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<b>let </b><font color="Maroon">f</font> be   <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>let </b><font color="Maroon">x</font> be   <a href="pre_topc.html#NM2">Point</a> of <a href="topmetr.html#K3">R^1</a> ;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:50"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font>
 <b>and </b><br/><a NAME="E2:50"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">g</font> <a href="fcont_1.html#R1">is_continuous_in</a> <font color="Maroon">x</font>
 ;<br/>

<b>let </b><font color="Maroon">G</font> be    <a href="connsp_2.html#M1">a_neighborhood</a> of <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="tmap_1.html#D2">TMAP_1:def 2</a><br/>

<b>consider </b><font color="Maroon">Z</font> being    <a href="rcomp_1.html#M1">Neighbourhood</a> of <font color="Maroon">g</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">x</font><b> such that </b><br/><a NAME="E4:50"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">Z</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">G</font>
 <b>by </b><i>, </i>;<br/>
<b>consider </b><font color="Maroon">N</font> being    <a href="rcomp_1.html#M1">Neighbourhood</a> of <font color="Maroon">x</font><b> such that </b><br/><a NAME="E6:50"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">g</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">N</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Z</font>
 <b>by </b><i>, <a class="ref" href="fcont_1.html#T5">FCONT_1:5</a></i>;<br/>
<b>reconsider </b><font color="Maroon">H</font> = <font color="Maroon">N</font> as    <a href="connsp_2.html#M1">a_neighborhood</a> of <font color="Maroon">x</font> <b>by </b><i>, <a class="ref" href="topmetr.html#T24">TOPMETR:24</a></i>;<br/>
<b>take </b>
<font color="Maroon">H</font>
;<br/>

<b>thus </b><a NAME="E8:50"/>
<font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">H</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">G</font>
 <b>by </b><i>, , , <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>


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