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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">f</font> be   <a href="partfun1.html#NM1">PartFunc</a> of  <a href="supinf_1.html#K3">REAL</a> , <a href="supinf_1.html#K3">REAL</a> ;<br/>



<b>assume </b><a NAME="E1:35"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">f</font> <a href="rfunct_4.html#R4" target="_self">is_strongly_quasiconvex_on</a> <font color="Maroon">X</font>
 ;<br/>

<a NAME="E2:35"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">X</font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E3:35"/>
for <font color="Olive">p</font> being  <a href="real_1.html#NM1">Real</a>  st 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">p</font> &amp; <font color="Olive">p</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1 holds <br/>for <font color="Olive">r</font>, <font color="Olive">s</font> being  <a href="real_1.html#NM1">Real</a>  st <font color="Olive">r</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp; <font color="Olive">s</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp; <span class="p1">(<span class="default"><font color="Olive">p</font> <a href="binop_2.html#K11">*</a> <font color="Olive">r</font></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="binop_2.html#K10">-</a> <font color="Olive">p</font></span>)</span> <a href="binop_2.html#K11">*</a> <font color="Olive">s</font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp; <font color="Maroon">f</font> <a href="seq_1.html#K2">.</a> <font color="Olive">r</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">f</font> <a href="seq_1.html#K2">.</a> <font color="Olive">s</font> holds <br/><font color="Maroon">f</font> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive">p</font> <a href="binop_2.html#K11">*</a> <font color="Olive">r</font></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="binop_2.html#K10">-</a> <font color="Olive">p</font></span>)</span> <a href="binop_2.html#K11">*</a> <font color="Olive">s</font></span>)</span></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="xxreal_0.html#K4">max</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="seq_1.html#K2">.</a> <font color="Olive">r</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="seq_1.html#K2">.</a> <font color="Olive">s</font></span>)</span>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E4:35"/>
<font color="Maroon">f</font> <a href="rfunct_4.html#R3" target="_self">is_strictly_quasiconvex_on</a> <font color="Maroon">X</font>
 <b>by </b><i>, </i>;<br/>


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