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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="fuzzy_3.html#NM1">RMembership_Func</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font>;<br/>



<b>set </b><font color="Maroon">c<sub>3</sub></font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span> ;<br/>
<b>set </b><font color="Maroon">c<sub>4</sub></font> =  <a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>;<br/>
<a NAME="E1:61"/><i><font color="Green">E40</font></i>: 
 <a href="yellow_0.html#K1">"\/"</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span> ,<span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="lfuzzy_0.html#K5">@</a> <span class="p1">(<span class="default"><a href="yellow_0.html#K1">"\/"</a> <span class="p2">{<span class="default"> <span class="p3">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span> ,<span class="p2">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p3"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="lfuzzy_0.html#D5">LFUZZY_0:def 5</a></i>;<br/>
<a NAME="E2:61"/><i><font color="Green">E41</font></i>: 
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="61_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:61_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E3:61_1"/><i><font color="Green">E42</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 ;<br/>
<a NAME="E4:61_1"/>
<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="lfuzzy_0.html#K6">@</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="lfuzzy_0.html#D6">LFUZZY_0:def 6</a></i>;<br/>
<b>hence </b><a NAME="E5:61_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span>
 <b>by </b><i><a class="txt" href="lfuzzy_1.html#E3:61_1"><i><font color="Green">E42</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:61"/><i><font color="Green">E42</font></i>: 
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p3">(<span class="default"><a href="lfuzzy_1.html#K5" target="_self">TrCl</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  </span>}</span>  <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="yellow_0.html#K1">"\/"</a> <span class="p3">{<span class="default"> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p5">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>2</sub></font></span>)</span></span>)</span> where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  </span>}</span> ,<span class="p3">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p4"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span></span>)</span> where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  </span>}</span> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="61_2"><b>proof </b></a><div class="add">

