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<b>let </b><font color="Maroon" title="c1">Y1</font>, <font color="Maroon" title="c2">Y</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#K1" title="NUMBERS:func.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">Y1</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="seq_4.html#V3" title="SEQ_4:attr.3">bounded</a> implies <font color="Maroon" title="c1">Y1</font> is <a href="seq_4.html#V3" title="SEQ_4:attr.3">bounded</a> )</span><br/>



<b>assume </b><a NAME="E1:5"/><i><font color="Green" title="E4">A1</font></i>: 
( <font color="Maroon" title="c1">Y1</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="seq_4.html#V3" title="SEQ_4:attr.3">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">Y1</font> is <a href="seq_4.html#V3" title="SEQ_4:attr.3">bounded</a></span><br/>

<a NAME="E2:5"/><b>then </b><i><font color="Green" title="E5">A2</font></i>: 
( <font color="Maroon" title="c2">Y</font> is <a href="seq_4.html#V1" title="SEQ_4:attr.1">bounded_above</a> &amp; <font color="Maroon" title="c2">Y</font> is <a href="seq_4.html#V2" title="SEQ_4:attr.2">bounded_below</a> )
 
<b>by </b><i><a class="ref" href="seq_4.html#D3" title="SEQ_4:def.3">SEQ_4:def 3</a></i>;<br/>
<a NAME="E3:5"/><b>then </b><i><font color="Green" title="E6">A3</font></i>: 
<font color="Maroon" title="c1">Y1</font> is <a href="seq_4.html#V1" title="SEQ_4:attr.1">bounded_above</a>
 
<b>by </b><i><a class="txt" href="rcomp_1.html#E1:5"><i><font color="Green" title="E4">A1</font></i></a>, <a class="ref" href="rcomp_1.html#T4" target="_self" title="RCOMP_1:th.4">Th4</a></i>;<br/>
<a NAME="E4:5"/>
<font color="Maroon" title="c1">Y1</font> is <a href="seq_4.html#V2" title="SEQ_4:attr.2">bounded_below</a>
 
<b>by </b><i><a class="txt" href="rcomp_1.html#E1:5"><i><font color="Green" title="E4">A1</font></i></a>, <a class="txt" href="rcomp_1.html#E2:5"><i><font color="Green" title="E5">A2</font></i></a>, <a class="ref" href="rcomp_1.html#T3" target="_self" title="RCOMP_1:th.3">Th3</a></i>;<br/>
<b>hence </b><a NAME="E5:5"/>
<font color="Maroon" title="c1">Y1</font> is <a href="seq_4.html#V3" title="SEQ_4:attr.3">bounded</a>
 <b>by </b><i><a class="txt" href="rcomp_1.html#E3:5"><i><font color="Green" title="E6">A3</font></i></a>, <a class="ref" href="seq_4.html#D3" title="SEQ_4:def.3">SEQ_4:def 3</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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