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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="seq_1.html#NM1">Real_Sequence</a>;<br/>



<b>assume </b><a NAME="E1:58"/><i><font color="Green">E54</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="seq_2.html#V1">bounded_above</a>
 ;<br/>

<a NAME="E2:58"/>
<span class="p1">(<span class="default"><a href="rinfsup1.html#K4" target="_self">superior_realsequence</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="square_1.html#K2">max</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rinfsup1.html#K4" target="_self">superior_realsequence</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="xxreal_0.html#T25">XXREAL_0:25</a></i>;<br/>
<b>hence </b><a NAME="E3:58"/>
<span class="p1">(<span class="default"><a href="rinfsup1.html#K4" target="_self">superior_realsequence</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="rinfsup1.html#K4" target="_self">superior_realsequence</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="rinfsup1.html#E1:58"><i><font color="Green">E54</font></i></a>, <a class="ref" href="rinfsup1.html#T49" target="_self">Th49</a></i>;<br/>


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