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<b>let </b><font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c2">b</font>, <font color="Maroon" title="c3">c</font>, <font color="Maroon" title="c4">d</font>, <font color="Maroon" title="c5">e</font>, <font color="Maroon" title="c6">f</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">b</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c3">c</font> &amp; <font color="Maroon" title="c4">d</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c5">e</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c6">f</font> implies  <a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c4">d</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c5">e</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c6">f</font></span>)</span> )</span><br/>

<b>assume </b><a NAME="E1:3"/>
( <font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">b</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c3">c</font> &amp; <font color="Maroon" title="c4">d</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c5">e</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c6">f</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c4">d</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c5">e</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c6">f</font></span>)</span></span><br/>

<a NAME="E2:3"/><b>then </b>
(  <a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c4">d</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">b</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c3">c</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">e</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c6">f</font></span>)</span> &amp;  <a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">b</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c3">c</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">e</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c6">f</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c5">e</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c6">f</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="topreal7.html#T2" target="_self" title="TOPREAL7:th.2">Th2</a>, <a class="ref" href="xxreal_0.html#T26" title="XXREAL_0:th.26">XXREAL_0:26</a></i>;<br/>
<b>hence </b><a NAME="E3:3"/>
 <a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c4">d</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c5">e</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c6">f</font></span>)</span>
 <b>by </b><i><a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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