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<span class="kw">let </span><font color="Maroon" title="c1">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</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">X</font>, <font color="Olive" title="b2">Y</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  holds  <span class="p1">(<span class="default"><a href="card_3.html#K5" title="CARD_3:func.5">pi</a> (<font color="Olive" title="b1">X</font>,<font color="Maroon" title="c1">x</font>)</span>)</span> <a href="xboole_0.html#K5" title="XBOOLE_0:func.5">\+\</a> <span class="p1">(<span class="default"><a href="card_3.html#K5" title="CARD_3:func.5">pi</a> (<font color="Olive" title="b2">Y</font>,<font color="Maroon" title="c1">x</font>)</span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="card_3.html#K5" title="CARD_3:func.5">pi</a> (<span class="p1">(<span class="default"><font color="Olive" title="b1">X</font> <a href="xboole_0.html#K5" title="XBOOLE_0:func.5">\+\</a> <font color="Olive" title="b2">Y</font></span>)</span>,<font color="Maroon" title="c1">x</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c2">X</font>, <font color="Maroon" title="c3">Y</font> be    <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"> <span class="p1">(<span class="default"><a href="card_3.html#K5" title="CARD_3:func.5">pi</a> (<font color="Maroon" title="c2">X</font>,<font color="Maroon" title="c1">x</font>)</span>)</span> <a href="xboole_0.html#K5" title="XBOOLE_0:func.5">\+\</a> <span class="p1">(<span class="default"><a href="card_3.html#K5" title="CARD_3:func.5">pi</a> (<font color="Maroon" title="c3">Y</font>,<font color="Maroon" title="c1">x</font>)</span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="card_3.html#K5" title="CARD_3:func.5">pi</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="xboole_0.html#K5" title="XBOOLE_0:func.5">\+\</a> <font color="Maroon" title="c3">Y</font></span>)</span>,<font color="Maroon" title="c1">x</font>)</span><br/>





<a NAME="E1:27"/><span class="lab"><font color="Green" title="E15">A1</font></span>: 
<span class="p1">(<span class="default"><a href="card_3.html#K5" title="CARD_3:func.5">pi</a> (<font color="Maroon" title="c2">X</font>,<font color="Maroon" title="c1">x</font>)</span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><a href="card_3.html#K5" title="CARD_3:func.5">pi</a> (<font color="Maroon" title="c3">Y</font>,<font color="Maroon" title="c1">x</font>)</span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="card_3.html#K5" title="CARD_3:func.5">pi</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c3">Y</font></span>)</span>,<font color="Maroon" title="c1">x</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_3.html#T18" target="_self" onmouseover="rs('card_3/T18')" onmouseout="rh()">Th18</a></span>;<br/>
<a NAME="E2:27"/><span class="lab"><font color="Green" title="E16">A2</font></span>: 
<span class="p1">(<span class="default"><a href="card_3.html#K5" title="CARD_3:func.5">pi</a> (<font color="Maroon" title="c3">Y</font>,<font color="Maroon" title="c1">x</font>)</span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><a href="card_3.html#K5" title="CARD_3:func.5">pi</a> (<font color="Maroon" title="c2">X</font>,<font color="Maroon" title="c1">x</font>)</span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="card_3.html#K5" title="CARD_3:func.5">pi</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c3">Y</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c2">X</font></span>)</span>,<font color="Maroon" title="c1">x</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_3.html#T18" target="_self" onmouseover="rs('card_3/T18')" onmouseout="rh()">Th18</a></span>;<br/>
<a NAME="E3:27"/>
<span class="p1">(<span class="default"><a href="card_3.html#K5" title="CARD_3:func.5">pi</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c3">Y</font></span>)</span>,<font color="Maroon" title="c1">x</font>)</span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="card_3.html#K5" title="CARD_3:func.5">pi</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">Y</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c2">X</font></span>)</span>,<font color="Maroon" title="c1">x</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_3.html#K5" title="CARD_3:func.5">pi</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c3">Y</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">Y</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c2">X</font></span>)</span></span>)</span>,<font color="Maroon" title="c1">x</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_3.html#T16" target="_self" onmouseover="rs('card_3/T16')" onmouseout="rh()">Th16</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:27"/>
<span class="p1">(<span class="default"><a href="card_3.html#K5" title="CARD_3:func.5">pi</a> (<font color="Maroon" title="c2">X</font>,<font color="Maroon" title="c1">x</font>)</span>)</span> <a href="xboole_0.html#K5" title="XBOOLE_0:func.5">\+\</a> <span class="p1">(<span class="default"><a href="card_3.html#K5" title="CARD_3:func.5">pi</a> (<font color="Maroon" title="c3">Y</font>,<font color="Maroon" title="c1">x</font>)</span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="card_3.html#K5" title="CARD_3:func.5">pi</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="xboole_0.html#K5" title="XBOOLE_0:func.5">\+\</a> <font color="Maroon" title="c3">Y</font></span>)</span>,<font color="Maroon" title="c1">x</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:27"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="txt" href="#E2:27"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="ref" href="xboole_1.html#T13" onmouseover="rs('xboole_1/T13')" onmouseout="rh()">XBOOLE_1:13</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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