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<span class="kw">let </span><font color="Maroon" title="c1">I</font> be   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <span class="p1"><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>; <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">N</font> being   <a href="fuzimpl3.html#NM1" title="FUZIMPL3:NM.1">Fuzzy_Negation</a>  st <font color="Maroon" title="c1">I</font> is <font color="Olive" title="b1">N</font> <a href="fuzimpl4.html#V1" title="FUZIMPL4:attr.1">-satisfying_CP</a>  &amp; <font color="Maroon" title="c1">I</font> is  <a href="fuzimpl2.html#NV6" title="FUZIMPL2:NV.6">satisfying_(I1)</a>  &amp; <font color="Maroon" title="c1">I</font> is  <a href="fuzimpl2.html#V1" title="FUZIMPL2:attr.1">satisfying_(NP)</a>  holds <br/>( <font color="Maroon" title="c1">I</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="fuzimpl1.html#K7" title="FUZIMPL1:func.7">FI</a>  &amp;  <a href="fuzimpl3.html#K4" title="FUZIMPL3:func.4">FNegation</a> <font color="Maroon" title="c1">I</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b1">N</font> &amp; <font color="Olive" title="b1">N</font> is  <a href="fuzimpl3.html#V9" title="FUZIMPL3:attr.9">negation-strong</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">N</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">I</font> is <font color="Maroon" title="c2">N</font> <a href="fuzimpl4.html#V1" title="FUZIMPL4:attr.1">-satisfying_CP</a>  &amp; <font color="Maroon" title="c1">I</font> is  <a href="fuzimpl2.html#NV6" title="FUZIMPL2:NV.6">satisfying_(I1)</a>  &amp; <font color="Maroon" title="c1">I</font> is  <a href="fuzimpl2.html#V1" title="FUZIMPL2:attr.1">satisfying_(NP)</a>  implies ( <font color="Maroon" title="c1">I</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="fuzimpl1.html#K7" title="FUZIMPL1:func.7">FI</a>  &amp;  <a href="fuzimpl3.html#K4" title="FUZIMPL3:func.4">FNegation</a> <font color="Maroon" title="c1">I</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">N</font> &amp; <font color="Maroon" title="c2">N</font> is  <a href="fuzimpl3.html#V9" title="FUZIMPL3:attr.9">negation-strong</a>  ) )</span><br/>



<span class="kw">assume </span><a NAME="E1:29"/><span class="lab"><font color="Green" title="E15">A1</font></span>: 
( <font color="Maroon" title="c1">I</font> is <font color="Maroon" title="c2">N</font> <a href="fuzimpl4.html#V1" title="FUZIMPL4:attr.1">-satisfying_CP</a>  &amp; <font color="Maroon" title="c1">I</font> is  <a href="fuzimpl2.html#NV6" title="FUZIMPL2:NV.6">satisfying_(I1)</a>  &amp; <font color="Maroon" title="c1">I</font> is  <a href="fuzimpl2.html#V1" title="FUZIMPL2:attr.1">satisfying_(NP)</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">I</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="fuzimpl1.html#K7" title="FUZIMPL1:func.7">FI</a>  &amp;  <a href="fuzimpl3.html#K4" title="FUZIMPL3:func.4">FNegation</a> <font color="Maroon" title="c1">I</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">N</font> &amp; <font color="Maroon" title="c2">N</font> is  <a href="fuzimpl3.html#V9" title="FUZIMPL3:attr.9">negation-strong</a>  )</span><br/>

<a NAME="E2:29"/><span class="lab"><font color="Green" title="E16">A4</font></span>: 
<font color="Maroon" title="c1">I</font> is  <a href="fuzimpl2.html#NV7" title="FUZIMPL2:NV.7">satisfying_(I2)</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:29"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="ref" href="fuzimpl4.html#T20" target="_self" onmouseover="rs('fuzimpl4/T20')" onmouseout="rh()">Corr157i</a></span>;<br/>
<a NAME="E3:29"/>
<font color="Maroon" title="c1">I</font> is  <a href="fuzimpl2.html#NV8" title="FUZIMPL2:NV.8">satisfying_(I3)</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:29"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="ref" href="fuzimpl4.html#T16" target="_self" onmouseover="rs('fuzimpl4/T16')" onmouseout="rh()">Lemma154vb</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:29"/>
<font color="Maroon" title="c1">I</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="fuzimpl1.html#K7" title="FUZIMPL1:func.7">FI</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:29"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="txt" href="#E2:29"><span class="lab"><font color="Green" title="E16">A4</font></span></a>, <a class="ref" href="fuzimpl1.html#D15" onmouseover="rs('fuzimpl1/D15')" onmouseout="rh()">FUZIMPL1:def 15</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="fuzimpl3.html#K4" title="FUZIMPL3:func.4">FNegation</a> <font color="Maroon" title="c1">I</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">N</font> &amp; <font color="Maroon" title="c2">N</font> is  <a href="fuzimpl3.html#V9" title="FUZIMPL3:attr.9">negation-strong</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E5:29"/>
 <a href="fuzimpl3.html#K4" title="FUZIMPL3:func.4">FNegation</a> <font color="Maroon" title="c1">I</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">N</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:29"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="ref" href="fuzimpl4.html#T15" target="_self" onmouseover="rs('fuzimpl4/T15')" onmouseout="rh()">Lemma154va</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"> <font color="Maroon" title="c2">N</font> is  <a href="fuzimpl3.html#V9" title="FUZIMPL3:attr.9">negation-strong</a> </span><br/>

<span class="kw">hence </span><a NAME="E6:29"/>
<font color="Maroon" title="c2">N</font> is  <a href="fuzimpl3.html#V9" title="FUZIMPL3:attr.9">negation-strong</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:29"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="ref" href="fuzimpl4.html#T15" target="_self" onmouseover="rs('fuzimpl4/T15')" onmouseout="rh()">Lemma154va</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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