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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> 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>  st <font color="Olive" title="b1">a</font> <a href="bvfunc_1.html#K10" title="BVFUNC_1:func.10">'eqv'</a> <font color="Olive" title="b2">b</font> <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> holds <br/><span class="p1">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <font color="Olive" title="b1">a</font></span>)</span> <a href="bvfunc_1.html#K10" title="BVFUNC_1:func.10">'eqv'</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <font color="Olive" title="b2">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><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#K10" title="BVFUNC_1:func.10">'eqv'</a> <font color="Maroon" title="c3">b</font> <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> implies <span class="p1">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="bvfunc_1.html#K10" title="BVFUNC_1:func.10">'eqv'</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</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><br/>



<span class="kw">assume </span><a NAME="E1:11"/>
<font color="Maroon" title="c2">a</font> <a href="bvfunc_1.html#K10" title="BVFUNC_1:func.10">'eqv'</a> <font color="Maroon" title="c3">b</font> <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>
 ; <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"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="bvfunc_1.html#K10" title="BVFUNC_1:func.10">'eqv'</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</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><br/>

<a NAME="E2:11"/><span class="kw">then </span>
<font color="Maroon" title="c2">a</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c3">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="bvfunc_1.html#T17" onmouseover="rs('bvfunc_1/T17')" onmouseout="rh()">BVFUNC_1:17</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:11"/>
<span class="p1">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="bvfunc_1.html#K10" title="BVFUNC_1:func.10">'eqv'</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</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_1.html#T17" onmouseover="rs('bvfunc_1/T17')" onmouseout="rh()">BVFUNC_1:17</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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