98_1"/><i><font color="Green">E62</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="pscomp_1.html#NM1">RealMap</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>1</sub></font> is <a href="pscomp_1.html#V9" target="_self">continuous</a> holds <br/><font color="Olive">b<sub>1</sub></font> is <a href="pscomp_1.html#V7" target="_self">with_max</a>
 ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="pscomp_1.html#NM1">RealMap</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>assume </b><a NAME="E2:98_1"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="pscomp_1.html#V9" target="_self">continuous</a>
 ;<br/><a NAME="E3:98_1"/><b>then </b>
 <a href="pscomp_1.html#K7" target="_self">-</a> <font color="Maroon">c<sub>2</sub></font> is <a href="pscomp_1.html#V9" target="_self">continuous</a>
 <b>by </b><i><a class="ref" href="pscomp_1.html#T55" target="_self">Th55</a></i>;<br/><a NAME="E4:98_1"/><b>then </b>
 <a href="pscomp_1.html#K7" target="_self">-</a> <font color="Maroon">c<sub>2</sub></font> is <a href="pscomp_1.html#V7" target="_self">with_max</a>
 <b>by </b><i><a class="txt" href="pscomp_1.html#E1:98_1"><i><font color="Green">E62</font></i></a></i>;<br/><b>hence </b><a NAME="E5:98_1"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="pscomp_1.html#V8" target="_self">with_min</a>
 <b>by </b><i><a class="ref" href="pscomp_1.html#T41" target="_self">Th41</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:98"/><i><font color="Green">E62</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="pscomp_1.html#NM1">RealMap</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>1</sub></font> is <a href="pscomp_1.html#V9" target="_self">continuous</a> holds <br/><font color="Olive">b<sub>1</sub></font> is <a href="pscomp_1.html#V8" target="_self">with_min</a>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="pscomp_1.html#NM1">RealMap</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>

<b>assume </b><a NAME="E3:98"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="pscomp_1.html#V9" target="_self">continuous</a>
 ;<br/>

<a NAME="E4:98"/><b>then </b>
 <a href="pscomp_1.html#K7" target="_self">-</a> <font color="Maroon">c<sub>2</sub></font> is <a href="pscomp_1.html#V9" target="_self">continuous</a>
 
<b>by </b><i><a class="ref" href="pscomp_1.html#T55" target="_self">Th55</a></i>;<br/>
<a NAME="E5:98"/><b>then </b><i><font color="Green">E63</font></i>: 
 <a href="pscomp_1.html#K7" target="_self">-</a> <font color="Maroon">c<sub>2</sub></font> is <a href="pscomp_1.html#V8" target="_self">with_min</a>
 
<b>by </b><i><a class="txt" href="pscomp_1.html#E2:98"><i><font color="Green">E62</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>2</sub></font> as   <a href="funct_2.html#NM1">Function</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>, <a href="numbers.html#K1">REAL</a>  ;<br/>
<a NAME="E7:98"/>
 <a href="pscomp_1.html#K7" target="_self">-</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K7" target="_self">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> is <a href="pscomp_1.html#V7" target="_self">with_max</a>
 
<b>by </b><i><a class="txt" href="pscomp_1.html#E5:98"><i><font color="Green">E63</font></i></a>, <a class="txt" href="pscomp_1.html#E64"><i><font color="Green">Lemma43</font></i></a></i>;<br/>
<b>hence </b><a NAME="E8:98"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="pscomp_1.html#V7" target="_self">with_max</a>
 ;<br/>


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