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<a NAME="E1:7_1_1"/>
 for <font color="Olive" title="b1">x</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</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> holds  <a href="fuzimpl3.html#K3" title="FUZIMPL3:func.3">N_CC</a> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="fuzimpl3.html#K3" title="FUZIMPL3:func.3">N_CC</a> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="7_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">x</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</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"> <a href="fuzimpl3.html#K3" title="FUZIMPL3:func.3">N_CC</a> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="fuzimpl3.html#K3" title="FUZIMPL3:func.3">N_CC</a> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">x</font></span><br/>

<a NAME="E1:7_1_1_1"/><span class="lab"><font color="Green" title="E1">A1</font></span>: 
1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fuznorm1.html#T7" onmouseover="rs('fuznorm1/T7')" onmouseout="rh()">FUZNORM1:7</a></span>;<br/>
<a href="fuzimpl3.html#K3" title="FUZIMPL3:func.3">N_CC</a> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="fuzimpl3.html#K3" title="FUZIMPL3:func.3">N_CC</a> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c1">x</font></span>)</span> = 
<a href="fuzimpl3.html#K3" title="FUZIMPL3:func.3">N_CC</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">x</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="fuzimpl3.html#D6" onmouseover="rs('fuzimpl3/D6')" onmouseout="rh()">FUZIMPL3:def 6</a></span>
<br/>.= 
1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">x</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:7_1_1_1"><span class="lab"><font color="Green" title="E1">A1</font></span></a>, <a class="ref" href="fuzimpl3.html#D6" onmouseover="rs('fuzimpl3/D6')" onmouseout="rh()">FUZIMPL3:def 6</a></span>
<br/>.= 
<font color="Maroon" title="c1">x</font>

;<br/>
<span class="kw">hence </span><a NAME="E3:7_1_1_1"/>
<a href="fuzimpl3.html#K3" title="FUZIMPL3:func.3">N_CC</a> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="fuzimpl3.html#K3" title="FUZIMPL3:func.3">N_CC</a> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">x</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"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E2:7_1_1"/><span class="kw">then </span>
 <a href="fuzimpl3.html#K3" title="FUZIMPL3:func.3">N_CC</a>  is  <a href="fuzimpl3.html#V4" title="FUZIMPL3:attr.4">involutive</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fuzimpl3.html#D8" onmouseover="rs('fuzimpl3/D8')" onmouseout="rh()">FUZIMPL3:def 8</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:7_1_1"/>
 <a href="fuzimpl3.html#K3" title="FUZIMPL3:func.3">N_CC</a>  is  <a href="fuzimpl3.html#V9" title="FUZIMPL3:attr.9">negation-strong</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fuzimpl3.html#D11" onmouseover="rs('fuzimpl3/D11')" onmouseout="rh()">FUZIMPL3:def 11</a>, <a class="ref" href="fuzimpl3.html#D13" onmouseover="rs('fuzimpl3/D13')" onmouseout="rh()">FUZIMPL3:def 13</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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