<b>set </b><font color="Maroon">c<sub>5</sub></font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p3">(<span class="default"><a href="lfuzzy_1.html#K5" target="_self">TrCl</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  </span>}</span> ;<br/>
<b>set </b><font color="Maroon">c<sub>6</sub></font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="yellow_0.html#K1">"\/"</a> <span class="p3">{<span class="default"> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p5">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>2</sub></font></span>)</span></span>)</span> where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  </span>}</span> ,<span class="p3">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p4"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span></span>)</span> where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  </span>}</span> ;<br/>
<b>thus </b><a NAME="E1:61_2"/>
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p3">(<span class="default"><a href="lfuzzy_1.html#K5" target="_self">TrCl</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  </span>}</span>  <a href="tarski.html#R1">c=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="yellow_0.html#K1">"\/"</a> <span class="p3">{<span class="default"> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p5">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>2</sub></font></span>)</span></span>)</span> where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  </span>}</span> ,<span class="p3">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p4"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span></span>)</span> where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  </span>}</span> 
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="61_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>7</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:61_2_1"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p3">(<span class="default"><a href="lfuzzy_1.html#K5" target="_self">TrCl</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>8</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span><b> such that </b><br/><a NAME="E3:61_2_1"/><i><font color="Green">E43</font></i>: 
( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p1">(<span class="default"><a href="lfuzzy_1.html#K5" target="_self">TrCl</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  )
 ;<br/>
<font color="Maroon">c<sub>7</sub></font> = 
<span class="p1">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <span class="p2">(<span class="default"><a href="yellow_0.html#K1">"\/"</a> <span class="p3">{<span class="default"> <span class="p4">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span> ,<span class="p3">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p4"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="lfuzzy_1.html#E1:61"><i><font color="Green">E40</font></i></a>, <a class="txt" href="lfuzzy_1.html#E3:61_2_1"><i><font color="Green">E43</font></i></a></i>
<br/>.= 
 <a href="yellow_0.html#K1">"\/"</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p3">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span>)</span> where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  </span>}</span> ,<span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span>
<b>by </b><i><a class="txt" href="lfuzzy_1.html#E2:61"><i><font color="Green">E41</font></i></a>, <a class="ref" href="lfuzzy_1.html#T34" target="_self">Th34</a></i>
;<br/>
<b>hence </b><a NAME="E5:61_2_1"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="yellow_0.html#K1">"\/"</a> <span class="p3">{<span class="default"> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p5">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>2</sub></font></span>)</span></span>)</span> where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  </span>}</span> ,<span class="p3">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p4"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span></span>)</span> where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  </span>}</span> 
 <b>by </b><i><a class="txt" href="lfuzzy_1.html#E3:61_2_1"><i><font color="Green">E43</font></i></a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E2:61_2"/>
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="yellow_0.html#K1">"\/"</a> <span class="p3">{<span class="default"> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p5">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>2</sub></font></span>)</span></span>)</span> where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  </span>}</span> ,<span class="p3">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p4"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span></span>)</span> where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  </span>}</span>  <a href="tarski.html#R1">c=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p3">(<span class="default"><a href="lfuzzy_1.html#K5" target="_self">TrCl</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  </span>}</span> 
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="61_2_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>7</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:61_2_2"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="yellow_0.html#K1">"\/"</a> <span class="p3">{<span class="default"> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p5">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>2</sub></font></span>)</span></span>)</span> where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  </span>}</span> ,<span class="p3">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p4"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span></span>)</span> where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>8</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span><b> such that </b><br/><a NAME="E3:61_2_2"/><i><font color="Green">E43</font></i>: 
( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#K1">"\/"</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p3">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span>)</span> where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  </span>}</span> ,<span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  )
 ;<br/>
<font color="Maroon">c<sub>7</sub></font> = 
<span class="p1">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <span class="p2">(<span class="default"><a href="yellow_0.html#K1">"\/"</a> <span class="p3">{<span class="default"> <span class="p4">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span> ,<span class="p3">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p4"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="lfuzzy_1.html#E2:61"><i><font color="Green">E41</font></i></a>, <a class="txt" href="lfuzzy_1.html#E3:61_2_2"><i><font color="Green">E43</font></i></a>, <a class="ref" href="lfuzzy_1.html#T34" target="_self">Th34</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p1">(<span class="default"><a href="lfuzzy_1.html#K5" target="_self">TrCl</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="lfuzzy_1.html#E1:61"><i><font color="Green">E40</font></i></a></i>
;<br/>
<b>hence </b><a NAME="E5:61_2_2"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p3">(<span class="default"><a href="lfuzzy_1.html#K5" target="_self">TrCl</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  </span>}</span> 
 <b>by </b><i><a class="txt" href="lfuzzy_1.html#E3:61_2_2"><i><font color="Green">E43</font></i></a></i>;<br/>


</div><b>end;</b></div>


</div><b>end;</b></div>
<a NAME="E4:61"/><i><font color="Green">E43</font></i>: 
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p3">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>2</sub></font></span>)</span></span>)</span> where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span>, B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  ) </span>}</span>  <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p3">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a>, B is   <a href="nat_1.html#NM1">Nat</a> : ( <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp; <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 ) </span>}</span> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="61_3"><b>proof </b></a><div class="add">

<b>set </b><font color="Maroon">c<sub>5</sub></font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p3">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>2</sub></font></span>)</span></span>)</span> where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span>, B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  ) </span>}</span> ;<br/>
<b>set </b><font color="Maroon">c<sub>6</sub></font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p3">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a>, B is   <a href="nat_1.html#NM1">Nat</a> : ( <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp; <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 ) </span>}</span> ;<br/>
<b>thus </b><a NAME="E1:61_3"/>
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p3">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>2</sub></font></span>)</span></span>)</span> where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span>, B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  ) </span>}</span>  <a href="tarski.html#R1">c=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p3">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a>, B is   <a href="nat_1.html#NM1">Nat</a> : ( <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp; <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 ) </span>}</span> 
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="61_3_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>7</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:61_3_1"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p3">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>2</sub></font></span>)</span></span>)</span> where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span>, B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  ) </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span><b> such that </b><br/><a NAME="E3:61_3_1"/><i><font color="Green">E44</font></i>: 
( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  &amp; <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  )
 ;<br/>
<b>consider </b><font color="Maroon">c<sub>10</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E5:61_3_1"/><i><font color="Green">E45</font></i>: 
( <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 <b>by </b><i><a class="txt" href="lfuzzy_1.html#E3:61_3_1"><i><font color="Green">E44</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>11</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E7:61_3_1"/><i><font color="Green">E46</font></i>: 
( <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 <b>by </b><i><a class="txt" href="lfuzzy_1.html#E3:61_3_1"><i><font color="Green">E44</font></i></a></i>;<br/>
<a NAME="E8:61_3_1"/>
( <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a>  <a href="lfuzzy_0.html#K5">@</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a>  <a href="lfuzzy_0.html#K5">@</a> <font color="Maroon">c<sub>9</sub></font> )
 
