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<b>let </b><font color="Maroon">c<sub>1</sub></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">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>



<b>assume </b><a NAME="E1:83"/>
<font color="Maroon">c<sub>1</sub></font> <a href="rfunct_3.html#R2" target="_self">is_convex_on</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E2:83"/><b>then </b>
 <a href="rfunct_3.html#K19" target="_self">max+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="rfunct_3.html#K21" target="_self">-</a> 0</span>)</span> <a href="rfunct_3.html#R2" target="_self">is_convex_on</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="rfunct_3.html#T62" target="_self">Th62</a></i>;<br/>
<b>hence </b><a NAME="E3:83"/>
 <a href="rfunct_3.html#K19" target="_self">max+</a> <font color="Maroon">c<sub>1</sub></font> <a href="rfunct_3.html#R2" target="_self">is_convex_on</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="rfunct_3.html#T51" target="_self">Th51</a></i>;<br/>


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