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<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">d</font> being <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a>  <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Maroon" title="c1">Y</font>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a>  holds <br/> (  <a href="bvfunc_1.html#K18" title="BVFUNC_1:func.18">B_INF</a> <font color="Olive" title="b1">d</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b1">d</font> &amp;  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">B_SUP</a> <font color="Olive" title="b1">d</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b1">d</font> )</span><br/><b>let </b><font color="Maroon" title="c2">d</font> be  <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a>  <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="bvfunc_1.html#K18" title="BVFUNC_1:func.18">B_INF</a> <font color="Maroon" title="c2">d</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">d</font> &amp;  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">B_SUP</a> <font color="Maroon" title="c2">d</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">d</font> )</span><br/>



<div><i><font color="Green" title="E23">A1</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="40_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:40_1"/><i><font color="Green" title="E24">A2</font></i>: 
( 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  <font color="Maroon" title="c2">d</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>  or 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  <font color="Maroon" title="c2">d</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#K7" title="MARGREL1:func.7">FALSE</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="bvfunc_1.html#K18" title="BVFUNC_1:func.18">B_INF</a> <font color="Maroon" title="c2">d</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">d</font> &amp;  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">B_SUP</a> <font color="Maroon" title="c2">d</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">d</font> )</span><br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="40_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="40_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:40_1_1_1"/>
( ( ( 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  <font color="Maroon" title="c2">d</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>  ) &amp; not 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  <font color="Maroon" title="c2">d</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#K7" title="MARGREL1:func.7">FALSE</a>  ) or ( ( 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  <font color="Maroon" title="c2">d</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#K7" title="MARGREL1:func.7">FALSE</a>  ) &amp; not 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  <font color="Maroon" title="c2">d</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>  ) or ( ( 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  <font color="Maroon" title="c2">d</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>  ) &amp; ( 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  <font color="Maroon" title="c2">d</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#K7" title="MARGREL1:func.7">FALSE</a>  ) ) )
 </span><b>by </b><i><a class="txt" href="bvfunc_1.html#E1:40_1"><i><font color="Green" title="E24">A2</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="40_1_1_1_1"><b>case </b></a><a NAME="E1:40_1_1_1_1"/><i><font color="Green" title="E25">A3</font></i>: 
( ( 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  <font color="Maroon" title="c2">d</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>  ) &amp; not 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  <font color="Maroon" title="c2">d</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#K7" title="MARGREL1:func.7">FALSE</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="bvfunc_1.html#K18" title="BVFUNC_1:func.18">B_INF</a> <font color="Maroon" title="c2">d</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">d</font> &amp;  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">B_SUP</a> <font color="Maroon" title="c2">d</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">d</font> )</span><br/><div class="add"><a NAME="E2:40_1_1_1_1"/><b>then </b>
<font color="Maroon" title="c2">d</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="bvfunc_1.html#K17" title="BVFUNC_1:func.17">I_el</a> <font color="Maroon" title="c1">Y</font>
 <b>by </b><i><a class="ref" href="bvfunc_1.html#D14" target="_self" title="BVFUNC_1:def.14">Def14</a></i>;<br/><b>hence </b><a NAME="E3:40_1_1_1_1"/>
(  <a href="bvfunc_1.html#K18" title="BVFUNC_1:func.18">B_INF</a> <font color="Maroon" title="c2">d</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">d</font> &amp;  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">B_SUP</a> <font color="Maroon" title="c2">d</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">d</font> )