<b>by </b><i><a class="ref" href="lfuzzy_0.html#D5">LFUZZY_0:def 5</a></i>;<br/>
<b>hence </b><a NAME="E9:61_3_1"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p3">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a>, B is   <a href="nat_1.html#NM1">Nat</a> : ( <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp; <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 ) </span>}</span> 
 <b>by </b><i><a class="txt" href="lfuzzy_1.html#E3:61_3_1"><i><font color="Green">E44</font></i></a>, <a class="txt" href="lfuzzy_1.html#E5:61_3_1"><i><font color="Green">E45</font></i></a>, <a class="txt" href="lfuzzy_1.html#E7:61_3_1"><i><font color="Green">E46</font></i></a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E2:61_3"/>
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p3">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a>, B is   <a href="nat_1.html#NM1">Nat</a> : ( <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp; <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 ) </span>}</span>  <a href="tarski.html#R1">c=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p3">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>2</sub></font></span>)</span></span>)</span> where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span>, B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  ) </span>}</span> 
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="61_3_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>7</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:61_3_2"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p3">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a>, B is   <a href="nat_1.html#NM1">Nat</a> : ( <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp; <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 ) </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E3:61_3_2"/><i><font color="Green">E44</font></i>: 
( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp; <font color="Maroon">c<sub>9</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 ;<br/>
<a NAME="E4:61_3_2"/><i><font color="Green">E45</font></i>: 
( <font color="Maroon">c<sub>8</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  &amp; <font color="Maroon">c<sub>9</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  )
 
<b>by </b><i><a class="txt" href="lfuzzy_1.html#E3:61_3_2"><i><font color="Green">E44</font></i></a></i>;<br/>
<a NAME="E5:61_3_2"/><i><font color="Green">E46</font></i>: 
( <font color="Maroon">c<sub>8</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="lfuzzy_0.html#K6">@</a>  &amp; <font color="Maroon">c<sub>9</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="lfuzzy_0.html#K6">@</a>  )
 
<b>by </b><i><a class="ref" href="lfuzzy_0.html#D6">LFUZZY_0:def 6</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>10</sub></font> = <font color="Maroon">c<sub>8</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> ;<br/>
<b>reconsider </b><font color="Maroon">c<sub>11</sub></font> = <font color="Maroon">c<sub>9</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> <b>by </b><i><a class="txt" href="lfuzzy_1.html#E5:61_3_2"><i><font color="Green">E46</font></i></a></i>;<br/>
<a NAME="E8:61_3_2"/>
(  <a href="lfuzzy_0.html#K5">@</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> &amp;  <a href="lfuzzy_0.html#K5">@</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font> )
 
<b>by </b><i><a class="ref" href="lfuzzy_0.html#D5">LFUZZY_0:def 5</a></i>;<br/>
<b>hence </b><a NAME="E9:61_3_2"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p3">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>2</sub></font></span>)</span></span>)</span> where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span>, B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  ) </span>}</span> 
 <b>by </b><i><a class="txt" href="lfuzzy_1.html#E3:61_3_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="lfuzzy_1.html#E4:61_3_2"><i><font color="Green">E45</font></i></a></i>;<br/>


