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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="firebrick">::  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> 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_1.html#K4" title="MCART_1:func.4">[</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></span><a href="mcart_1.html#K4" title="MCART_1:func.4">]</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_1.html#K4" title="MCART_1:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="recdef_2.html#K4" title="RECDEF_2:func.4">`1_4</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="recdef_2.html#K5" title="RECDEF_2:func.5">`2_4</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="recdef_2.html#K6" title="RECDEF_2:func.6">`3_4</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="recdef_2.html#K7" title="RECDEF_2:func.7">`4_4</a></span>)</span></span><a href="mcart_1.html#K4" title="MCART_1:func.4">]</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> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><a NAME="E2:6"/><span class="lab"><font color="Green" title="E11">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_1.html#K4" title="MCART_1:func.4">[</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></span><a href="mcart_1.html#K4" title="MCART_1:func.4">]</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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_1.html#K4" title="MCART_1:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="recdef_2.html#K4" title="RECDEF_2:func.4">`1_4</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="recdef_2.html#K5" title="RECDEF_2:func.5">`2_4</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="recdef_2.html#K6" title="RECDEF_2:func.6">`3_4</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="recdef_2.html#K7" title="RECDEF_2:func.7">`4_4</a></span>)</span></span><a href="mcart_1.html#K4" title="MCART_1:func.4">]</a></span></span><br/>

<a NAME="E3:6"/><span class="lab"><font color="Green" title="E12">A2</font></span>: 
<font color="Maroon" title="c1">z</font> <a href="recdef_2.html#K6" title="RECDEF_2:func.6">`3_4</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:6"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="ref" href="recdef_2.html#D6" target="_self" title="RECDEF_2:def.6">Def6</a></span>;<br/>
<a NAME="E4:6"/>
( <font color="Maroon" title="c1">z</font> <a href="recdef_2.html#K4" title="RECDEF_2:func.4">`1_4</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#K5" title="RECDEF_2:func.5">`2_4</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="#E2:6"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="ref" href="recdef_2.html#D4" target="_self" title="RECDEF_2:def.4">Def4</a>, <a class="ref" href="recdef_2.html#D5" target="_self" title="RECDEF_2:def.5">Def5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:6"/>
<font color="Maroon" title="c1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K4" title="MCART_1:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="recdef_2.html#K4" title="RECDEF_2:func.4">`1_4</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="recdef_2.html#K5" title="RECDEF_2:func.5">`2_4</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="recdef_2.html#K6" title="RECDEF_2:func.6">`3_4</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="recdef_2.html#K7" title="RECDEF_2:func.7">`4_4</a></span>)</span></span><a href="mcart_1.html#K4" title="MCART_1:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:6"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="txt" href="#E3:6"><span class="lab"><font color="Green" title="E12">A2</font></span></a>, <a class="ref" href="recdef_2.html#D7" target="_self" title="RECDEF_2:def.7">Def7</a></span>; <a class="txt" 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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