 <b>by </b><i><a class="txt" href="bvfunc_1.html#E1:40_1_1_1_1"><i><font color="Green" title="E25">A3</font></i></a>, <a class="ref" href="bvfunc_1.html#D16" target="_self" title="BVFUNC_1:def.16">Def16</a>, <a class="ref" href="bvfunc_1.html#D17" target="_self" title="BVFUNC_1:def.17">Def17</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="40_1_1_1_2"><b>case </b></a><a NAME="E1:40_1_1_1_2"/><i><font color="Green" title="E25">A4</font></i>: 
( ( 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  <font color="Maroon" title="c2">d</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#K7" title="MARGREL1:func.7">FALSE</a>  ) &amp; not 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  <font color="Maroon" title="c2">d</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>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="bvfunc_1.html#K18" title="BVFUNC_1:func.18">B_INF</a> <font color="Maroon" title="c2">d</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">d</font> &amp;  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">B_SUP</a> <font color="Maroon" title="c2">d</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">d</font> )</span><br/><div class="add"><a NAME="E2:40_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c2">d</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="bvfunc_1.html#K16" title="BVFUNC_1:func.16">O_el</a> <font color="Maroon" title="c1">Y</font>
 <b>by </b><i><a class="ref" href="bvfunc_1.html#D13" target="_self" title="BVFUNC_1:def.13">Def13</a></i>;<br/><b>hence </b><a NAME="E3:40_1_1_1_2"/>
(  <a href="bvfunc_1.html#K18" title="BVFUNC_1:func.18">B_INF</a> <font color="Maroon" title="c2">d</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">d</font> &amp;  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">B_SUP</a> <font color="Maroon" title="c2">d</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">d</font> )
 <b>by </b><i><a class="txt" href="bvfunc_1.html#E1:40_1_1_1_2"><i><font color="Green" title="E25">A4</font></i></a>, <a class="ref" href="bvfunc_1.html#D16" target="_self" title="BVFUNC_1:def.16">Def16</a>, <a class="ref" href="bvfunc_1.html#D17" target="_self" title="BVFUNC_1:def.17">Def17</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="40_1_1_1_3"><b>case </b></a><a NAME="E1:40_1_1_1_3"/><i><font color="Green" title="E25">A5</font></i>: 
( ( 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  <font color="Maroon" title="c2">d</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>  ) &amp; ( 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  <font color="Maroon" title="c2">d</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#K7" title="MARGREL1:func.7">FALSE</a>  ) )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> 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/> (  <a href="bvfunc_1.html#K18" title="BVFUNC_1:func.18">B_INF</a> <font color="Maroon" title="c2">d</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">d</font> &amp;  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">B_SUP</a> <font color="Maroon" title="c2">d</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">d</font> )</span><br/><div class="add"><b>let </b><font color="Maroon" title="c3">x</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="bvfunc_1.html#K18" title="BVFUNC_1:func.18">B_INF</a> <font color="Maroon" title="c2">d</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">d</font> &amp;  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">B_SUP</a> <font color="Maroon" title="c2">d</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">d</font> )</span><br/><a NAME="E2:40_1_1_1_3"/>
<font color="Maroon" title="c2">d</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
 <b>by </b><i><a class="txt" href="bvfunc_1.html#E1:40_1_1_1_3"><i><font color="Green" title="E25">A5</font></i></a></i>;<br/><b>hence </b><a NAME="E3:40_1_1_1_3"/>
(  <a href="bvfunc_1.html#K18" title="BVFUNC_1:func.18">B_INF</a> <font color="Maroon" title="c2">d</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">d</font> &amp;  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">B_SUP</a> <font color="Maroon" title="c2">d</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">d</font> )
 <b>by </b><i><a class="txt" href="bvfunc_1.html#E1:40_1_1_1_3"><i><font color="Green" title="E25">A5</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:40_1"/>
(  <a href="bvfunc_1.html#K18" title="BVFUNC_1:func.18">B_INF</a> <font color="Maroon" title="c2">d</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">d</font> &amp;  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">B_SUP</a> <font color="Maroon" title="c2">d</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">d</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="40_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:40_2"/><i><font color="Green" title="E24">A6</font></i>: 
