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

<span class="kw">set </span><font color="Maroon" title="c1">f</font> =  <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> ;<br/>
<a NAME="E1:31_1_1"/><span class="lab"><font color="Green" title="E16">b1</font></span>: 
 for <font color="Olive" title="b1">x1</font>, <font color="Olive" title="b2">x2</font>, <font color="Olive" title="b3">y</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>  st <font color="Olive" title="b1">x1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">x2</font> holds <br/><a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Olive" title="b1">x1</font>,<font color="Olive" title="b3">y</font>) <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Olive" title="b2">x2</font>,<font color="Olive" title="b3">y</font>)
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="31_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c2">x1</font>, <font color="Maroon" title="c3">x2</font>, <font color="Maroon" title="c4">y</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">x1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">x2</font> implies <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c4">y</font>) <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y</font>) )</span><br/>

<span class="kw">assume </span><a NAME="E1:31_1_1_1"/><span class="lab"><font color="Green" title="E17">Z1</font></span>: 
<font color="Maroon" title="c2">x1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">x2</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c4">y</font>) <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y</font>)</span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_1_1_1_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:31_1_1_1_1"/>
( <font color="Maroon" title="c3">x2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  or ( <font color="Maroon" title="c3">x2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Maroon" title="c2">x1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Maroon" title="c4">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  ) or ( <font color="Maroon" title="c3">x2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Maroon" title="c2">x1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Maroon" title="c4">y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  ) or ( <font color="Maroon" title="c3">x2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Maroon" title="c2">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Maroon" title="c4">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  ) or ( <font color="Maroon" title="c3">x2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Maroon" title="c2">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Maroon" title="c4">y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_1_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:31_1_1_1_1_1"/><span class="lab"><font color="Green" title="E18">Z0</font></span>: 
<font color="Maroon" title="c3">x2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c4">y</font>) <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y</font>)</span><br/><div class="add"><a NAME="E2:31_1_1_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:31_1_1_1"><span class="lab"><font color="Green" title="E17">Z1</font></span></a>, <a class="ref" href="xxreal_1.html#T1" onmouseover="rs('xxreal_1/T1')" onmouseout="rh()">XXREAL_1:1</a></span>;<br/><span class="kw">hence </span><a NAME="E3:31_1_1_1_1_1"/>
<a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c4">y</font>) <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:31_1_1_1_1_1"><span class="lab"><font color="Green" title="E18">Z0</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_1_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:31_1_1_1_1_2"/>
( <font color="Maroon" title="c3">x2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Maroon" title="c2">x1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Maroon" title="c4">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c4">y</font>) <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y</font>)</span><br/><div class="add"><a NAME="E2:31_1_1_1_1_2"/><span class="kw">then </span>
<a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fuzimpl4.html#D4" target="_self" onmouseover="rs('fuzimpl4/D4')" onmouseout="rh()">II3Def</a></span>;<br/><span class="kw">hence </span><a NAME="E3:31_1_1_1_1_2"/>
<a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c4">y</font>) <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_1.html#T1" onmouseover="rs('xxreal_1/T1')" onmouseout="rh()">XXREAL_1:1</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_1_1_1_1_3"><span class="kw">suppose </span></a><a NAME="E1:31_1_1_1_1_3"/>
( <font color="Maroon" title="c3">x2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Maroon" title="c2">x1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Maroon" title="c4">y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c4">y</font>) <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y</font>)</span><br/><div class="add"><a NAME="E2:31_1_1_1_1_3"/><span class="kw">then </span>
( <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c4">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fuzimpl4.html#D4" target="_self" onmouseover="rs('fuzimpl4/D4')" onmouseout="rh()">II3Def</a></span>;<br/><span class="kw">hence </span><a NAME="E3:31_1_1_1_1_3"/>
<a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c4">y</font>) <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y</font>)
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_1_1_1_1_4"><span class="kw">suppose </span></a><a NAME="E1:31_1_1_1_1_4"/>
( <font color="Maroon" title="c3">x2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Maroon" title="c2">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Maroon" title="c4">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c4">y</font>) <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y</font>)</span><br/><div class="add"><a NAME="E2:31_1_1_1_1_4"/><span class="kw">then </span>
( <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c4">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fuzimpl4.html#D4" target="_self" onmouseover="rs('fuzimpl4/D4')" onmouseout="rh()">II3Def</a></span>;<br/><span class="kw">hence </span><a NAME="E3:31_1_1_1_1_4"/>
<a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c4">y</font>) <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y</font>)
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_1_1_1_1_5"><span class="kw">suppose </span></a><a NAME="E1:31_1_1_1_1_5"/><span class="lab"><font color="Green" title="E18">Z1</font></span>: 
( <font color="Maroon" title="c3">x2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Maroon" title="c2">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Maroon" title="c4">y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c4">y</font>) <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y</font>)</span><br/><div class="add"><a NAME="E2:31_1_1_1_1_5"/><span class="kw">then </span>
<a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fuzimpl4.html#D4" target="_self" onmouseover="rs('fuzimpl4/D4')" onmouseout="rh()">II3Def</a></span>;<br/><span class="kw">hence </span><a NAME="E3:31_1_1_1_1_5"/>
<a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c4">y</font>) <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:31_1_1_1_1_5"><span class="lab"><font color="Green" title="E18">Z1</font></span></a>, <a class="ref" href="fuzimpl4.html#D4" target="_self" onmouseover="rs('fuzimpl4/D4')" onmouseout="rh()">II3Def</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div><span class="kw">end;</span></div>
<a NAME="E2:31_1_1"/><span class="lab"><font color="Green" title="E17">b2</font></span>: 
 for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y1</font>, <font color="Olive" title="b3">y2</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>  st <font color="Olive" title="b2">y1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b3">y2</font> holds <br/><a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y1</font>) <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Olive" title="b1">x</font>,<font color="Olive" title="b3">y2</font>)
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="31_1_1_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y1</font>, <font color="Maroon" title="c4">y2</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">y1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">y2</font> implies <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y1</font>) <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c4">y2</font>) )</span><br/>

