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<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="31_1"><span class="kw">now </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">  for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><a href="ordinal1.html#K5" title="ORDINAL1:func.5">0</a>,1,2</span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span> holds   <a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> (<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><a href="ordinal1.html#K5" title="ORDINAL1:func.5">0</a>,1,2</span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">y</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><a href="ordinal1.html#K5" title="ORDINAL1:func.5">0</a>,1,2</span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</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">  <a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> (<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><a href="ordinal1.html#K5" title="ORDINAL1:func.5">0</a>,1,2</span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span></span><br/><a NAME="E1:31_1"/>
(  <a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> (<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">x</font> or  <a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> (<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">y</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_0.html#T15" onmouseover="rs('xxreal_0/T15')" onmouseout="rh()">XXREAL_0:15</a></span>;<br/><span class="kw">hence </span><a NAME="E2:31_1"/>
 <a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> (<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><a href="ordinal1.html#K5" title="ORDINAL1:func.5">0</a>,1,2</span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</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/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E2:31"/>
( 2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><a href="ordinal1.html#K5" title="ORDINAL1:func.5">0</a>,1,2</span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span> &amp; (  for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><a href="ordinal1.html#K5" title="ORDINAL1:func.5">0</a>,1,2</span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span> holds   <a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> (<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><a href="ordinal1.html#K5" title="ORDINAL1:func.5">0</a>,1,2</span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span> ) )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="enumset1.html#D1" onmouseover="rs('enumset1/D1')" onmouseout="rh()">ENUMSET1:def 1</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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