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<b>let </b><font color="Maroon" title="c1">X</font>, <font color="Maroon" title="c2">Y</font> be  <a href="membered.html#V2" title="MEMBERED:attr.2">ext-real-membered</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</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">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">Y</font> &amp; <font color="Maroon" title="c2">Y</font> is <a href="xxreal_2.html#V3" title="XXREAL_2:attr.3">bounded_below</a> implies <font color="Maroon" title="c1">X</font> is <a href="xxreal_2.html#V3" title="XXREAL_2:attr.3">bounded_below</a> )</span><br/>

<b>assume </b><a NAME="E1:82"/><i><font color="Green" title="E56">A1</font></i>: 
<font color="Maroon" title="c1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">Y</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c2">Y</font> is <a href="xxreal_2.html#V3" title="XXREAL_2:attr.3">bounded_below</a> or <font color="Maroon" title="c1">X</font> is <a href="xxreal_2.html#V3" title="XXREAL_2:attr.3">bounded_below</a> )</span><br/>

<b>given </b><font color="Maroon" title="c3">r</font> being  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> <b> such that </b><a NAME="E3:82"/><i><font color="Green" title="E57">G</font></i>: 
<font color="Maroon" title="c3">r</font> is    <a href="xxreal_2.html#M2" title="XXREAL_2:mode.2">LowerBound</a> of <font color="Maroon" title="c2">Y</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="xxreal_2.html#D9" target="_self" title="XXREAL_2:def.9">XXREAL_2:def 9</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">X</font> is <a href="xxreal_2.html#V3" title="XXREAL_2:attr.3">bounded_below</a></span><br/>

<b>take </b>
<font color="Maroon" title="c3">r</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="xxreal_2.html#D9" target="_self" title="XXREAL_2:def.9">XXREAL_2:def 9</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">r</font> is    <a href="xxreal_2.html#M2" title="XXREAL_2:mode.2">LowerBound</a> of <font color="Maroon" title="c1">X</font></span><br/>

<b>thus </b><a NAME="E4:82"/>
<font color="Maroon" title="c3">r</font> is    <a href="xxreal_2.html#M2" title="XXREAL_2:mode.2">LowerBound</a> of <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="txt" href="#E1:82"><i><font color="Green" title="E56">A1</font></i></a>, <a class="txt" href="#E3:82"><i><font color="Green" title="E57">G</font></i></a>, <a class="ref" href="xxreal_2.html#T5" target="_self" title="XXREAL_2:th.5">Th4</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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