</div><b>end;</b></div>


</div><b>end;</b></div>
<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span>,  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span>) <b>-&gt; </b>   <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> = <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Maroon">a<sub>1</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p2">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Maroon">a<sub>2</sub></font></span>)</span></span>)</span> <a href="lfuzzy_0.html#K6">@</a> ;<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span>] means <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span> ;<br/>
<b>defpred </b><font color="Maroon">S<sub>2</sub></font>[  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span>] means <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span> ;<br/>
<a NAME="E5:61"/><i><font color="Green">E44</font></i>: 
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="yellow_0.html#K1">"\/"</a> <span class="p3">{<span class="default"> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p5">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>2</sub></font></span>)</span></span>)</span> where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  </span>}</span> ,<span class="p3">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p4"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span></span>)</span> where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  </span>}</span>  <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="yellow_0.html#K1">"\/"</a> <span class="p3">{<span class="default"> <span class="p4">(<span class="default"><span class="p5"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p0">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>2</sub></font></span>)</span></span>)</span> <a href="lfuzzy_0.html#K6">@</a> </span>)</span> where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  </span>}</span> ,<span class="p3">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p4"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span></span>)</span> where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  </span>}</span> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="61_4"><b>proof </b></a><div class="add">

<b>defpred </b><font color="Maroon">S<sub>3</sub></font>[  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span>] means <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span> ;<br/>
<b>deffunc </b><font color="Maroon">H<sub>2</sub></font>(  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span>) <b>-&gt; </b>   <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> =  <a href="yellow_0.html#K1">"\/"</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Maroon">a<sub>1</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p3">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span>)</span> where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  </span>}</span> ,<span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>3</sub></font>(  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span>) <b>-&gt; </b>   <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> =  <a href="yellow_0.html#K1">"\/"</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Maroon">a<sub>1</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p4">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span>)</span> <a href="lfuzzy_0.html#K6">@</a> </span>)</span> where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  </span>}</span> ,<span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span>;<br/>
<a NAME="E1:61_4"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> holds  <a href="yellow_0.html#K1">"\/"</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p3">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>2</sub></font></span>)</span></span>)</span> where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  </span>}</span> ,<span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#K1">"\/"</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p4">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>2</sub></font></span>)</span></span>)</span> <a href="lfuzzy_0.html#K6">@</a> </span>)</span> where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  </span>}</span> ,<span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="61_4_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span>;<br/>

<a NAME="E1:61_4_1"/>
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p3">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span>)</span> where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  </span>}</span>  <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p4">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span>)</span> <a href="lfuzzy_0.html#K6">@</a> </span>)</span> where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  </span>}</span> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="61_4_1_1"><b>proof </b></a><div class="add">

<b>defpred </b><font color="Maroon">S<sub>4</sub></font>[  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span>] means <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span> ;<br/>
<b>deffunc </b><font color="Maroon">H<sub>4</sub></font>(  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span>) <b>-&gt; </b>   <a href="fuzzy_1.html#M1">Membership_Func</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span> = <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Maroon">a<sub>1</sub></font></span>)</span>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>5</sub></font>(  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span>) <b>-&gt; </b>   <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> = <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p2">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Maroon">a<sub>1</sub></font></span>)</span></span>)</span> <a href="lfuzzy_0.html#K6">@</a> ;<br/>
<a NAME="E1:61_4_1_1"/><i><font color="Green">E45</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> holds <font color="Maroon">H<sub>4</sub></font>(<font color="Olive">b<sub>1</sub></font>) <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>5</sub></font>(<font color="Olive">b<sub>1</sub></font>)
 
<b>by </b><i><a class="ref" href="lfuzzy_0.html#D6">LFUZZY_0:def 6</a></i>;<br/>
<a NAME="E2:61_4_1_1"/>
<span class="p1">{<span class="default"> <font color="Maroon">H<sub>4</sub></font>(<font color="Olive">b<sub>1</sub></font>) where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : <font color="Maroon">S<sub>4</sub></font>[<font color="Olive">b<sub>1</sub></font>] </span>}</span>  <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Maroon">H<sub>5</sub></font>(<font color="Olive">b<sub>1</sub></font>) where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : <font color="Maroon">S<sub>4</sub></font>[<font color="Olive">b<sub>1</sub></font>] </span>}</span> 
 
