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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#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>, <font color="Olive" title="b3">c</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  <span class="p1">(<span class="default"><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></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#K9" title="BVFUNC_1:func.9">'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#K9" title="BVFUNC_1:func.9">'imp'</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">b</font> <a href="bvfunc_1.html#K5" title="BVFUNC_1:func.5">'or'</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <font color="Olive" title="b3">c</font></span>)</span></span>)</span></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#K9" title="BVFUNC_1:func.9">'imp'</a> <font color="Olive" title="b3">c</font></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#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"> <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#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#K9" title="BVFUNC_1:func.9">'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#K9" title="BVFUNC_1:func.9">'imp'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="bvfunc_1.html#K5" title="BVFUNC_1:func.5">'or'</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <font color="Maroon" title="c4">c</font></span>)</span></span>)</span></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#K9" title="BVFUNC_1:func.9">'imp'</a> <font color="Maroon" title="c4">c</font></span>)</span></span><br/>



<a NAME="E1:171"/>
<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#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#K9" title="BVFUNC_1:func.9">'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="c2">a</font> <a href="bvfunc_1.html#K9" title="BVFUNC_1:func.9">'imp'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="bvfunc_1.html#K5" title="BVFUNC_1:func.5">'or'</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <font color="Maroon" title="c4">c</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="bvfunc_6.html#T161" target="_self" onmouseover="rs('bvfunc_6/T161')" onmouseout="rh()">Th20</a></span>;<br/>
<a NAME="E2:171"/><span class="kw">then </span><span class="lab"><font color="Green" title="E42">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#K9" title="BVFUNC_1:func.9">'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#K9" title="BVFUNC_1:func.9">'imp'</a> <font color="Maroon" title="c4">c</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> <span class="p2">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="bvfunc_1.html#K5" title="BVFUNC_1:func.5">'or'</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <font color="Maroon" title="c4">c</font></span>)</span></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_1.html#T16" onmouseover="rs('bvfunc_1/T16')" onmouseout="rh()">BVFUNC_1:16</a></span>;<br/>
<a NAME="E3:171"/>
<span class="p1">(<span class="default"><span class="p2">(<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#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#K9" title="BVFUNC_1:func.9">'imp'</a> <font color="Maroon" title="c4">c</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="c3">b</font> <a href="bvfunc_1.html#K9" title="BVFUNC_1:func.9">'imp'</a> <font color="Maroon" title="c4">c</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_6.html#T38" target="_self" onmouseover="rs('bvfunc_6/T38')" onmouseout="rh()">Th38</a></span>;<br/>
<a NAME="E4:171"/><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#K9" title="BVFUNC_1:func.9">'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#K9" title="BVFUNC_1:func.9">'imp'</a> <font color="Maroon" title="c4">c</font></span>)</span></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"><font color="Maroon" title="c2">a</font> <a href="bvfunc_1.html#K9" title="BVFUNC_1:func.9">'imp'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="bvfunc_1.html#K5" title="BVFUNC_1:func.5">'or'</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <font color="Maroon" title="c4">c</font></span>)</span></span>)</span></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#K9" title="BVFUNC_1:func.9">'imp'</a> <font color="Maroon" title="c4">c</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="txt" href="#E2:171"><span class="lab"><font color="Green" title="E42">A1</font></span></a>, <a class="ref" href="bvfunc_6.html#T18" target="_self" onmouseover="rs('bvfunc_6/T18')" onmouseout="rh()">th18</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:171"/>
<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#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#K9" title="BVFUNC_1:func.9">'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#K9" title="BVFUNC_1:func.9">'imp'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="bvfunc_1.html#K5" title="BVFUNC_1:func.5">'or'</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <font color="Maroon" title="c4">c</font></span>)</span></span>)</span></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#K9" title="BVFUNC_1:func.9">'imp'</a> <font color="Maroon" title="c4">c</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>; <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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