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

<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#V8" title="FUZIMPL3:attr.8">negation-strict</a>  <a href="fuzimpl3.html#NM1" title="FUZIMPL3:NM.1">Fuzzy_Negation</a><br/>  for <font color="Olive" title="b2">N1</font> being   <a href="fuzimpl3.html#NM1" title="FUZIMPL3:NM.1">Fuzzy_Negation</a>  st <font color="Olive" title="b1">N</font> <a href="relat_1.html#K2" title="RELAT_1:func.2">~</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">N1</font> holds <br/>( <font color="Maroon" title="c1">I</font> is <font color="Olive" title="b1">N</font> <a href="fuzimpl4.html#V2" title="FUZIMPL4:attr.2">-satisfying_L-CP</a>  iff <font color="Maroon" title="c1">I</font> is <font color="Olive" title="b2">N1</font> <a href="fuzimpl4.html#V3" title="FUZIMPL4:attr.3">-satisfying_R-CP</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">N</font> be   <a href="fuzimpl3.html#V8" title="FUZIMPL3:attr.8">negation-strict</a>  <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">  for <font color="Olive" title="b1">N1</font> being   <a href="fuzimpl3.html#NM1" title="FUZIMPL3:NM.1">Fuzzy_Negation</a>  st <font color="Maroon" title="c2">N</font> <a href="relat_1.html#K2" title="RELAT_1:func.2">~</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">N1</font> holds <br/>( <font color="Maroon" title="c1">I</font> is <font color="Maroon" title="c2">N</font> <a href="fuzimpl4.html#V2" title="FUZIMPL4:attr.2">-satisfying_L-CP</a>  iff <font color="Maroon" title="c1">I</font> is <font color="Olive" title="b1">N1</font> <a href="fuzimpl4.html#V3" title="FUZIMPL4:attr.3">-satisfying_R-CP</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">N1</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="c2">N</font> <a href="relat_1.html#K2" title="RELAT_1:func.2">~</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">N1</font> implies ( <font color="Maroon" title="c1">I</font> is <font color="Maroon" title="c2">N</font> <a href="fuzimpl4.html#V2" title="FUZIMPL4:attr.2">-satisfying_L-CP</a>  iff <font color="Maroon" title="c1">I</font> is <font color="Maroon" title="c3">N1</font> <a href="fuzimpl4.html#V3" title="FUZIMPL4:attr.3">-satisfying_R-CP</a>  ) )</span><br/>





<span class="kw">assume </span><a NAME="E1:17"/><span class="lab"><font color="Green" title="E3">A0</font></span>: 
<font color="Maroon" title="c2">N</font> <a href="relat_1.html#K2" title="RELAT_1:func.2">~</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">N1</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"> ( <font color="Maroon" title="c1">I</font> is <font color="Maroon" title="c2">N</font> <a href="fuzimpl4.html#V2" title="FUZIMPL4:attr.2">-satisfying_L-CP</a>  iff <font color="Maroon" title="c1">I</font> is <font color="Maroon" title="c3">N1</font> <a href="fuzimpl4.html#V3" title="FUZIMPL4:attr.3">-satisfying_R-CP</a>  )</span><br/>

<a NAME="E2:17"/><span class="kw">then </span>
<font color="Maroon" title="c2">N</font> is  <a href="funct_2.html#V2" title="FUNCT_2:attr.2">onto</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fuzimpl4.html#T4" target="_self" onmouseover="rs('fuzimpl4/T4')" onmouseout="rh()">LemmaOnto2</a></span>;<br/>
<a NAME="E3:17"/><span class="kw">then </span><span class="lab"><font color="Green" title="E4">A2</font></span>: 
 <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c2">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="funct_2.html#D3" onmouseover="rs('funct_2/D3')" onmouseout="rh()">FUNCT_2:def 3</a></span>;<br/>
<a NAME="E4:17"/><span class="lab"><font color="Green" title="E5">DD</font></span>: 
<font color="Maroon" title="c2">N</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">N</font> <a href="relat_1.html#K2" title="RELAT_1:func.2">~</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D5" onmouseover="rs('funct_1/D5')" onmouseout="rh()">FUNCT_1:def 5</a></span>;<br/>
<span class="kw">thus </span><a NAME="E5:17"/>
( <font color="Maroon" title="c1">I</font> is <font color="Maroon" title="c2">N</font> <a href="fuzimpl4.html#V2" title="FUZIMPL4:attr.2">-satisfying_L-CP</a>  implies <font color="Maroon" title="c1">I</font> is <font color="Maroon" title="c3">N1</font> <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"> ( <font color="Maroon" title="c1">I</font> is <font color="Maroon" title="c3">N1</font> <a href="fuzimpl4.html#V3" title="FUZIMPL4:attr.3">-satisfying_R-CP</a>  implies <font color="Maroon" title="c1">I</font> is <font color="Maroon" title="c2">N</font> <a href="fuzimpl4.html#V2" title="FUZIMPL4:attr.2">-satisfying_L-CP</a>  )</span><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="17_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:17_1"/><span class="lab"><font color="Green" title="E6">a1</font></span>: 
<font color="Maroon" title="c1">I</font> is <font color="Maroon" title="c2">N</font> <a href="fuzimpl4.html#V2" title="FUZIMPL4:attr.2">-satisfying_L-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"> <font color="Maroon" title="c1">I</font> is <font color="Maroon" title="c3">N1</font> <a href="fuzimpl4.html#V3" title="FUZIMPL4:attr.3">-satisfying_R-CP</a> </span><br/>

