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

<span class="kw">let </span><font color="Maroon" title="c1">Y</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">a</font> being    <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Maroon" title="c1">Y</font>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a>) holds   <a href="bvfunc_1.html#K21" title="BVFUNC_1:func.21">B_SUP</a> (<font color="Olive" title="b1">a</font>,<span class="p1">(<span class="default"><a href="partit1.html#NK6" title="PARTIT1:NK.6">%I</a> <font color="Maroon" title="c1">Y</font></span>)</span>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b1">a</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font> be    <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Maroon" title="c1">Y</font>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a>); <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="bvfunc_1.html#K21" title="BVFUNC_1:func.21">B_SUP</a> (<font color="Maroon" title="c2">a</font>,<span class="p1">(<span class="default"><a href="partit1.html#NK6" title="PARTIT1:NK.6">%I</a> <font color="Maroon" title="c1">Y</font></span>)</span>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">a</font></span><br/>



<span class="kw">consider </span><font color="Maroon" title="c3">k3</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><span class="kw"> such that </span><br/><a NAME="E2:58"/><span class="lab"><font color="Green" title="E26">A1</font></span>: 
 <a href="bvfunc_1.html#K21" title="BVFUNC_1:func.21">B_SUP</a> (<font color="Maroon" title="c2">a</font>,<span class="p1">(<span class="default"><a href="partit1.html#NK6" title="PARTIT1:NK.6">%I</a> <font color="Maroon" title="c1">Y</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">k3</font>
 <span class="kw">and </span><br/><a NAME="E3:58"/><span class="lab"><font color="Green" title="E27">A2</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">k3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">Y</font>
 <span class="kw">and </span><br/><a NAME="E4:58"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">k3</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D2" title="FUNCT_2:def.2">FUNCT_2:def 2</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c4">k4</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><span class="kw"> such that </span><br/><a NAME="E6:58"/><span class="lab"><font color="Green" title="E28">A3</font></span>: 
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">k4</font>
 <span class="kw">and </span><br/><a NAME="E7:58"/><span class="lab"><font color="Green" title="E29">A4</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">k4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">Y</font>
 <span class="kw">and </span><br/><a NAME="E8:58"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c4">k4</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D2" title="FUNCT_2:def.2">FUNCT_2:def 2</a></span>;<br/>
<a NAME="E9:58"/>
 for <font color="Olive" title="b1">y</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">Y</font> holds  <span class="p1">(<span class="default"><a href="bvfunc_1.html#K21" title="BVFUNC_1:func.21">B_SUP</a> (<font color="Maroon" title="c2">a</font>,<span class="p2">(<span class="default"><a href="partit1.html#NK6" title="PARTIT1:NK.6">%I</a> <font color="Maroon" title="c1">Y</font></span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">y</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c5">y</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">Y</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K21" title="BVFUNC_1:func.21">B_SUP</a> (<font color="Maroon" title="c2">a</font>,<span class="p2">(<span class="default"><a href="partit1.html#NK6" title="PARTIT1:NK.6">%I</a> <font color="Maroon" title="c1">Y</font></span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">y</font></span><br/>

<div><span class="lab"><font color="Green" title="E30">A5</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1_1"><span class="kw">now </span></a><div class="add"><a NAME="E1:58_1_1"/>
 <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> (<font color="Maroon" title="c5">y</font>,<span class="p1">(<span class="default"><a href="partit1.html#NK6" title="PARTIT1:NK.6">%I</a> <font color="Maroon" title="c1">Y</font></span>)</span>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="partit1.html#NK6" title="PARTIT1:NK.6">%I</a> <font color="Maroon" title="c1">Y</font>
 ;<br/><a NAME="E2:58_1_1"/><span class="kw">then </span>
