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<b>let </b><font color="Maroon">f</font> be  <a href="funct_1.html#V2">one-to-one</a> <a href="pre_topc.html#V5">continuous</a> <a href="struct_0.html#NM6">Function</a> of <a href="topmetr.html#K3">R^1</a> ,<a href="topmetr.html#K3">R^1</a> ;<br/><b>let </b><font color="Maroon">g</font> be   <a href="partfun1.html#NM1">PartFunc</a> of  <a href="numbers.html#K1">REAL</a> , <a href="numbers.html#K1">REAL</a> ;<br/>



<b>assume </b><a NAME="E1:13"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font>
 ;<br/>

<a NAME="E2:13"/><b>then </b>
<font color="Maroon">g</font> <a href="fcont_1.html#R2">is_continuous_on</a>  <a href="numbers.html#K1">REAL</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E3:13"/><b>then </b>
<font color="Maroon">g</font> <a href="fcont_1.html#R2">is_continuous_on</a> <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default">0,1</span><a href="rcomp_1.html#K1">.]</a></span>
 
<b>by </b><i><a class="ref" href="fcont_1.html#T17">FCONT_1:17</a></i>;<br/>
<b>hence </b><a NAME="E4:13"/>
( <font color="Maroon">g</font> <a href="rfunct_2.html#R1">is_increasing_on</a> <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default">0,1</span><a href="rcomp_1.html#K1">.]</a></span> or <font color="Maroon">g</font> <a href="rfunct_2.html#R2">is_decreasing_on</a> <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default">0,1</span><a href="rcomp_1.html#K1">.]</a></span> )
 <b>by </b><i>, <a class="ref" href="fcont_2.html#T18">FCONT_2:18</a></i>;<br/>


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