( not <!--HUMANRECFAILED-->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  <font color="Maroon" title="c2">d</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>  &amp; not <!--HUMANRECFAILED-->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  <font color="Maroon" title="c2">d</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#K7" title="MARGREL1:func.7">FALSE</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="bvfunc_1.html#K18" title="BVFUNC_1:func.18">B_INF</a> <font color="Maroon" title="c2">d</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">d</font> &amp;  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">B_SUP</a> <font color="Maroon" title="c2">d</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">d</font> )</span><br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="40_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="40_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:40_2_1_1"/>
( <font color="Maroon" title="c2">d</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="bvfunc_1.html#K16" title="BVFUNC_1:func.16">O_el</a> <font color="Maroon" title="c1">Y</font> or <font color="Maroon" title="c2">d</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="bvfunc_1.html#K17" title="BVFUNC_1:func.17">I_el</a> <font color="Maroon" title="c1">Y</font> )
 </span><b>by </b><i><a class="ref" href="bvfunc_1.html#T24" target="_self" title="BVFUNC_1:th.24">Th24</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="40_2_1_1_1"><b>case </b></a><a NAME="E1:40_2_1_1_1"/>
<font color="Maroon" title="c2">d</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="bvfunc_1.html#K16" title="BVFUNC_1:func.16">O_el</a> <font color="Maroon" title="c1">Y</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="bvfunc_1.html#K18" title="BVFUNC_1:func.18">B_INF</a> <font color="Maroon" title="c2">d</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">d</font> &amp;  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">B_SUP</a> <font color="Maroon" title="c2">d</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">d</font> )</span><br/><div class="add"><b>hence </b><a NAME="E2:40_2_1_1_1"/>
(  <a href="bvfunc_1.html#K18" title="BVFUNC_1:func.18">B_INF</a> <font color="Maroon" title="c2">d</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">d</font> &amp;  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">B_SUP</a> <font color="Maroon" title="c2">d</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">d</font> )
 <b>by </b><i><a class="txt" href="bvfunc_1.html#E1:40_2"><i><font color="Green" title="E24">A6</font></i></a>, <a class="ref" href="bvfunc_1.html#D13" target="_self" title="BVFUNC_1:def.13">Def13</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="40_2_1_1_2"><b>case </b></a><a NAME="E1:40_2_1_1_2"/>
<font color="Maroon" title="c2">d</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="bvfunc_1.html#K17" title="BVFUNC_1:func.17">I_el</a> <font color="Maroon" title="c1">Y</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="bvfunc_1.html#K18" title="BVFUNC_1:func.18">B_INF</a> <font color="Maroon" title="c2">d</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">d</font> &amp;  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">B_SUP</a> <font color="Maroon" title="c2">d</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">d</font> )</span><br/><div class="add"><b>hence </b><a NAME="E2:40_2_1_1_2"/>
(  <a href="bvfunc_1.html#K18" title="BVFUNC_1:func.18">B_INF</a> <font color="Maroon" title="c2">d</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">d</font> &amp;  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">B_SUP</a> <font color="Maroon" title="c2">d</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">d</font> )
 <b>by </b><i><a class="txt" href="bvfunc_1.html#E1:40_2"><i><font color="Green" title="E24">A6</font></i></a>, <a class="ref" href="bvfunc_1.html#D14" target="_self" title="BVFUNC_1:def.14">Def14</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:40_2"/>
(  <a href="bvfunc_1.html#K18" title="BVFUNC_1:func.18">B_INF</a> <font color="Maroon" title="c2">d</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">d</font> &amp;  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">B_SUP</a> <font color="Maroon" title="c2">d</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">d</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:40"/>
(  <a href="bvfunc_1.html#K18" title="BVFUNC_1:func.18">B_INF</a> <font color="Maroon" title="c2">d</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">d</font> &amp;  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">B_SUP</a> <font color="Maroon" title="c2">d</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">d</font> )
 <b>by </b><i><a class="txt" href="bvfunc_1.html#E1:40"><i><font color="Green" title="E23">A1</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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