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<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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/>

<b>given </b><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> <b> such that </b><a NAME="E2:6"/><i><font color="Green" title="E10">A1</font></i>: 
<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:()"><i><font color="Red">::  thesis: </font></i></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"/>
( <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> &amp; <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> &amp; <font color="Maroon" title="c1">z</font> <a href="recdef_2.html#K7" title="RECDEF_2:func.7">`4_4</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">d</font> )
 
<b>by </b><i><a class="txt" href="recdef_2.html#E2:6"><i><font color="Green" title="E10">A1</font></i></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>, <a class="ref" href="recdef_2.html#D6" target="_self" title="RECDEF_2:def.6">Def6</a>, <a class="ref" href="recdef_2.html#D7" target="_self" title="RECDEF_2:def.7">Def7</a></i>;<br/>
<b>hence </b><a NAME="E4:6"/>
<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>
 <b>by </b><i><a class="txt" href="recdef_2.html#E2:6"><i><font color="Green" title="E10">A1</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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