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<b>let </b><font color="Maroon" title="c1">f</font>, <font color="Maroon" title="c2">g</font> be  <a href="jordan16.html#V1" title="JORDAN16:attr.1">continuous</a> <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> , <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ;<br/>

<b>reconsider </b><font color="Maroon" title="c3">h</font> = <font color="Maroon" title="c2">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c1">f</font> as   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> , <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  ;<br/>
<a NAME="E2:28"/>
<font color="Maroon" title="c1">f</font> <a href="fcont_1.html#R2" title="FCONT_1:pred.2">is_continuous_on</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c1">f</font>
 
<b>by </b><i><a class="ref" href="jordan16.html#D1" target="_self" title="JORDAN16:def.1">Def1</a></i>;<br/>
<a NAME="E3:28"/><b>then </b><i><font color="Green" title="E15">A1</font></i>: 
<font color="Maroon" title="c1">f</font> <a href="fcont_1.html#R2" title="FCONT_1:pred.2">is_continuous_on</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">h</font>
 
<b>by </b><i><a class="ref" href="fcont_1.html#T17" title="FCONT_1:th.17">FCONT_1:17</a>, <a class="ref" href="relat_1.html#T44" title="RELAT_1:th.44">RELAT_1:44</a></i>;<br/>
<a NAME="E4:28"/>
<font color="Maroon" title="c2">g</font> <a href="fcont_1.html#R2" title="FCONT_1:pred.2">is_continuous_on</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">g</font>
 
<b>by </b><i><a class="ref" href="jordan16.html#D1" target="_self" title="JORDAN16:def.1">Def1</a></i>;<br/>
<a NAME="E5:28"/><b>then </b>
<font color="Maroon" title="c2">g</font> <a href="fcont_1.html#R2" title="FCONT_1:pred.2">is_continuous_on</a> <font color="Maroon" title="c1">f</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">h</font></span>)</span>
 
<b>by </b><i><a class="ref" href="fcont_1.html#T17" title="FCONT_1:th.17">FCONT_1:17</a>, <a class="ref" href="funct_3.html#T2" title="FUNCT_3:th.2">FUNCT_3:2</a></i>;<br/>
<a NAME="E6:28"/><b>then </b>
<font color="Maroon" title="c3">h</font> <a href="fcont_1.html#R2" title="FCONT_1:pred.2">is_continuous_on</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">h</font>
 
<b>by </b><i><a class="txt" href="jordan16.html#E3:28"><i><font color="Green" title="E15">A1</font></i></a>, <a class="ref" href="fcont_1.html#T26" title="FCONT_1:th.26">FCONT_1:26</a></i>;<br/>
<b>hence </b><a NAME="E7:28"/>
<font color="Maroon" title="c2">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c1">f</font> is  <a href="jordan16.html#V1" title="JORDAN16:attr.1">continuous</a> <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> , <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> 
 <b>by </b><i><a class="ref" href="jordan16.html#D1" target="_self" title="JORDAN16:def.1">Def1</a></i>;<br/>


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