<a NAME="E2:17_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  <font color="Maroon" title="c1">I</font> <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"><font color="Maroon" title="c3">N1</font> <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> <font color="Maroon" title="c1">I</font> <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"><font color="Maroon" title="c3">N1</font> <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="17_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c4">x</font>, <font color="Maroon" title="c5">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"> <font color="Maroon" title="c1">I</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c4">x</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">N1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">y</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">I</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c5">y</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">N1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">x</font></span>)</span>)</span><br/>

<font color="Maroon" title="c1">I</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c4">x</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">N1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">y</font></span>)</span>) = 
<font color="Maroon" title="c1">I</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">N1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">x</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">N1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">y</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:17"><span class="lab"><font color="Green" title="E3">A0</font></span></a>, <a class="txt" href="#E3:17"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="ref" href="funct_1.html#T35" onmouseover="rs('funct_1/T35')" onmouseout="rh()">FUNCT_1:35</a>, <a class="txt" href="#E4:17"><span class="lab"><font color="Green" title="E5">DD</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c1">I</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">N1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">y</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">N1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">x</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:17_1"><span class="lab"><font color="Green" title="E6">a1</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c1">I</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c5">y</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">N1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">x</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:17"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="txt" href="#E4:17"><span class="lab"><font color="Green" title="E5">DD</font></span></a>, <a class="txt" href="#E1:17"><span class="lab"><font color="Green" title="E3">A0</font></span></a>, <a class="ref" href="funct_1.html#T35" onmouseover="rs('funct_1/T35')" onmouseout="rh()">FUNCT_1:35</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E2:17_1_1"/>
<font color="Maroon" title="c1">I</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c4">x</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">N1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">y</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">I</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c5">y</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">N1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">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>
<span class="kw">hence </span><a NAME="E3:17_1"/>
<font color="Maroon" title="c1">I</font> is <font color="Maroon" title="c3">N1</font> <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><span class="kw">end;</span></div>

<span class="kw">assume </span><a NAME="E6:17"/><span class="lab"><font color="Green" title="E6">a1</font></span>: 
<font color="Maroon" title="c1">I</font> is <font color="Maroon" title="c3">N1</font> <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"> <font color="Maroon" title="c1">I</font> is <font color="Maroon" title="c2">N</font> <a href="fuzimpl4.html#V2" title="FUZIMPL4:attr.2">-satisfying_L-CP</a> </span><br/>

<a NAME="E7:17"/><span class="lab"><font color="Green" title="E7">C1</font></span>: 
 <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c2">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="funct_2.html#D1" onmouseover="rs('funct_2/D1')" onmouseout="rh()">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E8:17"/>
 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  <font color="Maroon" title="c1">I</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font></span>)</span>,<font color="Olive" title="b2">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">I</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">y</font></span>)</span>,<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="17_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c4">x</font>, <font color="Maroon" title="c5">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"> <font color="Maroon" title="c1">I</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">x</font></span>)</span>,<font color="Maroon" title="c5">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">I</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">y</font></span>)</span>,<font color="Maroon" title="c4">x</font>)</span><br/>

<a NAME="E1:17_2"/><span class="lab"><font color="Green" title="E8">B2</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">N1</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c2">N</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:17"><span class="lab"><font color="Green" title="E3">A0</font></span></a>, <a class="txt" href="#E7:17"><span class="lab"><font color="Green" title="E7">C1</font></span></a>, <a class="ref" href="funct_1.html#T34" onmouseover="rs('funct_1/T34')" onmouseout="rh()">FUNCT_1:34</a>, <a class="txt" href="#E4:17"><span class="lab"><font color="Green" title="E5">DD</font></span></a></span>;<br/>
<a NAME="E2:17_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">N1</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c2">N</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">N1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">y</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:17"><span class="lab"><font color="Green" title="E7">C1</font></span></a>, <a class="ref" href="funct_1.html#T13" onmouseover="rs('funct_1/T13')" onmouseout="rh()">FUNCT_1:13</a></span>;<br/>
<span class="kw">then </span><font color="Maroon" title="c1">I</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">x</font></span>)</span>,<font color="Maroon" title="c5">y</font>) = 
<font color="Maroon" title="c1">I</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">y</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">N1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">x</font></span>)</span></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:17"><span class="lab"><font color="Green" title="E6">a1</font></span></a>, <a class="txt" href="#E1:17_2"><span class="lab"><font color="Green" title="E8">B2</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c1">I</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">y</font></span>)</span>,<font color="Maroon" title="c4">x</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:17"><span class="lab"><font color="Green" title="E3">A0</font></span></a>, <a class="txt" href="#E7:17"><span class="lab"><font color="Green" title="E7">C1</font></span></a>, <a class="ref" href="funct_1.html#T34" onmouseover="rs('funct_1/T34')" onmouseout="rh()">FUNCT_1:34</a>, <a class="txt" href="#E4:17"><span class="lab"><font color="Green" title="E5">DD</font></span></a></span>
;<br/>
<span class="kw">hence </span><a NAME="E4:17_2"/>
<font color="Maroon" title="c1">I</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">x</font></span>)</span>,<font color="Maroon" title="c5">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">I</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">y</font></span>)</span>,<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>
<span class="kw">hence </span><a NAME="E9:17"/>
<font color="Maroon" title="c1">I</font> is <font color="Maroon" title="c2">N</font> <a href="fuzimpl4.html#V2" title="FUZIMPL4:attr.2">-satisfying_L-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>
