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<b>let </b><font color="Maroon" title="c1">T</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:95_1"/><i><font color="Green" title="E56">A1</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>
 ;<br/><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="E2:95_1"/>
<font color="Maroon" title="c2">f</font> is <a href="pscomp_1.html#V9" title="PSCOMP_1:attr.9">continuous</a>
 ;<br/><a NAME="E3:95_1"/><b>then </b>
 <a href="valued_1.html#K32" title="VALUED_1:func.32">-</a> <font color="Maroon" title="c2">f</font> is <a href="pscomp_1.html#V9" title="PSCOMP_1:attr.9">continuous</a>
 <b>by </b><i><a class="ref" href="pscomp_1.html#T55" target="_self" title="PSCOMP_1:th.55">Th55</a></i>;<br/><a NAME="E4:95_1"/><b>then </b>
 <a href="valued_1.html#K32" title="VALUED_1:func.32">-</a> <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#E1:95_1"><i><font color="Green" title="E56">A1</font></i></a></i>;<br/><b>hence </b><a NAME="E5:95_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="ref" href="pscomp_1.html#T41" target="_self" title="PSCOMP_1:th.41">Th41</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:95"/><i><font color="Green" title="E56">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="pscomp_1.html#V8" title="PSCOMP_1:attr.8">with_min</a>
 ;<br/>

<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="E3:95"/>
<font color="Maroon" title="c2">f</font> is <a href="pscomp_1.html#V9" title="PSCOMP_1:attr.9">continuous</a>
 ;<br/>

<a NAME="E4:95"/><b>then </b><i><font color="Green" title="E57">A3</font></i>: 
 <a href="valued_1.html#K32" title="VALUED_1:func.32">-</a> <font color="Maroon" title="c2">f</font> is <a href="pscomp_1.html#V9" title="PSCOMP_1:attr.9">continuous</a>
 
<b>by </b><i><a class="ref" href="pscomp_1.html#T55" target="_self" title="PSCOMP_1:th.55">Th55</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c3">Xf</font> = <font color="Maroon" title="c2">f</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">T</font>, <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  ;<br/>
<a NAME="E6:95"/>
 <a href="valued_1.html#K32" title="VALUED_1:func.32">-</a> <span class="p1">(<span class="default"><a href="valued_1.html#K32" title="VALUED_1:func.32">-</a> <font color="Maroon" title="c3">Xf</font></span>)</span> 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#E2:95"><i><font color="Green" title="E56">A2</font></i></a>, <a class="txt" href="pscomp_1.html#E4:95"><i><font color="Green" title="E57">A3</font></i></a>, <a class="txt" href="pscomp_1.html#E63"><i><font color="Green" title="E41">Lm8</font></i></a></i>;<br/>
<b>hence </b><a NAME="E7:95"/>
<font color="Maroon" title="c2">f</font> is <a href="pscomp_1.html#V7" title="PSCOMP_1:attr.7">with_max</a>
 ;<br/>


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