<b>from </b><i><a class="ref" href="fraenkel.html#S5">FRAENKEL:sch 5</a>(<a class="txt" href="lfuzzy_1.html#E1:61_4_1_1"><i><font color="Green">E45</font></i></a>);<br/></i>
<b>hence </b><a NAME="E3:61_4_1_1"/>
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p3">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span>)</span> where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  </span>}</span>  <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p4">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span>)</span> <a href="lfuzzy_0.html#K6">@</a> </span>)</span> where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  </span>}</span> 
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:61_4_1"/>
 <a href="yellow_0.html#K1">"\/"</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p3">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span>)</span> where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  </span>}</span> ,<span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#K1">"\/"</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p4">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span>)</span> <a href="lfuzzy_0.html#K6">@</a> </span>)</span> where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  </span>}</span> ,<span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E2:61_4"/><b>then </b><i><font color="Green">E45</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> holds <font color="Maroon">H<sub>2</sub></font>(<font color="Olive">b<sub>1</sub></font>) <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Olive">b<sub>1</sub></font>)
 
;<br/>
<a NAME="E3:61_4"/>
<span class="p1">{<span class="default"> <font color="Maroon">H<sub>2</sub></font>(<font color="Olive">b<sub>1</sub></font>) where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : <font color="Maroon">S<sub>3</sub></font>[<font color="Olive">b<sub>1</sub></font>] </span>}</span>  <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Maroon">H<sub>3</sub></font>(<font color="Olive">b<sub>1</sub></font>) where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : <font color="Maroon">S<sub>3</sub></font>[<font color="Olive">b<sub>1</sub></font>] </span>}</span> 
 
<b>from </b><i><a class="ref" href="fraenkel.html#S5">FRAENKEL:sch 5</a>(<a class="txt" href="lfuzzy_1.html#E2:61_4"><i><font color="Green">E45</font></i></a>);<br/></i>
<b>hence </b><a NAME="E4:61_4"/>
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="yellow_0.html#K1">"\/"</a> <span class="p3">{<span class="default"> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p5">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>2</sub></font></span>)</span></span>)</span> where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  </span>}</span> ,<span class="p3">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p4"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span></span>)</span> where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  </span>}</span>  <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="yellow_0.html#K1">"\/"</a> <span class="p3">{<span class="default"> <span class="p4">(<span class="default"><span class="p5"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p0">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>2</sub></font></span>)</span></span>)</span> <a href="lfuzzy_0.html#K6">@</a> </span>)</span> where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  </span>}</span> ,<span class="p3">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p4"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span></span>)</span> where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  </span>}</span> 
 ;<br/>


</div><b>end;</b></div>
<a NAME="E6:61"/><i><font color="Green">E45</font></i>: 
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p4">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>2</sub></font></span>)</span></span>)</span> <a href="lfuzzy_0.html#K6">@</a> </span>)</span> where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span>, B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  ) </span>}</span>  <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p3">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>2</sub></font></span>)</span></span>)</span> where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span>, B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  ) </span>}</span> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="61_5"><b>proof </b></a><div class="add">

<b>defpred </b><font color="Maroon">S<sub>3</sub></font>[  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span>,  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span>] means ( <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  &amp; <font color="Maroon">a<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  );<br/>
<b>deffunc </b><font color="Maroon">H<sub>2</sub></font>(  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span>,  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span>) <b>-&gt; </b>   <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> = <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Maroon">a<sub>1</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p2">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Maroon">a<sub>2</sub></font></span>)</span></span>)</span> <a href="lfuzzy_0.html#K6">@</a> ;<br/>
<b>deffunc </b><font color="Maroon">H<sub>3</sub></font>(  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span>,  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span>) <b>-&gt; </b>   <a href="fuzzy_1.html#M1">Membership_Func</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span> = <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Maroon">a<sub>1</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Maroon">a<sub>2</sub></font></span>)</span>;<br/>
<a NAME="E1:61_5"/><i><font color="Green">E46</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> holds <font color="Maroon">H<sub>2</sub></font>(<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>) <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>)
 
