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<span class="kw">set </span><font color="Maroon" title="c1">N</font> =  <a href="fuzimpl3.html#K6" title="FUZIMPL3:func.6">NegationD2</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c2">I</font> =  <a href="fuzimpl2.html#NK8" title="FUZIMPL2:NK.8">I_WB</a> ;<br/>
<a NAME="E1:66_1_1"/>
 for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</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="fuzimpl2.html#NK8" title="FUZIMPL2:NK.8">I_WB</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Olive" title="b1">x</font>,<span class="p1">(<span class="default"><a href="fuzimpl3.html#K6" title="FUZIMPL3:func.6">NegationD2</a> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">y</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="fuzimpl2.html#NK8" title="FUZIMPL2:NK.8">I_WB</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Olive" title="b2">y</font>,<span class="p1">(<span class="default"><a href="fuzimpl3.html#K6" title="FUZIMPL3:func.6">NegationD2</a> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font></span>)</span>)
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="66_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c3">x</font>, <font color="Maroon" title="c4">y</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="fuzimpl2.html#NK8" title="FUZIMPL2:NK.8">I_WB</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">x</font>,<span class="p1">(<span class="default"><a href="fuzimpl3.html#K6" title="FUZIMPL3:func.6">NegationD2</a> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">y</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="fuzimpl2.html#NK8" title="FUZIMPL2:NK.8">I_WB</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c4">y</font>,<span class="p1">(<span class="default"><a href="fuzimpl3.html#K6" title="FUZIMPL3:func.6">NegationD2</a> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">x</font></span>)</span>)</span><br/>

<a NAME="E1:66_1_1_1"/>
<font color="Maroon" title="c3">x</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1
 