 <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> (<font color="Maroon" title="c5">y</font>,<span class="p1">(<span class="default"><a href="partit1.html#NK6" title="PARTIT1:NK.6">%I</a> <font color="Maroon" title="c1">Y</font></span>)</span>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">B</font> where <font color="Olive" title="b1">B</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">Y</font> :  ex <font color="Olive" title="b2">z</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Olive" title="b1">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Olive" title="b2">z</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp; <font color="Olive" title="b2">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">Y</font> ) </span> } </span> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="partit1.html#T31" title="PARTIT1:th.31">PARTIT1:31</a></span>;<br/><a NAME="E3:58_1_1"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">B</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">Y</font> st <br/>(  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> (<font color="Maroon" title="c5">y</font>,<span class="p1">(<span class="default"><a href="partit1.html#NK6" title="PARTIT1:NK.6">%I</a> <font color="Maroon" title="c1">Y</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">B</font> &amp;  ex <font color="Olive" title="b2">z</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Olive" title="b1">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Olive" title="b2">z</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp; <font color="Olive" title="b2">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">Y</font> ) )
 ;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">z</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E5:58_1_1"/><span class="lab"><font color="Green" title="E31">A6</font></span>: 
 <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> (<font color="Maroon" title="c5">y</font>,<span class="p1">(<span class="default"><a href="partit1.html#NK6" title="PARTIT1:NK.6">%I</a> <font color="Maroon" title="c1">Y</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c6">z</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">and </span><br/><a NAME="E6:58_1_1"/>
<font color="Maroon" title="c6">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">Y</font>
 ;<br/><a NAME="E7:58_1_1"/><span class="lab"><font color="Green" title="E32">A7</font></span>: 
<font color="Maroon" title="c5">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c6">z</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:58_1_1"><span class="lab"><font color="Green" title="E31">A6</font></span></a>, <a class="ref" href="eqrel_1.html#D6" title="EQREL_1:def.6">EQREL_1:def 6</a></span>;<br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E8:58_1_1"/><span class="lab"><font color="Green" title="E33">A8</font></span>: 
 ex <font color="Olive" title="b1">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">Y</font> st <br/>( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> (<font color="Maroon" title="c5">y</font>,<span class="p1">(<span class="default"><a href="partit1.html#NK6" title="PARTIT1:NK.6">%I</a> <font color="Maroon" title="c1">Y</font></span>)</span>) &amp; <font color="Maroon" title="c2">a</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  )
 <span class="kw">and </span><br/><a NAME="E9:58_1_1"/><span class="lab"><font color="Green" title="E34">A9</font></span>: 
<font color="Maroon" title="c2">a</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><span class="kw">consider </span><font color="Maroon" title="c7">x1</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">Y</font><span class="kw"> such that </span><br/><a NAME="E11:58_1_1"/><span class="lab"><font color="Green" title="E35">A10</font></span>: 
<font color="Maroon" title="c7">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> (<font color="Maroon" title="c5">y</font>,<span class="p1">(<span class="default"><a href="partit1.html#NK6" title="PARTIT1:NK.6">%I</a> <font color="Maroon" title="c1">Y</font></span>)</span>)
 <span class="kw">and </span><br/><a NAME="E12:58_1_1"/><span class="lab"><font color="Green" title="E36">A11</font></span>: 
<font color="Maroon" title="c2">a</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:58_1_1"><span class="lab"><font color="Green" title="E33">A8</font></span></a></span>;<br/><a NAME="E13:58_1_1"/>
<font color="Maroon" title="c7">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">z</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:58_1_1"><span class="lab"><font color="Green" title="E35">A10</font></span></a>, <a class="txt" href="#E5:58_1_1"><span class="lab"><font color="Green" title="E31">A6</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E14:58_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:58_1_1"><span class="lab"><font color="Green" title="E34">A9</font></span></a>, <a class="txt" href="#E12:58_1_1"><span class="lab"><font color="Green" title="E36">A11</font></span></a>, <a class="txt" href="#E7:58_1_1"><span class="lab"><font color="Green" title="E32">A7</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>; <a class="txt" 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="lab"><font color="Green" title="E31">A12</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:58_1_2"/><span class="lab"><font color="Green" title="E32">A13</font></span>: 
