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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="supinf_1.html#V5" title="SUPINF_1:attr.5">bounded</a> implies <font color="Maroon" title="c1">X</font> is <a href="supinf_1.html#V5" title="SUPINF_1:attr.5">bounded</a> )</span><br/>

<b>assume </b><a NAME="E1:25"/><i><font color="Green" title="E14">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="supinf_1.html#V5" title="SUPINF_1:attr.5">bounded</a> or <font color="Maroon" title="c1">X</font> is <a href="supinf_1.html#V5" title="SUPINF_1:attr.5">bounded</a> )</span><br/>

<b>assume </b><a NAME="E2:25"/>
<font color="Maroon" title="c2">Y</font> is <a href="supinf_1.html#V5" title="SUPINF_1:attr.5">bounded</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="supinf_1.html#V5" title="SUPINF_1:attr.5">bounded</a></span><br/>

<a NAME="E3:25"/><b>then </b>
( <font color="Maroon" title="c2">Y</font> is <a href="supinf_1.html#V3" title="SUPINF_1:attr.3">bounded_above</a> &amp; <font color="Maroon" title="c2">Y</font> is <a href="supinf_1.html#V4" title="SUPINF_1:attr.4">bounded_below</a> )
 
<b>by </b><i><a class="ref" href="supinf_1.html#D13" target="_self" title="SUPINF_1:def.13">Def13</a></i>;<br/>
<a NAME="E4:25"/><b>then </b>
( <font color="Maroon" title="c1">X</font> is <a href="supinf_1.html#V3" title="SUPINF_1:attr.3">bounded_above</a> &amp; <font color="Maroon" title="c1">X</font> is <a href="supinf_1.html#V4" title="SUPINF_1:attr.4">bounded_below</a> )
 
<b>by </b><i><a class="txt" href="supinf_1.html#E1:25"><i><font color="Green" title="E14">A1</font></i></a>, <a class="ref" href="supinf_1.html#T44" target="_self" title="SUPINF_1:th.44">Th44</a>, <a class="ref" href="supinf_1.html#T47" target="_self" title="SUPINF_1:th.47">Th47</a></i>;<br/>
<b>hence </b><a NAME="E5:25"/>
<font color="Maroon" title="c1">X</font> is <a href="supinf_1.html#V5" title="SUPINF_1:attr.5">bounded</a>
 <b>by </b><i><a class="ref" href="supinf_1.html#D13" target="_self" title="SUPINF_1:def.13">Def13</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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