<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/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="66_1_1_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="E1:66_1_1_1_1"/><span class="kw">then </span>
( <font color="Maroon" title="c3">x</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1 or <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 </span><span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_0.html#T1" onmouseover="rs('xxreal_0/T1')" onmouseout="rh()">XXREAL_0:1</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="66_1_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:66_1_1_1_1_1"/><span class="lab"><font color="Green" title="E28">F1</font></span>: 
<font color="Maroon" title="c3">x</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1
 ; <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="fuzimpl2.html#NK8" title="FUZIMPL2:NK.8">I_WB</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">x</font>,<span class="p1">(<span class="default"><a href="fuzimpl3.html#K6" title="FUZIMPL3:func.6">NegationD2</a> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">y</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="fuzimpl2.html#NK8" title="FUZIMPL2:NK.8">I_WB</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c4">y</font>,<span class="p1">(<span class="default"><a href="fuzimpl3.html#K6" title="FUZIMPL3:func.6">NegationD2</a> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">x</font></span>)</span>)</span><br/><div class="add"><a NAME="E2:66_1_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E29">F2</font></span>: 
<a href="fuzimpl3.html#K6" title="FUZIMPL3:func.6">NegationD2</a> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fuzimpl3.html#D18" onmouseover="rs('fuzimpl3/D18')" onmouseout="rh()">FUZIMPL3:def 18</a></span>;<br/><a href="fuzimpl2.html#NK8" title="FUZIMPL2:NK.8">I_WB</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">x</font>,<span class="p1">(<span class="default"><a href="fuzimpl3.html#K6" title="FUZIMPL3:func.6">NegationD2</a> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">y</font></span>)</span>) = 
1
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:66_1_1_1_1_1"><span class="lab"><font color="Green" title="E28">F1</font></span></a>, <a class="ref" href="fuzimpl1.html#D22" onmouseover="rs('fuzimpl1/D22')" onmouseout="rh()">FUZIMPL1:def 22</a></span>
<br/>.= 
<a href="fuzimpl2.html#NK8" title="FUZIMPL2:NK.8">I_WB</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c4">y</font>,<span class="p1">(<span class="default"><a href="fuzimpl3.html#K6" title="FUZIMPL3:func.6">NegationD2</a> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">x</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:66_1_1_1_1_1"><span class="lab"><font color="Green" title="E29">F2</font></span></a>, <a class="ref" href="fuzimpl1.html#T8" onmouseover="rs('fuzimpl1/T8')" onmouseout="rh()">FUZIMPL1:8</a></span>
;<br/><span class="kw">hence </span><a NAME="E4:66_1_1_1_1_1"/>
<a href="fuzimpl2.html#NK8" title="FUZIMPL2:NK.8">I_WB</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">x</font>,<span class="p1">(<span class="default"><a href="fuzimpl3.html#K6" title="FUZIMPL3:func.6">NegationD2</a> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">y</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="fuzimpl2.html#NK8" title="FUZIMPL2:NK.8">I_WB</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c4">y</font>,<span class="p1">(<span class="default"><a href="fuzimpl3.html#K6" title="FUZIMPL3:func.6">NegationD2</a> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">x</font></span>)</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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="66_1_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:66_1_1_1_1_2"/><span class="lab"><font color="Green" title="E28">F1</font></span>: 
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ; <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="fuzimpl2.html#NK8" title="FUZIMPL2:NK.8">I_WB</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">x</font>,<span class="p1">(<span class="default"><a href="fuzimpl3.html#K6" title="FUZIMPL3:func.6">NegationD2</a> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">y</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="fuzimpl2.html#NK8" title="FUZIMPL2:NK.8">I_WB</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c4">y</font>,<span class="p1">(<span class="default"><a href="fuzimpl3.html#K6" title="FUZIMPL3:func.6">NegationD2</a> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">x</font></span>)</span>)</span><br/><div class="add"><span class="kw">then </span><a href="fuzimpl2.html#NK8" title="FUZIMPL2:NK.8">I_WB</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">x</font>,<span class="p1">(<span class="default"><a href="fuzimpl3.html#K6" title="FUZIMPL3:func.6">NegationD2</a> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">y</font></span>)</span>) = 
<a href="fuzimpl3.html#K6" title="FUZIMPL3:func.6">NegationD2</a> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">y</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="fuzimpl1.html#D22" onmouseover="rs('fuzimpl1/D22')" onmouseout="rh()">FUZIMPL1:def 22</a></span>
<br/>.= 
<a href="fuzimpl2.html#NK8" title="FUZIMPL2:NK.8">I_WB</a> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c4">y</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>, <a class="ref" href="fuzimpl3.html#T27" onmouseover="rs('fuzimpl3/T27')" onmouseout="rh()">FUZIMPL3:27</a></span>
<br/>.= 
<a href="fuzimpl2.html#NK8" title="FUZIMPL2:NK.8">I_WB</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c4">y</font>,<span class="p1">(<span class="default"><a href="fuzimpl3.html#K6" title="FUZIMPL3:func.6">NegationD2</a> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">x</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:66_1_1_1_1_2"><span class="lab"><font color="Green" title="E28">F1</font></span></a>, <a class="ref" href="fuzimpl3.html#D18" onmouseover="rs('fuzimpl3/D18')" onmouseout="rh()">FUZIMPL3:def 18</a></span>
;<br/><span class="kw">hence </span><a NAME="E3:66_1_1_1_1_2"/>
<a href="fuzimpl2.html#NK8" title="FUZIMPL2:NK.8">I_WB</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">x</font>,<span class="p1">(<span class="default"><a href="fuzimpl3.html#K6" title="FUZIMPL3:func.6">NegationD2</a> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">y</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="fuzimpl2.html#NK8" title="FUZIMPL2:NK.8">I_WB</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c4">y</font>,<span class="p1">(<span class="default"><a href="fuzimpl3.html#K6" title="FUZIMPL3:func.6">NegationD2</a> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">x</font></span>)</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></div><span class="kw">end;</span></div>

</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E2:66_1_1"/>
 <a href="fuzimpl2.html#NK8" title="FUZIMPL2:NK.8">I_WB</a>  is  <a href="fuzimpl3.html#K6" title="FUZIMPL3:func.6">NegationD2</a>  <a href="fuzimpl4.html#V3" title="FUZIMPL4:attr.3">-satisfying_R-CP</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"> verum</span><br/>


</div>