 for <font color="Olive" title="b1">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">Y</font>  holds <br/>(  not <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> (<font color="Maroon" title="c5">y</font>,<span class="p1">(<span class="default"><a href="partit1.html#NK6" title="PARTIT1:NK.6">%I</a> <font color="Maroon" title="c1">Y</font></span>)</span>) or  not <font color="Maroon" title="c2">a</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  )
 <span class="kw">and </span><br/><a NAME="E2:58_1_2"/><span class="lab"><font color="Green" title="E33">A14</font></span>: 
<font color="Maroon" title="c2">a</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K21" title="BVFUNC_1:func.21">B_SUP</a> (<font color="Maroon" title="c2">a</font>,<span class="p2">(<span class="default"><a href="partit1.html#NK6" title="PARTIT1:NK.6">%I</a> <font color="Maroon" title="c1">Y</font></span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">y</font></span><br/><a NAME="E3:58_1_2"/>
<font color="Maroon" title="c2">a</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">FALSE</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:58_1_2"><span class="lab"><font color="Green" title="E33">A14</font></span></a>, <a class="ref" href="xboolean.html#D3" title="XBOOLEAN:def.3">XBOOLEAN:def 3</a></span>;<br/><span class="kw">hence </span><a NAME="E4:58_1_2"/>
<span class="p1">(<span class="default"><a href="bvfunc_1.html#K21" title="BVFUNC_1:func.21">B_SUP</a> (<font color="Maroon" title="c2">a</font>,<span class="p2">(<span class="default"><a href="partit1.html#NK6" title="PARTIT1:NK.6">%I</a> <font color="Maroon" title="c1">Y</font></span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:58_1_2"><span class="lab"><font color="Green" title="E32">A13</font></span></a>, <a class="ref" href="bvfunc_1.html#D17" target="_self" title="BVFUNC_1:def.17">Def20</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E3:58_1"/>
<font color="Maroon" title="c5">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> (<font color="Maroon" title="c5">y</font>,<span class="p1">(<span class="default"><a href="partit1.html#NK6" title="PARTIT1:NK.6">%I</a> <font color="Maroon" title="c1">Y</font></span>)</span>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="eqrel_1.html#D6" title="EQREL_1:def.6">EQREL_1:def 6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:58_1"/>
<span class="p1">(<span class="default"><a href="bvfunc_1.html#K21" title="BVFUNC_1:func.21">B_SUP</a> (<font color="Maroon" title="c2">a</font>,<span class="p2">(<span class="default"><a href="partit1.html#NK6" title="PARTIT1:NK.6">%I</a> <font color="Maroon" title="c1">Y</font></span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:58_1"><span class="lab"><font color="Green" title="E30">A5</font></span></a>, <a class="txt" href="#E2:58_1"><span class="lab"><font color="Green" title="E31">A12</font></span></a>, <a class="ref" href="bvfunc_1.html#D17" target="_self" title="BVFUNC_1:def.17">Def20</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E10:58"/><span class="kw">then </span>
 for <font color="Olive" title="b1">u</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">Y</font> holds <br/><font color="Maroon" title="c3">k3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">k4</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">u</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:58"><span class="lab"><font color="Green" title="E26">A1</font></span></a>, <a class="txt" href="#E6:58"><span class="lab"><font color="Green" title="E28">A3</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E11:58"/>
 <a href="bvfunc_1.html#K21" title="BVFUNC_1:func.21">B_SUP</a> (<font color="Maroon" title="c2">a</font>,<span class="p1">(<span class="default"><a href="partit1.html#NK6" title="PARTIT1:NK.6">%I</a> <font color="Maroon" title="c1">Y</font></span>)</span>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:58"><span class="lab"><font color="Green" title="E26">A1</font></span></a>, <a class="txt" href="#E3:58"><span class="lab"><font color="Green" title="E27">A2</font></span></a>, <a class="txt" href="#E6:58"><span class="lab"><font color="Green" title="E28">A3</font></span></a>, <a class="txt" href="#E7:58"><span class="lab"><font color="Green" title="E29">A4</font></span></a>, <a class="ref" href="funct_1.html#T2" title="FUNCT_1:th.2">FUNCT_1:2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
