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<span class="kw">let </span><font color="Maroon" title="c1">N1</font>, <font color="Maroon" title="c2">N2</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="fuzimpl4.html#K5" title="FUZIMPL4:func.5">Fuzzy_Negations</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">  for <font color="Olive" title="b1">NN1</font>, <font color="Olive" title="b2">NN2</font> being   <a href="fuzimpl3.html#NM1" title="FUZIMPL3:NM.1">Fuzzy_Negation</a>  st <font color="Maroon" title="c1">N1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">NN1</font> &amp; <font color="Maroon" title="c2">N2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">NN2</font> holds <br/><font color="Maroon" title="c1">N1</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c2">N2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fuzimpl4.html#K4" title="FUZIMPL4:func.4">min</a> (<font color="Olive" title="b1">NN1</font>,<font color="Olive" title="b2">NN2</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c3">NN1</font>, <font color="Maroon" title="c4">NN2</font> be   <a href="fuzimpl3.html#NM1" title="FUZIMPL3:NM.1">Fuzzy_Negation</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="c1">N1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">NN1</font> &amp; <font color="Maroon" title="c2">N2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">NN2</font> implies <font color="Maroon" title="c1">N1</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c2">N2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fuzimpl4.html#K4" title="FUZIMPL4:func.4">min</a> (<font color="Maroon" title="c3">NN1</font>,<font color="Maroon" title="c4">NN2</font>) )</span><br/>



<span class="kw">assume </span><a NAME="E1:89"/><span class="lab"><font color="Green" title="E42">A0</font></span>: 
( <font color="Maroon" title="c1">N1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">NN1</font> &amp; <font color="Maroon" title="c2">N2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">NN2</font> )
 ; <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="c1">N1</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c2">N2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fuzimpl4.html#K4" title="FUZIMPL4:func.4">min</a> (<font color="Maroon" title="c3">NN1</font>,<font color="Maroon" title="c4">NN2</font>)</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c5">s</font> = <font color="Maroon" title="c1">N1</font>, <font color="Maroon" title="c6">t</font> = <font color="Maroon" title="c2">N2</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4" title="LFUZZY_0:func.4">FuzzyLattice</a> <span class="p2"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T58" onmouseover="rs('yellow_0/T58')" onmouseout="rh()">YELLOW_0:58</a></span>;<br/>
<a NAME="E3:89"/><span class="lab"><font color="Green" title="E43">A4</font></span>: 
<font color="Maroon" title="c5">s</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c6">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">N1</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c2">N2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T69" onmouseover="rs('yellow_0/T69')" onmouseout="rh()">YELLOW_0:69</a></span>;<br/>
<a NAME="E4:89"/>
<font color="Maroon" title="c5">s</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c6">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fuzzy_1.html#K1" title="FUZZY_1:func.1">min</a> (<span class="p1">(<span class="default"><a href="lfuzzy_0.html#K5" title="LFUZZY_0:func.5">@</a> <font color="Maroon" title="c5">s</font></span>)</span>,<span class="p1">(<span class="default"><a href="lfuzzy_0.html#K5" title="LFUZZY_0:func.5">@</a> <font color="Maroon" title="c6">t</font></span>)</span>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lfuzzy_0.html#T21" onmouseover="rs('lfuzzy_0/T21')" onmouseout="rh()">LFUZZY_0:21</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:89"/>
<font color="Maroon" title="c1">N1</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c2">N2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fuzimpl4.html#K4" title="FUZIMPL4:func.4">min</a> (<font color="Maroon" title="c3">NN1</font>,<font color="Maroon" title="c4">NN2</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:89"><span class="lab"><font color="Green" title="E42">A0</font></span></a>, <a class="txt" href="#E3:89"><span class="lab"><font color="Green" title="E43">A4</font></span></a>, <a class="ref" href="fuzimpl4.html#T33" target="_self" onmouseover="rs('fuzimpl4/T33')" onmouseout="rh()">MinEqMin</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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