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<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">X1</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">f1</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">f2</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="E1:20"/><i><font color="Green">E38</font></i>: 
( <font color="Maroon">f1</font> <a href="fcont_1.html#R2" target="_self">is_continuous_on</a> <font color="Maroon">X</font> &amp; <font color="Maroon">f2</font> <a href="fcont_1.html#R2" target="_self">is_continuous_on</a> <font color="Maroon">X1</font> )
 ;<br/>

<a NAME="E2:20"/>
( <font color="Maroon">X</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">X1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">X</font> &amp; <font color="Maroon">X</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">X1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">X1</font> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/>
<a NAME="E3:20"/><b>then </b>
( <font color="Maroon">f1</font> <a href="fcont_1.html#R2" target="_self">is_continuous_on</a> <font color="Maroon">X</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">X1</font> &amp; <font color="Maroon">f2</font> <a href="fcont_1.html#R2" target="_self">is_continuous_on</a> <font color="Maroon">X</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">X1</font> )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E4:20"/>
( <font color="Maroon">f1</font> <a href="seq_1.html#K6">+</a> <font color="Maroon">f2</font> <a href="fcont_1.html#R2" target="_self">is_continuous_on</a> <font color="Maroon">X</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">X1</font> &amp; <font color="Maroon">f1</font> <a href="seq_1.html#K7">-</a> <font color="Maroon">f2</font> <a href="fcont_1.html#R2" target="_self">is_continuous_on</a> <font color="Maroon">X</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">X1</font> &amp; <font color="Maroon">f1</font> <a href="seq_1.html#K8">(#)</a> <font color="Maroon">f2</font> <a href="fcont_1.html#R2" target="_self">is_continuous_on</a> <font color="Maroon">X</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">X1</font> )
 <b>by </b><i/>;<br/>


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