<?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#M2" title="HIDDEN:mode.2">set</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">Y</font>,<a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</a> holds  <font color="Olive" title="b1">a</font> <a href="bvfunc_1.html#K9" title="BVFUNC_1:func.9">'imp'</a> <font color="Olive" title="b2">b</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><a href="margrel1.html#K14" title="MARGREL1:func.14">'not'</a> <font color="Olive" title="b2">b</font></span>)</span> <a href="bvfunc_1.html#K9" title="BVFUNC_1:func.9">'imp'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K14" title="MARGREL1:func.14">'not'</a> <font color="Olive" title="b1">a</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">Y</font>,<a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">a</font> <a href="bvfunc_1.html#K9" title="BVFUNC_1:func.9">'imp'</a> <font color="Maroon" title="c3">b</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><a href="margrel1.html#K14" title="MARGREL1:func.14">'not'</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="bvfunc_1.html#K9" title="BVFUNC_1:func.9">'imp'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K14" title="MARGREL1:func.14">'not'</a> <font color="Maroon" title="c2">a</font></span>)</span></span><br/>





<a NAME="E1:2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="bvfunc_1.html#K9" title="BVFUNC_1:func.9">'imp'</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="bvfunc_1.html#K9" title="BVFUNC_1:func.9">'imp'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="margrel1.html#K14" title="MARGREL1:func.14">'not'</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="bvfunc_1.html#K9" title="BVFUNC_1:func.9">'imp'</a> <span class="p2">(<span class="default"><a href="margrel1.html#K14" title="MARGREL1:func.14">'not'</a> <font color="Maroon" title="c2">a</font></span>)</span></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="bvfunc_1.html#K12" title="BVFUNC_1:func.12">I_el</a> <font color="Maroon" title="c1">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="bvfunc_5.html#T32" onmouseover="rs('bvfunc_5/T32')" onmouseout="rh()">BVFUNC_5:32</a></span>;<br/>
<a NAME="E2:2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E3">A1</font></span>: 
<font color="Maroon" title="c2">a</font> <a href="bvfunc_1.html#K9" title="BVFUNC_1:func.9">'imp'</a> <font color="Maroon" title="c3">b</font> <a href="bvfunc_1.html#R1" title="BVFUNC_1:pred.1">'&lt;'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K14" title="MARGREL1:func.14">'not'</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="bvfunc_1.html#K9" title="BVFUNC_1:func.9">'imp'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K14" title="MARGREL1:func.14">'not'</a> <font color="Maroon" title="c2">a</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="bvfunc_1.html#T16" onmouseover="rs('bvfunc_1/T16')" onmouseout="rh()">BVFUNC_1:16</a></span>;<br/>
<a NAME="E3:2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="margrel1.html#K14" title="MARGREL1:func.14">'not'</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="bvfunc_1.html#K9" title="BVFUNC_1:func.9">'imp'</a> <span class="p2">(<span class="default"><a href="margrel1.html#K14" title="MARGREL1:func.14">'not'</a> <font color="Maroon" title="c2">a</font></span>)</span></span>)</span> <a href="bvfunc_1.html#K9" title="BVFUNC_1:func.9">'imp'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="bvfunc_1.html#K9" title="BVFUNC_1:func.9">'imp'</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="bvfunc_1.html#K12" title="BVFUNC_1:func.12">I_el</a> <font color="Maroon" title="c1">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="bvfunc_5.html#T31" onmouseover="rs('bvfunc_5/T31')" onmouseout="rh()">BVFUNC_5:31</a></span>;<br/>
<a NAME="E4:2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="margrel1.html#K14" title="MARGREL1:func.14">'not'</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="bvfunc_1.html#K9" title="BVFUNC_1:func.9">'imp'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K14" title="MARGREL1:func.14">'not'</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="bvfunc_1.html#R1" title="BVFUNC_1:pred.1">'&lt;'</a> <font color="Maroon" title="c2">a</font> <a href="bvfunc_1.html#K9" title="BVFUNC_1:func.9">'imp'</a> <font color="Maroon" title="c3">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="bvfunc_1.html#T16" onmouseover="rs('bvfunc_1/T16')" onmouseout="rh()">BVFUNC_1:16</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:2"/>
<font color="Maroon" title="c2">a</font> <a href="bvfunc_1.html#K9" title="BVFUNC_1:func.9">'imp'</a> <font color="Maroon" title="c3">b</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><a href="margrel1.html#K14" title="MARGREL1:func.14">'not'</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="bvfunc_1.html#K9" title="BVFUNC_1:func.9">'imp'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K14" title="MARGREL1:func.14">'not'</a> <font color="Maroon" title="c2">a</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:2"><span class="lab"><font color="Green" title="E3">A1</font></span></a>, <a class="ref" href="bvfunc_1.html#T15" onmouseover="rs('bvfunc_1/T15')" onmouseout="rh()">BVFUNC_1:15</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>
