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<b>let </b><font color="Maroon" title="c1">k</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c2">X</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> ;<br/>



<b>assume </b><a NAME="E1:44"/><i><font color="Green" title="E34">A1</font></i>: 
(  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c1">k</font> &amp; <font color="Maroon" title="c1">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="card_1.html#NR1" title="CARD_1:NR.1">&lt;=`</a>  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c2">X</font> )
 ;<br/>

<b>let </b><font color="Maroon" title="c3">T1</font>, <font color="Maroon" title="c4">T2</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="incsp_1.html#U1" title="INCSP_1:sel.1">Points</a> of <span class="p1">(<span class="default"><a href="combgras.html#K1" title="COMBGRAS:func.1">G_</a> <font color="Maroon" title="c1">k</font>,<font color="Maroon" title="c2">X</font></span>)</span>;<br/>

<b>assume </b><a NAME="E2:44"/><i><font color="Green" title="E35">A2</font></i>: 
( <font color="Maroon" title="c3">T1</font> is <a href="combgras.html#V3" title="COMBGRAS:attr.3">STAR</a> &amp; <font color="Maroon" title="c4">T2</font> is <a href="combgras.html#V3" title="COMBGRAS:attr.3">STAR</a> &amp;  <a href="setfam_1.html#K1" title="SETFAM_1:func.1">meet</a> <font color="Maroon" title="c3">T1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="setfam_1.html#K1" title="SETFAM_1:func.1">meet</a> <font color="Maroon" title="c4">T2</font> )
 ;<br/>

<b>consider </b><font color="Maroon" title="c5">S1</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c2">X</font><b> such that </b><br/><a NAME="E4:44"/><i><font color="Green" title="E36">A3</font></i>: 
(  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c5">S1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">k</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 1 &amp; <font color="Maroon" title="c3">T1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">A</font> where <font color="Olive" title="b1">A</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c2">X</font> : (  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">k</font> &amp; <font color="Maroon" title="c5">S1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">A</font> ) </span>}</span>  )
 <b>by </b><i><a class="txt" href="combgras.html#E2:44"><i><font color="Green" title="E35">A2</font></i></a>, <a class="ref" href="combgras.html#D4" target="_self" title="COMBGRAS:def.4">Def4</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c6">S2</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c2">X</font><b> such that </b><br/><a NAME="E6:44"/><i><font color="Green" title="E37">A4</font></i>: 
(  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c6">S2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">k</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 1 &amp; <font color="Maroon" title="c4">T2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">A</font> where <font color="Olive" title="b1">A</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c2">X</font> : (  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">k</font> &amp; <font color="Maroon" title="c6">S2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">A</font> ) </span>}</span>  )
 <b>by </b><i><a class="txt" href="combgras.html#E2:44"><i><font color="Green" title="E35">A2</font></i></a>, <a class="ref" href="combgras.html#D4" target="_self" title="COMBGRAS:def.4">Def4</a></i>;<br/>
<a NAME="E7:44"/>
( <font color="Maroon" title="c5">S1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="setfam_1.html#K1" title="SETFAM_1:func.1">meet</a> <font color="Maroon" title="c3">T1</font> &amp; <font color="Maroon" title="c6">S2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="setfam_1.html#K1" title="SETFAM_1:func.1">meet</a> <font color="Maroon" title="c4">T2</font> )
 
<b>by </b><i><a class="txt" href="combgras.html#E1:44"><i><font color="Green" title="E34">A1</font></i></a>, <a class="txt" href="combgras.html#E4:44"><i><font color="Green" title="E36">A3</font></i></a>, <a class="txt" href="combgras.html#E6:44"><i><font color="Green" title="E37">A4</font></i></a>, <a class="ref" href="combgras.html#T26" target="_self" title="COMBGRAS:th.26">Th26</a></i>;<br/>
<b>hence </b><a NAME="E8:44"/>
<font color="Maroon" title="c3">T1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">T2</font>
 <b>by </b><i><a class="txt" href="combgras.html#E2:44"><i><font color="Green" title="E35">A2</font></i></a>, <a class="txt" href="combgras.html#E4:44"><i><font color="Green" title="E36">A3</font></i></a>, <a class="txt" href="combgras.html#E6:44"><i><font color="Green" title="E37">A4</font></i></a></i>;<br/>


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