<?xml version="1.0"?>
<div class="add">

<span class="kw">set </span><font color="Maroon" title="c1">I</font> =  <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c2">f</font> =  <a href="fuzimpl3.html#K4" title="FUZIMPL3:func.4">FNegation</a> <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a>;<br/>
<span class="kw">set </span><font color="Maroon" title="c3">g</font> =  <a href="fuzimpl3.html#K5" title="FUZIMPL3:func.5">NegationD1</a> ;<br/>
<a NAME="E1:32"/><span class="lab"><font color="Green" title="E17">A1</font></span>: 
 <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <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="xxreal_1.html#T1" onmouseover="rs('xxreal_1/T1')" onmouseout="rh()">XXREAL_1:1</a></span>;<br/>
<a NAME="E2:32"/>
 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  <span class="p1">(<span class="default"><a href="fuzimpl3.html#K4" title="FUZIMPL3:func.4">FNegation</a> <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="fuzimpl3.html#K5" title="FUZIMPL3:func.5">NegationD1</a> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</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="32_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c4">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"> <span class="p1">(<span class="default"><a href="fuzimpl3.html#K4" title="FUZIMPL3:func.4">FNegation</a> <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="fuzimpl3.html#K5" title="FUZIMPL3:func.5">NegationD1</a> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">x</font></span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="32_1_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:32_1_1"/>
( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  or <font color="Maroon" title="c4">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="32_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:32_1_1_1"/><span class="lab"><font color="Green" title="E18">B1</font></span>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</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"> <span class="p1">(<span class="default"><a href="fuzimpl3.html#K4" title="FUZIMPL3:func.4">FNegation</a> <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="fuzimpl3.html#K5" title="FUZIMPL3:func.5">NegationD1</a> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">x</font></span><br/><div class="add"><span class="p1">(<span class="default"><a href="fuzimpl3.html#K4" title="FUZIMPL3:func.4">FNegation</a> <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">x</font> = 
<a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c4">x</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="fuzimpl3.html#D16" onmouseover="rs('fuzimpl3/D16')" onmouseout="rh()">FUZIMPL3:def 16</a></span>
<br/>.= 
1
<span class="kw">by</span> <span class="lab"><a class="ref" href="fuzimpl4.html#D4" target="_self" onmouseover="rs('fuzimpl4/D4')" onmouseout="rh()">II3Def</a>, <a class="txt" href="#E1:32_1_1_1"><span class="lab"><font color="Green" title="E18">B1</font></span></a></span>
<br/>.= 
<a href="fuzimpl3.html#K5" title="FUZIMPL3:func.5">NegationD1</a> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">x</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="fuzimpl3.html#D17" onmouseover="rs('fuzimpl3/D17')" onmouseout="rh()">FUZIMPL3:def 17</a>, <a class="txt" href="#E1:32_1_1_1"><span class="lab"><font color="Green" title="E18">B1</font></span></a></span>
;<br/><span class="kw">hence </span><a NAME="E3:32_1_1_1"/>
<span class="p1">(<span class="default"><a href="fuzimpl3.html#K4" title="FUZIMPL3:func.4">FNegation</a> <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="fuzimpl3.html#K5" title="FUZIMPL3:func.5">NegationD1</a> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="32_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:32_1_1_2"/><span class="lab"><font color="Green" title="E18">B1</font></span>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</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"> <span class="p1">(<span class="default"><a href="fuzimpl3.html#K4" title="FUZIMPL3:func.4">FNegation</a> <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="fuzimpl3.html#K5" title="FUZIMPL3:func.5">NegationD1</a> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">x</font></span><br/><div class="add"><span class="p1">(<span class="default"><a href="fuzimpl3.html#K4" title="FUZIMPL3:func.4">FNegation</a> <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">x</font> = 
<a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c4">x</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="fuzimpl3.html#D16" onmouseover="rs('fuzimpl3/D16')" onmouseout="rh()">FUZIMPL3:def 16</a></span>
<br/>.= 
 <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:32"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="txt" href="#E1:32_1_1_2"><span class="lab"><font color="Green" title="E18">B1</font></span></a>, <a class="ref" href="fuzimpl4.html#D4" target="_self" onmouseover="rs('fuzimpl4/D4')" onmouseout="rh()">II3Def</a></span>
<br/>.= 
<a href="fuzimpl3.html#K5" title="FUZIMPL3:func.5">NegationD1</a> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">x</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="fuzimpl3.html#D17" onmouseover="rs('fuzimpl3/D17')" onmouseout="rh()">FUZIMPL3:def 17</a>, <a class="txt" href="#E1:32_1_1_2"><span class="lab"><font color="Green" title="E18">B1</font></span></a></span>
;<br/><span class="kw">hence </span><a NAME="E3:32_1_1_2"/>
<span class="p1">(<span class="default"><a href="fuzimpl3.html#K4" title="FUZIMPL3:func.4">FNegation</a> <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="fuzimpl3.html#K5" title="FUZIMPL3:func.5">NegationD1</a> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">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></div><span class="kw">end;</span></div>

</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:32"/>
 <a href="fuzimpl3.html#K4" title="FUZIMPL3:func.4">FNegation</a> <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="fuzimpl3.html#K5" title="FUZIMPL3:func.5">NegationD1</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T63" onmouseover="rs('funct_2/T63')" onmouseout="rh()">FUNCT_2:63</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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