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<b>set </b><font color="Maroon">c</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font>;<br/>
<b>reconsider </b><font color="Maroon">F</font> = <font color="Maroon">f</font> as  <a href="pre_topc.html#V5">continuous</a> <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">T</font>,<a href="topalg_2.html#K3">R^1</a>  <b>by </b><i><a class="ref" href="topmetr.html#T24">TOPMETR:24</a>, <a class="ref" href="topreal6.html#T83">TOPREAL6:83</a></i>;<br/>
<a NAME="E2:93_1_1"/>
for <font color="Olive">q</font> being  <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font>  holds <font color="Maroon">f</font> <a href="seq_1.html#K2">.</a> <font color="Olive">q</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="93_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">q</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font>;<br/>

<a NAME="E1:93_1_1_1"/>
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E2:93_1_1_1"/><b>then </b>
<font color="Maroon">f</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">q</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">f</font>
 
<b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<b>hence </b><a NAME="E3:93_1_1_1"/>
<font color="Maroon">f</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">q</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 <b>by </b><i><a class="ref" href="relat_1.html#D9">RELAT_1:def 9</a></i>;<br/>


</div><b>end;</b></div>
<b>then consider </b><font color="Maroon">H</font> being   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">T</font>,<a href="topalg_2.html#K3">R^1</a> <b> such that </b><br/><a NAME="E4:93_1_1"/><i><font color="Green">E29</font></i>: 
for <font color="Olive">p</font> being  <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font><br/> for <font color="Olive">r1</font> being <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a>   st <font color="Maroon">F</font> <a href="funct_2.html#K3">.</a> <font color="Olive">p</font> <a href="hidden.html#R1">=</a> <font color="Olive">r1</font> holds <br/><font color="Maroon">H</font> <a href="funct_2.html#K3">.</a> <font color="Olive">p</font> <a href="hidden.html#R1">=</a> 1 <a href="xcmplx_0.html#K7">/</a> <font color="Olive">r1</font>
 <b>and </b><br/><a NAME="E5:93_1_1"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">H</font> is <a href="pre_topc.html#V5">continuous</a>
 <b>by </b><i><a class="ref" href="jgraph_2.html#T36">JGRAPH_2:36</a></i>;<br/>
<b>reconsider </b><font color="Maroon">h</font> = <font color="Maroon">H</font> as   <a href="pscomp_1.html#NM1">RealMap</a> of <font color="Maroon">T</font> <b>by </b><i><a class="ref" href="topmetr.html#T24">TOPMETR:24</a></i>;<br/>
<i><font color="Green">E43</font></i>:  <a href="relset_1.html#K4">dom</a> <font color="Maroon">h</font> = 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font>
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span></span>)</span>
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="93_1_1_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">a</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:93_1_1_3"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">h</font>
 ;<br/><b>hence </b><font color="Maroon">h</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">a</font> = 
1 <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">a</font></span>)</span>
<b>by </b><i/>
<br/>.= 
1 <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">a</font></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_0.html#D9">XCMPLX_0:def 9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">a</font></span>)</span> <a href="real_1.html#K2">"</a> 

;<br/><br/></div><b>end;</b></div>
<a NAME="E9:93_1_1"/><b>then </b>
<font color="Maroon">h</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">f</font> <a href="partfun3.html#K10" target="_self">^</a> 
 
<b>by </b><i>, <a class="ref" href="rfunct_1.html#D8">RFUNCT_1:def 8</a></i>;<br/>
<b>hence </b><a NAME="E10:93_1_1"/>
<font color="Maroon">f</font> <a href="rfunct_1.html#K3">^</a>  is  <a href="pscomp_1.html#V9">continuous</a> <a href="pscomp_1.html#NM1">RealMap</a> of <font color="Maroon">T</font>
 <b>by </b><i>, <a class="ref" href="topreal6.html#T83">TOPREAL6:83</a></i>;<br/>


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