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<b>set </b><font color="Maroon" title="c6">EE</font> =  <a href="group_10.html#K3" title="GROUP_10:func.3">the_subsets_of_card</a> <font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c1">E</font>;<br/>
<b>let </b><font color="Maroon" title="c7">IT1</font>, <font color="Maroon" title="c8">IT2</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="group_10.html#K3" title="GROUP_10:func.3">the_subsets_of_card</a> <font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c1">E</font>, <a href="group_10.html#K3" title="GROUP_10:func.3">the_subsets_of_card</a> <font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c1">E</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( for <font color="Olive" title="b1">X</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="group_10.html#K3" title="GROUP_10:func.3">the_subsets_of_card</a> <font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c1">E</font> holds  <font color="Maroon" title="c7">IT1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">LO</font> <a href="group_10.html#K1" title="GROUP_10:func.1">^</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Olive" title="b1">X</font> ) &amp; ( for <font color="Olive" title="b1">X</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="group_10.html#K3" title="GROUP_10:func.3">the_subsets_of_card</a> <font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c1">E</font> holds  <font color="Maroon" title="c8">IT2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">LO</font> <a href="group_10.html#K1" title="GROUP_10:func.1">^</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Olive" title="b1">X</font> ) implies <font color="Maroon" title="c7">IT1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">IT2</font> )</span><br/>

<b>assume </b><b>that </b><br/><a NAME="E1:14_1_2"/><i><font color="Green" title="E7">A21</font></i>: 
for <font color="Olive" title="b1">X</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="group_10.html#K3" title="GROUP_10:func.3">the_subsets_of_card</a> <font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c1">E</font> holds  <font color="Maroon" title="c7">IT1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">LO</font> <a href="group_10.html#K1" title="GROUP_10:func.1">^</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Olive" title="b1">X</font>
 <b>and </b><br/><a NAME="E2:14_1_2"/><i><font color="Green" title="E8">A22</font></i>: 
for <font color="Olive" title="b1">X</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="group_10.html#K3" title="GROUP_10:func.3">the_subsets_of_card</a> <font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c1">E</font> holds  <font color="Maroon" title="c8">IT2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">LO</font> <a href="group_10.html#K1" title="GROUP_10:func.1">^</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Olive" title="b1">X</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c7">IT1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">IT2</font></span><br/>

<b>let </b><font color="Maroon" title="c9">x</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="group_10.html#K3" title="GROUP_10:func.3">the_subsets_of_card</a> <font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c1">E</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="funct_2.html#D9" title="FUNCT_2:def.9">FUNCT_2:def 9</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="group_10.html#NK1" title="GROUP_10:NK.1">^</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_10.html#NK1" title="GROUP_10:NK.1">^</a> </span><br/>

<b>thus </b><font color="Maroon" title="c7">IT1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">x</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">LO</font> <a href="group_10.html#K1" title="GROUP_10:func.1">^</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c9">x</font>
<b>by </b><i><a class="txt" href="#E1:14_1_2"><i><font color="Green" title="E7">A21</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c8">IT2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">x</font>
<b>by </b><i><a class="txt" href="#E2:14_1_2"><i><font color="Green" title="E8">A22</font></i></a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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