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<b>let </b><font color="Maroon" title="c1">X</font>, <font color="Maroon" title="c2">X1</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c3">f1</font>, <font color="Maroon" title="c4">f2</font> be   <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>assume </b><a NAME="E1:20"/>
( <font color="Maroon" title="c3">f1</font> <a href="fcont_1.html#R2" title="FCONT_1:pred.2">is_continuous_on</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c4">f2</font> <a href="fcont_1.html#R2" title="FCONT_1:pred.2">is_continuous_on</a> <font color="Maroon" title="c2">X1</font> )
 ;<br/>

<a NAME="E2:20"/><b>then </b>
( <font color="Maroon" title="c3">f1</font> <a href="fcont_1.html#R2" title="FCONT_1:pred.2">is_continuous_on</a> <font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c2">X1</font> &amp; <font color="Maroon" title="c4">f2</font> <a href="fcont_1.html#R2" title="FCONT_1:pred.2">is_continuous_on</a> <font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c2">X1</font> )
 
<b>by </b><i><a class="ref" href="fcont_1.html#T17" target="_self" title="FCONT_1:th.17">Th17</a>, <a class="ref" href="xboole_1.html#T17" title="XBOOLE_1:th.17">XBOOLE_1:17</a></i>;<br/>
<b>hence </b><a NAME="E3:20"/>
( <font color="Maroon" title="c3">f1</font> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <font color="Maroon" title="c4">f2</font> <a href="fcont_1.html#R2" title="FCONT_1:pred.2">is_continuous_on</a> <font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c2">X1</font> &amp; <font color="Maroon" title="c3">f1</font> <a href="valued_1.html#K47" title="VALUED_1:func.47">-</a> <font color="Maroon" title="c4">f2</font> <a href="fcont_1.html#R2" title="FCONT_1:pred.2">is_continuous_on</a> <font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c2">X1</font> &amp; <font color="Maroon" title="c3">f1</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c4">f2</font> <a href="fcont_1.html#R2" title="FCONT_1:pred.2">is_continuous_on</a> <font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c2">X1</font> )
 <b>by </b><i><a class="ref" href="fcont_1.html#T19" target="_self" title="FCONT_1:th.19">Th19</a></i>;<br/>


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