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<span class="kw">let </span><font color="Maroon" title="c4">x</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="classes1.html#D1" onmouseover="rs('classes1/D1')" onmouseout="rh()">CLASSES1:def 1</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">b<sub>1</sub></font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   holds <br/>(  not <font color="Maroon" title="c4">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="simplex0.html#K3" title="SIMPLEX0:func.3">the_subsets_with_limited_card</a> (<font color="Maroon" title="c3">n</font>,<font color="Maroon" title="c2">X</font>,<font color="Maroon" title="c1">Y</font>) or  not <font color="Olive">b<sub>1</sub></font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">x</font> or <font color="Olive">b<sub>1</sub></font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="simplex0.html#K3" title="SIMPLEX0:func.3">the_subsets_with_limited_card</a> (<font color="Maroon" title="c3">n</font>,<font color="Maroon" title="c2">X</font>,<font color="Maroon" title="c1">Y</font>) )</span><br/><span class="kw">let </span><font color="Maroon" title="c5">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"> (  not <font color="Maroon" title="c4">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="simplex0.html#K3" title="SIMPLEX0:func.3">the_subsets_with_limited_card</a> (<font color="Maroon" title="c3">n</font>,<font color="Maroon" title="c2">X</font>,<font color="Maroon" title="c1">Y</font>) or  not <font color="Maroon" title="c5">y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">x</font> or <font color="Maroon" title="c5">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="simplex0.html#K3" title="SIMPLEX0:func.3">the_subsets_with_limited_card</a> (<font color="Maroon" title="c3">n</font>,<font color="Maroon" title="c2">X</font>,<font color="Maroon" title="c1">Y</font>) )</span><br/>



<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:22_1_1"/><span class="lab"><font color="Green" title="E9">A1</font></span>: 
<font color="Maroon" title="c4">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="simplex0.html#K3" title="SIMPLEX0:func.3">the_subsets_with_limited_card</a> (<font color="Maroon" title="c3">n</font>,<font color="Maroon" title="c2">X</font>,<font color="Maroon" title="c1">Y</font>)
 <span class="kw">and </span><br/><a NAME="E2:22_1_1"/><span class="lab"><font color="Green" title="E10">A2</font></span>: 
<font color="Maroon" title="c5">y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">x</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"> <font color="Maroon" title="c5">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="simplex0.html#K3" title="SIMPLEX0:func.3">the_subsets_with_limited_card</a> (<font color="Maroon" title="c3">n</font>,<font color="Maroon" title="c2">X</font>,<font color="Maroon" title="c1">Y</font>)</span><br/>

<a NAME="E3:22_1_1"/>
<font color="Maroon" title="c4">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22_1_1"><span class="lab"><font color="Green" title="E9">A1</font></span></a>, <a class="ref" href="simplex0.html#D2" target="_self" onmouseover="rs('simplex0/D2')" onmouseout="rh()">Def2</a></span>;<br/>
<a NAME="E4:22_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E11">A3</font></span>: 
<font color="Maroon" title="c5">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:22_1_1"><span class="lab"><font color="Green" title="E10">A2</font></span></a>, <a class="ref" href="classes1.html#D1" onmouseover="rs('classes1/D1')" onmouseout="rh()">CLASSES1:def 1</a></span>;<br/>
<a NAME="E5:22_1_1"/>
(  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c4">x</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c3">n</font> &amp;  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c5">y</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c4">x</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22_1_1"><span class="lab"><font color="Green" title="E9">A1</font></span></a>, <a class="txt" href="#E2:22_1_1"><span class="lab"><font color="Green" title="E10">A2</font></span></a>, <a class="ref" href="simplex0.html#D2" target="_self" onmouseover="rs('simplex0/D2')" onmouseout="rh()">Def2</a>, <a class="ref" href="card_1.html#T11" onmouseover="rs('card_1/T11')" onmouseout="rh()">CARD_1:11</a></span>;<br/>
<a NAME="E6:22_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E12">A4</font></span>: 
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c5">y</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c3">n</font>
 
;<br/>
<a NAME="E7:22_1_1"/>
<font color="Maroon" title="c5">y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22_1_1"><span class="lab"><font color="Green" title="E9">A1</font></span></a>, <a class="txt" href="#E2:22_1_1"><span class="lab"><font color="Green" title="E10">A2</font></span></a>, <a class="ref" href="xboole_1.html#T1" onmouseover="rs('xboole_1/T1')" onmouseout="rh()">XBOOLE_1:1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:22_1_1"/>
<font color="Maroon" title="c5">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="simplex0.html#K3" title="SIMPLEX0:func.3">the_subsets_with_limited_card</a> (<font color="Maroon" title="c3">n</font>,<font color="Maroon" title="c2">X</font>,<font color="Maroon" title="c1">Y</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:22_1_1"><span class="lab"><font color="Green" title="E11">A3</font></span></a>, <a class="txt" href="#E6:22_1_1"><span class="lab"><font color="Green" title="E12">A4</font></span></a>, <a class="ref" href="simplex0.html#D2" target="_self" onmouseover="rs('simplex0/D2')" onmouseout="rh()">Def2</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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