<b>by </b><i><a class="ref" href="lfuzzy_0.html#D6">LFUZZY_0:def 6</a></i>;<br/>
<a NAME="E2:61_5"/>
<span class="p1">{<span class="default"> <font color="Maroon">H<sub>2</sub></font>(<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>) where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span>, B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : <font color="Maroon">S<sub>3</sub></font>[<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>] </span>}</span>  <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Maroon">H<sub>3</sub></font>(<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>) where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span>, B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : <font color="Maroon">S<sub>3</sub></font>[<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>] </span>}</span> 
 
<b>from </b><i><a class="ref" href="fraenkel.html#S7">FRAENKEL:sch 7</a>(<a class="txt" href="lfuzzy_1.html#E1:61_5"><i><font color="Green">E46</font></i></a>);<br/></i>
<b>hence </b><a NAME="E3:61_5"/>
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p4">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>2</sub></font></span>)</span></span>)</span> <a href="lfuzzy_0.html#K6">@</a> </span>)</span> where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span>, B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  ) </span>}</span>  <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p3">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <font color="Olive">b<sub>2</sub></font></span>)</span></span>)</span> where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span>, B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span>  ) </span>}</span> 
 ;<br/>


</div><b>end;</b></div>
<b>thus </b><span class="p1">(<span class="default"><a href="lfuzzy_1.html#K5" target="_self">TrCl</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p1">(<span class="default"><a href="lfuzzy_1.html#K5" target="_self">TrCl</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="lfuzzy_0.html#K5">@</a> <span class="p2">(<span class="default"><a href="yellow_0.html#K1">"\/"</a> <span class="p3">{<span class="default"> <span class="p4">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 </span>}</span> ,<span class="p3">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p4"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p1">(<span class="default"><a href="lfuzzy_1.html#K5" target="_self">TrCl</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="lfuzzy_1.html#E1:61"><i><font color="Green">E40</font></i></a></i>
<br/>.= 
 <a href="yellow_0.html#K1">"\/"</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="yellow_0.html#K1">"\/"</a> <span class="p3">{<span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>) where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : <font color="Maroon">S<sub>2</sub></font>[<font color="Olive">b<sub>2</sub></font>] </span>}</span> ,<span class="p3">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p4"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span></span>)</span> where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>] </span>}</span> ,<span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span>
<b>by </b><i><a class="txt" href="lfuzzy_1.html#E2:61"><i><font color="Green">E41</font></i></a>, <a class="txt" href="lfuzzy_1.html#E3:61"><i><font color="Green">E42</font></i></a>, <a class="txt" href="lfuzzy_1.html#E5:61"><i><font color="Green">E44</font></i></a>, <a class="ref" href="lfuzzy_1.html#T35" target="_self">Th35</a></i>
<br/>.= 
 <a href="yellow_0.html#K1">"\/"</a> <span class="p1">{<span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>) where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span>, B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> : ( <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>] &amp; <font color="Maroon">S<sub>2</sub></font>[<font color="Olive">b<sub>2</sub></font>] ) </span>}</span> ,<span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span>
<b>from </b><i><a class="ref" href="lfuzzy_0.html#S1">LFUZZY_0:sch 1</a>()</i>
<br/>.= 
 <a href="yellow_0.html#K1">"\/"</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <span class="p3">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="lfuzzy_1.html#K4" target="_self">iter</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a>, B is   <a href="nat_1.html#NM1">Nat</a> : ( <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp; <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 ) </span>}</span> ,<span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span>
<b>by </b><i><a class="txt" href="lfuzzy_1.html#E4:61"><i><font color="Green">E43</font></i></a>, <a class="txt" href="lfuzzy_1.html#E6:61"><i><font color="Green">E45</font></i></a></i>
;<br/>


</div>
