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<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>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</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  <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="bvfunc_1.html#K13" title="BVFUNC_1:func.13">'imp'</a> <font color="Olive" title="b2">b</font></span>)</span> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">b</font> <a href="bvfunc_1.html#K13" title="BVFUNC_1:func.13">'imp'</a> <font color="Olive" title="b3">c</font></span>)</span> <a href="bvfunc_1.html#R1" title="BVFUNC_1:pred.1">'&lt;'</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="bvfunc_1.html#K13" title="BVFUNC_1:func.13">'imp'</a> <font color="Olive" title="b2">b</font></span>)</span> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">b</font> <a href="bvfunc_1.html#K13" title="BVFUNC_1:func.13">'imp'</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">c</font> <a href="bvfunc_1.html#K7" title="BVFUNC_1:func.7">'or'</a> <font color="Olive" title="b1">a</font></span>)</span></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font>, <font color="Maroon" title="c4">c</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"> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="bvfunc_1.html#K13" title="BVFUNC_1:func.13">'imp'</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="bvfunc_1.html#K13" title="BVFUNC_1:func.13">'imp'</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="bvfunc_1.html#R1" title="BVFUNC_1:pred.1">'&lt;'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="bvfunc_1.html#K13" title="BVFUNC_1:func.13">'imp'</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="bvfunc_1.html#K13" title="BVFUNC_1:func.13">'imp'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="bvfunc_1.html#K7" title="BVFUNC_1:func.7">'or'</a> <font color="Maroon" title="c2">a</font></span>)</span></span>)</span></span><br/>



<a NAME="E1:27"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="bvfunc_1.html#K13" title="BVFUNC_1:func.13">'imp'</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="bvfunc_1.html#K13" title="BVFUNC_1:func.13">'imp'</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="bvfunc_1.html#R1" title="BVFUNC_1:pred.1">'&lt;'</a> <font color="Maroon" title="c3">b</font> <a href="bvfunc_1.html#K13" title="BVFUNC_1:func.13">'imp'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="bvfunc_1.html#K7" title="BVFUNC_1:func.7">'or'</a> <font color="Maroon" title="c2">a</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="bvfunc10.html#T21" target="_self" title="BVFUNC10:th.21">Th21</a></span>;<br/>
<a NAME="E2:27"/><span class="kw">then </span><span class="lab"><font color="Green" title="E9">A1</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="bvfunc_1.html#K13" title="BVFUNC_1:func.13">'imp'</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="bvfunc_1.html#K13" title="BVFUNC_1:func.13">'imp'</a> <font color="Maroon" title="c4">c</font></span>)</span></span>)</span> <a href="bvfunc_1.html#K13" title="BVFUNC_1:func.13">'imp'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="bvfunc_1.html#K13" title="BVFUNC_1:func.13">'imp'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="bvfunc_1.html#K7" title="BVFUNC_1:func.7">'or'</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#K16" title="BVFUNC_1:func.16">I_el</a> <font color="Maroon" title="c1">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="bvfunc_1.html#T16" title="BVFUNC_1:th.16">BVFUNC_1:16</a></span>;<br/>
<a NAME="E3:27"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="bvfunc_1.html#K13" title="BVFUNC_1:func.13">'imp'</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="bvfunc_1.html#K13" title="BVFUNC_1:func.13">'imp'</a> <font color="Maroon" title="c4">c</font></span>)</span></span>)</span> <a href="bvfunc_1.html#K13" title="BVFUNC_1:func.13">'imp'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="bvfunc_1.html#K13" title="BVFUNC_1:func.13">'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#K16" title="BVFUNC_1:func.16">I_el</a> <font color="Maroon" title="c1">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="bvfunc_6.html#T38" title="BVFUNC_6:th.38">BVFUNC_6:38</a></span>;<br/>
<a NAME="E4:27"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="bvfunc_1.html#K13" title="BVFUNC_1:func.13">'imp'</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="bvfunc_1.html#K13" title="BVFUNC_1:func.13">'imp'</a> <font color="Maroon" title="c4">c</font></span>)</span></span>)</span> <a href="bvfunc_1.html#K13" title="BVFUNC_1:func.13">'imp'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="bvfunc_1.html#K13" title="BVFUNC_1:func.13">'imp'</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="bvfunc_1.html#K13" title="BVFUNC_1:func.13">'imp'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="bvfunc_1.html#K7" title="BVFUNC_1:func.7">'or'</a> <font color="Maroon" title="c2">a</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="bvfunc_1.html#K16" title="BVFUNC_1:func.16">I_el</a> <font color="Maroon" title="c1">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:27"><span class="lab"><font color="Green" title="E9">A1</font></span></a>, <a class="ref" href="bvfunc_6.html#T18" title="BVFUNC_6:th.18">BVFUNC_6:18</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:27"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="bvfunc_1.html#K13" title="BVFUNC_1:func.13">'imp'</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="bvfunc_1.html#K13" title="BVFUNC_1:func.13">'imp'</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="bvfunc_1.html#R1" title="BVFUNC_1:pred.1">'&lt;'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="bvfunc_1.html#K13" title="BVFUNC_1:func.13">'imp'</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="bvfunc_1.html#K13" title="BVFUNC_1:func.13">'imp'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="bvfunc_1.html#K7" title="BVFUNC_1:func.7">'or'</a> <font color="Maroon" title="c2">a</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="bvfunc_1.html#T16" title="BVFUNC_1:th.16">BVFUNC_1:16</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/>


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