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<span class="kw">let </span><font color="Maroon" title="c1">i</font>, <font color="Maroon" title="c2">j</font>, <font color="Maroon" title="c3">l</font> be   <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">Number</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="c3">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> (<font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font>) implies <span class="p1">(<span class="default"><a href="finseq_1.html#K1" title="FINSEQ_1:func.1">Seg</a> <font color="Maroon" title="c1">i</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K1" title="FINSEQ_1:func.1">Seg</a> <font color="Maroon" title="c2">j</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K1" title="FINSEQ_1:func.1">Seg</a> <font color="Maroon" title="c3">l</font> )</span><br/>





<a NAME="E1:2"/>
( <font color="Maroon" title="c1">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">j</font> or <font color="Maroon" title="c2">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">i</font> )
 
;<br/>
<a NAME="E2:2"/><span class="kw">then </span>
( ( <font color="Maroon" title="c1">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">j</font> &amp; <span class="p1">(<span class="default"><a href="finseq_1.html#K1" title="FINSEQ_1:func.1">Seg</a> <font color="Maroon" title="c1">i</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K1" title="FINSEQ_1:func.1">Seg</a> <font color="Maroon" title="c2">j</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K1" title="FINSEQ_1:func.1">Seg</a> <font color="Maroon" title="c1">i</font> ) or ( <font color="Maroon" title="c2">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">i</font> &amp; <span class="p1">(<span class="default"><a href="finseq_1.html#K1" title="FINSEQ_1:func.1">Seg</a> <font color="Maroon" title="c1">i</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K1" title="FINSEQ_1:func.1">Seg</a> <font color="Maroon" title="c2">j</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K1" title="FINSEQ_1:func.1">Seg</a> <font color="Maroon" title="c2">j</font> ) )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T7" onmouseover="rs('finseq_1/T7')" onmouseout="rh()">FINSEQ_1:7</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:2"/>
( <font color="Maroon" title="c3">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> (<font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font>) implies <span class="p1">(<span class="default"><a href="finseq_1.html#K1" title="FINSEQ_1:func.1">Seg</a> <font color="Maroon" title="c1">i</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K1" title="FINSEQ_1:func.1">Seg</a> <font color="Maroon" title="c2">j</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K1" title="FINSEQ_1:func.1">Seg</a> <font color="Maroon" title="c3">l</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_0.html#D9" onmouseover="rs('xxreal_0/D9')" onmouseout="rh()">XXREAL_0:def 9</a></span>; <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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