<span class="kw">assume </span><a NAME="E1:31_1_1_2"/><span class="lab"><font color="Green" title="E18">SA</font></span>: 
<font color="Maroon" title="c3">y1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">y2</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y1</font>) <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c4">y2</font>)</span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_1_1_2_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:31_1_1_2_1"/>
( <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  or ( <font color="Maroon" title="c2">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Maroon" title="c3">y1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  ) or ( <font color="Maroon" title="c2">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Maroon" title="c3">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Maroon" title="c4">y2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  ) or ( <font color="Maroon" title="c2">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Maroon" title="c3">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Maroon" title="c4">y2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_1_1_2_1_1"><span class="kw">suppose </span></a><a NAME="E1:31_1_1_2_1_1"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y1</font>) <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c4">y2</font>)</span><br/><div class="add"><a NAME="E2:31_1_1_2_1_1"/><span class="kw">then </span>
( <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c4">y2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fuzimpl4.html#D4" target="_self" onmouseover="rs('fuzimpl4/D4')" onmouseout="rh()">II3Def</a></span>;<br/><span class="kw">hence </span><a NAME="E3:31_1_1_2_1_1"/>
<a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y1</font>) <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c4">y2</font>)
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_1_1_2_1_2"><span class="kw">suppose </span></a><a NAME="E1:31_1_1_2_1_2"/><span class="lab"><font color="Green" title="E19">Z1</font></span>: 
( <font color="Maroon" title="c2">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Maroon" title="c3">y1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y1</font>) <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c4">y2</font>)</span><br/><div class="add"><a NAME="E2:31_1_1_2_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c4">y2</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:31_1_1_2"><span class="lab"><font color="Green" title="E18">SA</font></span></a>, <a class="ref" href="xxreal_1.html#T1" onmouseover="rs('xxreal_1/T1')" onmouseout="rh()">XXREAL_1:1</a></span>;<br/><a NAME="E3:31_1_1_2_1_2"/><span class="kw">then </span>
( <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c4">y2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:31_1_1_2_1_2"><span class="lab"><font color="Green" title="E19">Z1</font></span></a>, <a class="ref" href="fuzimpl4.html#D4" target="_self" onmouseover="rs('fuzimpl4/D4')" onmouseout="rh()">II3Def</a></span>;<br/><span class="kw">hence </span><a NAME="E4:31_1_1_2_1_2"/>
<a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y1</font>) <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c4">y2</font>)
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_1_1_2_1_3"><span class="kw">suppose </span></a><a NAME="E1:31_1_1_2_1_3"/>
( <font color="Maroon" title="c2">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Maroon" title="c3">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Maroon" title="c4">y2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y1</font>) <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c4">y2</font>)</span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:31_1_1_2_1_3"/>
<a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y1</font>) <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c4">y2</font>)
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_1_1_2_1_4"><span class="kw">suppose </span></a><a NAME="E1:31_1_1_2_1_4"/>
( <font color="Maroon" title="c2">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Maroon" title="c3">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Maroon" title="c4">y2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y1</font>) <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c4">y2</font>)</span><br/><div class="add"><a NAME="E2:31_1_1_2_1_4"/><span class="kw">then </span>
( <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c4">y2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fuzimpl4.html#D4" target="_self" onmouseover="rs('fuzimpl4/D4')" onmouseout="rh()">II3Def</a></span>;<br/><span class="kw">hence </span><a NAME="E3:31_1_1_2_1_4"/>
<a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y1</font>) <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c4">y2</font>)
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div><span class="kw">end;</span></div>
<a NAME="E3:31_1_1"/>
(  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> &amp; 1 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_1.html#T1" onmouseover="rs('xxreal_1/T1')" onmouseout="rh()">XXREAL_1:1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:31_1_1"/>
(  <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a>  is  <a href="fuzimpl1.html#V1" title="FUZIMPL1:attr.1">decreasing_on_1st</a>  &amp;  <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a>  is  <a href="fuzimpl1.html#V2" title="FUZIMPL1:attr.2">increasing_on_2nd</a>  &amp;  <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a>  is  <a href="fuzimpl1.html#V3" title="FUZIMPL1:attr.3">00-dominant</a>  &amp;  <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a>  is  <a href="fuzimpl1.html#V4" title="FUZIMPL1:attr.4">11-dominant</a>  &amp;  <a href="fuzimpl4.html#K1" title="FUZIMPL4:func.1">I_I3</a>  is  <a href="fuzimpl1.html#V5" title="FUZIMPL1:attr.5">10-weak</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:31_1_1"><span class="lab"><font color="Green" title="E16">b1</font></span></a>, <a class="txt" href="#E2:31_1_1"><span class="lab"><font color="Green" title="E17">b2</font></span></a>, <a class="ref" href="fuzimpl4.html#D4" target="_self" onmouseover="rs('fuzimpl4/D4')" onmouseout="rh()">II3Def</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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