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<span class="kw">let </span><font color="Maroon" title="c1">X</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</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">X</font> is  <a href="membered.html#V3" title="MEMBERED:attr.3">real-membered</a>  implies <font color="Maroon" title="c1">X</font> is  <a href="membered.html#V2" title="MEMBERED:attr.2">ext-real-membered</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:2_4_1"/><span class="lab"><font color="Green" title="E7">A4</font></span>: 
<font color="Maroon" title="c1">X</font> is  <a href="membered.html#V3" title="MEMBERED:attr.3">real-membered</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">X</font> is  <a href="membered.html#V2" title="MEMBERED:attr.2">ext-real-membered</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c2">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="membered.html#D2" target="_self" onmouseover="rs('membered/D2')" onmouseout="rh()">MEMBERED:def 2</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="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> implies <font color="Maroon" title="c2">x</font> is  <a href="xxreal_0.html#V1" title="XXREAL_0:attr.1">ext-real</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E2:2_4_1"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font>
 ; <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="c2">x</font> is  <a href="xxreal_0.html#V1" title="XXREAL_0:attr.1">ext-real</a> </span><br/>

<a NAME="E3:2_4_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">x</font> is  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:2_4_1"><span class="lab"><font color="Green" title="E7">A4</font></span></a></span>;<br/>
<a NAME="E4:2_4_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> 
 
;<br/>
<span class="kw">hence </span><a NAME="E5:2_4_1"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">ExtREAL</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="numbers.html#T31" onmouseover="rs('numbers/T31')" onmouseout="rh()">NUMBERS:31</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="xxreal_0.html#D1" onmouseover="rs('xxreal_0/D1')" onmouseout="rh()">XXREAL_0:def 1</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"> verum</span><br/>


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