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

<span class="kw">set </span><font color="Maroon" title="c1">I</font> =  <a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> ;<br/>
<a NAME="E1:38_1_1"/>
 ex <font color="Olive" title="b1">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> st <a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (1,<font color="Olive" title="b1">y</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">y</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="38_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">reconsider </span><font color="Maroon" title="c2">y</font> = 1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2 as    <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> <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/>
<span class="kw">take </span>
<font color="Maroon" title="c2">y</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"> <a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (1,<font color="Maroon" title="c2">y</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">y</font></span><br/>

<a NAME="E2:38_1_1_1"/>
1 <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/>
<span class="kw">hence </span><a NAME="E3:38_1_1_1"/>
<a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (1,<font color="Maroon" title="c2">y</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">y</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fuzimpl4.html#D5" target="_self" onmouseover="rs('fuzimpl4/D5')" onmouseout="rh()">II4Def</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/>


</div><span class="kw">end;</span></div>
<a NAME="E2:38_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E19">T1</font></span>: 
 not  <a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a>  is  <a href="fuzimpl2.html#V1" title="FUZIMPL2:attr.1">satisfying_(NP)</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fuzimpl2.html#D1" onmouseover="rs('fuzimpl2/D1')" onmouseout="rh()">FUZIMPL2:def 1</a></span>;<br/>
<a NAME="E3:38_1_1"/>
 for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font>, <font color="Olive" title="b3">z</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="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</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="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Olive" title="b2">y</font>,<font color="Olive" title="b3">z</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</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="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Olive" title="b1">x</font>,<font color="Olive" title="b3">z</font>)</span>)</span>)
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="38_1_1_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</font>, <font color="Maroon" title="c4">z</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="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<span class="p1">(<span class="default"><a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">y</font>,<span class="p1">(<span class="default"><a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c4">z</font>)</span>)</span>)</span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="38_1_1_2_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="E1:38_1_1_2_1"/>
( <font color="Maroon" title="c4">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or ( <font color="Maroon" title="c4">z</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 &amp; <font color="Maroon" title="c3">y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 &amp; <font color="Maroon" title="c2">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 ) or ( <font color="Maroon" title="c4">z</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 &amp; <font color="Maroon" title="c3">y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 &amp; <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) or ( <font color="Maroon" title="c4">z</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 &amp; <font color="Maroon" title="c3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) or ( <font color="Maroon" title="c4">z</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 &amp; <font color="Maroon" title="c3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c2">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="38_1_1_2_1_1"><span class="kw">suppose </span></a><a NAME="E1:38_1_1_2_1_1"/><span class="lab"><font color="Green" title="E20">D1</font></span>: 
<font color="Maroon" title="c4">z</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="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<span class="p1">(<span class="default"><a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">y</font>,<span class="p1">(<span class="default"><a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c4">z</font>)</span>)</span>)</span><br/><div class="add"><a NAME="E2:38_1_1_2_1_1"/><span class="kw">then </span>
( <a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c4">z</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fuzimpl4.html#D5" target="_self" onmouseover="rs('fuzimpl4/D5')" onmouseout="rh()">II4Def</a></span>;<br/><span class="kw">hence </span><a NAME="E3:38_1_1_2_1_1"/>
<a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<span class="p1">(<span class="default"><a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">y</font>,<span class="p1">(<span class="default"><a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c4">z</font>)</span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:38_1_1_2_1_1"><span class="lab"><font color="Green" title="E20">D1</font></span></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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="38_1_1_2_1_2"><span class="kw">suppose </span></a><a NAME="E1:38_1_1_2_1_2"/><span class="lab"><font color="Green" title="E20">f2</font></span>: 
( <font color="Maroon" title="c4">z</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 &amp; <font color="Maroon" title="c3">y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 &amp; <font color="Maroon" title="c2">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</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="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<span class="p1">(<span class="default"><a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">y</font>,<span class="p1">(<span class="default"><a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c4">z</font>)</span>)</span>)</span><br/><div class="add"><span class="kw">then </span><a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<span class="p1">(<span class="default"><a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font>)</span>)</span>) = 
1
<span class="kw">by</span> <span class="lab"><a class="ref" href="fuzimpl4.html#D5" target="_self" onmouseover="rs('fuzimpl4/D5')" onmouseout="rh()">II4Def</a></span>
<br/>.= 
