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<span class="kw">let </span><font color="Maroon" title="c1">p</font>, <font color="Maroon" title="c2">r</font>, <font color="Maroon" title="c3">s</font> be   <a href="xxreal_0.html#NM1" title="XXREAL_0:NM.1">ExtReal</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">p</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">r</font> implies <span class="p1"><a href="xxreal_1.html#K4" title="XXREAL_1:func.4">].</a><span class="default"><font color="Maroon" title="c2">r</font>,<font color="Maroon" title="c3">s</font></span><a href="xxreal_1.html#K4" title="XXREAL_1:func.4">.[</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="xxreal_1.html#K4" title="XXREAL_1:func.4">].</a><span class="default"><font color="Maroon" title="c1">p</font>,<a href="xxreal_0.html#K1" title="XXREAL_0:func.1">+infty</a></span><a href="xxreal_1.html#K4" title="XXREAL_1:func.4">.[</a></span> )</span><br/>





<a NAME="E1:248"/>
<font color="Maroon" title="c3">s</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="xxreal_0.html#K1" title="XXREAL_0:func.1">+infty</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_0.html#T3" onmouseover="rs('xxreal_0/T3')" onmouseout="rh()">XXREAL_0:3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:248"/>
( <font color="Maroon" title="c1">p</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">r</font> implies <span class="p1"><a href="xxreal_1.html#K4" title="XXREAL_1:func.4">].</a><span class="default"><font color="Maroon" title="c2">r</font>,<font color="Maroon" title="c3">s</font></span><a href="xxreal_1.html#K4" title="XXREAL_1:func.4">.[</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="xxreal_1.html#K4" title="XXREAL_1:func.4">].</a><span class="default"><font color="Maroon" title="c1">p</font>,<a href="xxreal_0.html#K1" title="XXREAL_0:func.1">+infty</a></span><a href="xxreal_1.html#K4" title="XXREAL_1:func.4">.[</a></span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_1.html#T46" target="_self" onmouseover="rs('xxreal_1/T46')" onmouseout="rh()">Th46</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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