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<span class="kw">let </span><font color="Maroon" title="c1">L</font> be    <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">L</font> is  <a href="yellow_0.html#V3" title="YELLOW_0:attr.3">bounded</a>  iff <font color="Maroon" title="c1">L</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a>  is  <a href="yellow_0.html#V3" title="YELLOW_0:attr.3">bounded</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E1:39"/>
( <font color="Maroon" title="c1">L</font> is  <a href="yellow_0.html#V3" title="YELLOW_0:attr.3">bounded</a>  implies <font color="Maroon" title="c1">L</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a>  is  <a href="yellow_0.html#V3" title="YELLOW_0:attr.3">bounded</a>  )
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">L</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a>  is  <a href="yellow_0.html#V3" title="YELLOW_0:attr.3">bounded</a>  implies <font color="Maroon" title="c1">L</font> is  <a href="yellow_0.html#V3" title="YELLOW_0:attr.3">bounded</a>  )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:39_1"/>
( <font color="Maroon" title="c1">L</font> is  <a href="yellow_0.html#V1" title="YELLOW_0:attr.1">lower-bounded</a>  &amp; <font color="Maroon" title="c1">L</font> is  <a href="yellow_0.html#V2" title="YELLOW_0:attr.2">upper-bounded</a>  )
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="yellow_0.html#D6" title="YELLOW_0:def.6">YELLOW_0:def 6</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">L</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a>  is  <a href="yellow_0.html#V3" title="YELLOW_0:attr.3">bounded</a> </span><br/>

<span class="kw">hence </span><a NAME="E2:39_1"/>
( <font color="Maroon" title="c1">L</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a>  is  <a href="yellow_0.html#V1" title="YELLOW_0:attr.1">lower-bounded</a>  &amp; <font color="Maroon" title="c1">L</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a>  is  <a href="yellow_0.html#V2" title="YELLOW_0:attr.2">upper-bounded</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_7.html#T30" target="_self" title="YELLOW_7:th.30">Th30</a>, <a class="ref" href="yellow_7.html#T31" target="_self" title="YELLOW_7:th.31">Th31</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="yellow_0.html#D6" title="YELLOW_0:def.6">YELLOW_0:def 6</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>

<span class="kw">assume </span><a NAME="E2:39"/>
( <font color="Maroon" title="c1">L</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a>  is  <a href="yellow_0.html#V1" title="YELLOW_0:attr.1">lower-bounded</a>  &amp; <font color="Maroon" title="c1">L</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a>  is  <a href="yellow_0.html#V2" title="YELLOW_0:attr.2">upper-bounded</a>  )
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="yellow_0.html#D6" title="YELLOW_0:def.6">YELLOW_0:def 6</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">L</font> is  <a href="yellow_0.html#V3" title="YELLOW_0:attr.3">bounded</a> </span><br/>

<span class="kw">hence </span><a NAME="E3:39"/>
( <font color="Maroon" title="c1">L</font> is  <a href="yellow_0.html#V1" title="YELLOW_0:attr.1">lower-bounded</a>  &amp; <font color="Maroon" title="c1">L</font> is  <a href="yellow_0.html#V2" title="YELLOW_0:attr.2">upper-bounded</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_7.html#T30" target="_self" title="YELLOW_7:th.30">Th30</a>, <a class="ref" href="yellow_7.html#T31" target="_self" title="YELLOW_7:th.31">Th31</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="yellow_0.html#D6" title="YELLOW_0:def.6">YELLOW_0:def 6</a> <a class="txt" 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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