<a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">y</font>,<span class="p1">(<span class="default"><a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c4">z</font>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:38_1_1_2_1_2"><span class="lab"><font color="Green" title="E20">f2</font></span></a>, <a class="ref" href="fuzimpl4.html#D5" target="_self" onmouseover="rs('fuzimpl4/D5')" onmouseout="rh()">II4Def</a></span>
;<br/><span class="kw">hence </span><a NAME="E3:38_1_1_2_1_2"/>
<a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<span class="p1">(<span class="default"><a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">y</font>,<span class="p1">(<span class="default"><a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c4">z</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="38_1_1_2_1_3"><span class="kw">suppose </span></a><a NAME="E1:38_1_1_2_1_3"/><span class="lab"><font color="Green" title="E20">F1</font></span>: 
( <font color="Maroon" title="c4">z</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 &amp; <font color="Maroon" title="c3">y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 &amp; <font color="Maroon" title="c2">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="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<span class="p1">(<span class="default"><a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">y</font>,<span class="p1">(<span class="default"><a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c4">z</font>)</span>)</span>)</span><br/><div class="add"><a NAME="E2:38_1_1_2_1_3"/><span class="kw">then </span>
( <a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c4">z</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fuzimpl4.html#D5" target="_self" onmouseover="rs('fuzimpl4/D5')" onmouseout="rh()">II4Def</a></span>;<br/><span class="kw">then </span><a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<span class="p1">(<span class="default"><a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font>)</span>)</span>) = 
1
<span class="kw">by</span> <span class="lab"><a class="ref" href="fuzimpl4.html#D5" target="_self" onmouseover="rs('fuzimpl4/D5')" onmouseout="rh()">II4Def</a></span>
<br/>.= 
<a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">y</font>,<span class="p1">(<span class="default"><a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c4">z</font>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:38_1_1_2_1_3"><span class="lab"><font color="Green" title="E20">F1</font></span></a>, <a class="ref" href="fuzimpl4.html#D5" target="_self" onmouseover="rs('fuzimpl4/D5')" onmouseout="rh()">II4Def</a></span>
;<br/><span class="kw">hence </span><a NAME="E4:38_1_1_2_1_3"/>
<a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<span class="p1">(<span class="default"><a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">y</font>,<span class="p1">(<span class="default"><a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c4">z</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="38_1_1_2_1_4"><span class="kw">suppose </span></a><a NAME="E1:38_1_1_2_1_4"/>
( <font color="Maroon" title="c4">z</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 &amp; <font color="Maroon" title="c3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c2">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="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<span class="p1">(<span class="default"><a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">y</font>,<span class="p1">(<span class="default"><a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c4">z</font>)</span>)</span>)</span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:38_1_1_2_1_4"/>
<a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<span class="p1">(<span class="default"><a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">y</font>,<span class="p1">(<span class="default"><a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c4">z</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="38_1_1_2_1_5"><span class="kw">suppose </span></a><a NAME="E1:38_1_1_2_1_5"/><span class="lab"><font color="Green" title="E20">F1</font></span>: 
( <font color="Maroon" title="c4">z</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 &amp; <font color="Maroon" title="c3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c2">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</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="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<span class="p1">(<span class="default"><a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">y</font>,<span class="p1">(<span class="default"><a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c4">z</font>)</span>)</span>)</span><br/><div class="add"><a NAME="E2:38_1_1_2_1_5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E21">F3</font></span>: 
<a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c4">z</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fuzimpl4.html#D5" target="_self" onmouseover="rs('fuzimpl4/D5')" onmouseout="rh()">II4Def</a></span>;<br/><a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<span class="p1">(<span class="default"><a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font>)</span>)</span>) = 
1
<span class="kw">by</span> <span class="lab"><a class="ref" href="fuzimpl4.html#D5" target="_self" onmouseover="rs('fuzimpl4/D5')" onmouseout="rh()">II4Def</a>, <a class="txt" href="#E1:38_1_1_2_1_5"><span class="lab"><font color="Green" title="E20">F1</font></span></a></span>
<br/>.= 
<a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">y</font>,<span class="p1">(<span class="default"><a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c4">z</font>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:38_1_1_2_1_5"><span class="lab"><font color="Green" title="E21">F3</font></span></a>, <a class="ref" href="fuzimpl4.html#D5" target="_self" onmouseover="rs('fuzimpl4/D5')" onmouseout="rh()">II4Def</a></span>
;<br/><span class="kw">hence </span><a NAME="E4:38_1_1_2_1_5"/>
<a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<span class="p1">(<span class="default"><a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">y</font>,<span class="p1">(<span class="default"><a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c4">z</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="E4:38_1_1"/>
(  <a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a>  is  <a href="fuzimpl2.html#V2" title="FUZIMPL2:attr.2">satisfying_(EP)</a>  &amp;  not  <a href="fuzimpl4.html#K2" title="FUZIMPL4:func.2">I_I4</a>  is  <a href="fuzimpl2.html#V1" title="FUZIMPL2:attr.1">satisfying_(NP)</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:38_1_1"><span class="lab"><font color="Green" title="E19">T1</font></span></a>, <a class="ref" href="fuzimpl2.html#D2" onmouseover="rs('fuzimpl2/D2')" onmouseout="rh()">FUZIMPL2:def 2</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/>


</div>
