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<span class="kw">let </span><font color="Maroon" title="c1">z</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">d</font>, <font color="Olive" title="b5">e</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <font color="Maroon" title="c1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_2.html#K1" title="MCART_2:func.1">[</a><span class="default"><font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font>,<font color="Olive" title="b5">e</font></span><a href="mcart_2.html#K1" title="MCART_2:func.1">]</a></span> implies <font color="Maroon" title="c1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_2.html#K1" title="MCART_2:func.1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="recdef_2.html#K8" title="RECDEF_2:func.8">`1_5</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="recdef_2.html#K9" title="RECDEF_2:func.9">`2_5</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="recdef_2.html#K10" title="RECDEF_2:func.10">`3_5</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="recdef_2.html#K11" title="RECDEF_2:func.11">`4_5</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="recdef_2.html#K12" title="RECDEF_2:func.12">`5_5</a> </span>)</span></span><a href="mcart_2.html#K1" title="MCART_2:func.1">]</a></span> )</span><br/>

<span class="kw">given </span><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font>, <font color="Maroon" title="c4">c</font>, <font color="Maroon" title="c5">d</font>, <font color="Maroon" title="c6">e</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><a NAME="E2:10"/><span class="lab"><font color="Green" title="E16">A1</font></span>: 
<font color="Maroon" title="c1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_2.html#K1" title="MCART_2:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c6">e</font></span><a href="mcart_2.html#K1" title="MCART_2:func.1">]</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_2.html#K1" title="MCART_2:func.1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="recdef_2.html#K8" title="RECDEF_2:func.8">`1_5</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="recdef_2.html#K9" title="RECDEF_2:func.9">`2_5</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="recdef_2.html#K10" title="RECDEF_2:func.10">`3_5</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="recdef_2.html#K11" title="RECDEF_2:func.11">`4_5</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="recdef_2.html#K12" title="RECDEF_2:func.12">`5_5</a> </span>)</span></span><a href="mcart_2.html#K1" title="MCART_2:func.1">]</a></span></span><br/>

<a NAME="E3:10"/><span class="lab"><font color="Green" title="E17">A2</font></span>: 
( <font color="Maroon" title="c1">z</font> <a href="recdef_2.html#K10" title="RECDEF_2:func.10">`3_5</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c1">z</font> <a href="recdef_2.html#K11" title="RECDEF_2:func.11">`4_5</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">d</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10"><span class="lab"><font color="Green" title="E16">A1</font></span></a>, <a class="ref" href="recdef_2.html#D10" target="_self" title="RECDEF_2:def.10">Def10</a>, <a class="ref" href="recdef_2.html#D11" target="_self" title="RECDEF_2:def.11">Def11</a></span>;<br/>
<a NAME="E4:10"/>
( <font color="Maroon" title="c1">z</font> <a href="recdef_2.html#K8" title="RECDEF_2:func.8">`1_5</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> &amp; <font color="Maroon" title="c1">z</font> <a href="recdef_2.html#K9" title="RECDEF_2:func.9">`2_5</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10"><span class="lab"><font color="Green" title="E16">A1</font></span></a>, <a class="ref" href="recdef_2.html#D8" target="_self" title="RECDEF_2:def.8">Def8</a>, <a class="ref" href="recdef_2.html#D9" target="_self" title="RECDEF_2:def.9">Def9</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:10"/>
<font color="Maroon" title="c1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_2.html#K1" title="MCART_2:func.1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="recdef_2.html#K8" title="RECDEF_2:func.8">`1_5</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="recdef_2.html#K9" title="RECDEF_2:func.9">`2_5</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="recdef_2.html#K10" title="RECDEF_2:func.10">`3_5</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="recdef_2.html#K11" title="RECDEF_2:func.11">`4_5</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="recdef_2.html#K12" title="RECDEF_2:func.12">`5_5</a> </span>)</span></span><a href="mcart_2.html#K1" title="MCART_2:func.1">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10"><span class="lab"><font color="Green" title="E16">A1</font></span></a>, <a class="txt" href="#E3:10"><span class="lab"><font color="Green" title="E17">A2</font></span></a>, <a class="ref" href="recdef_2.html#D12" target="_self" title="RECDEF_2:def.12">Def12</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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