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<span class="kw">let </span><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">x1</font>, <font color="Maroon" title="c3">x2</font>, <font color="Maroon" title="c4">x3</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">X</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <span class="p1"><a href="xtuple_0.html#K6" title="XTUPLE_0:func.6">[</a><span class="default"><font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">x3</font></span><a href="xtuple_0.html#K6" title="XTUPLE_0:func.6">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">X</font> holds <br/><font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="xtuple_0.html#K14" title="XTUPLE_0:func.14">proj2_4</a> <font color="Olive" title="b1">X</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">X</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1"><a href="xtuple_0.html#K6" title="XTUPLE_0:func.6">[</a><span class="default"><font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">x3</font></span><a href="xtuple_0.html#K6" title="XTUPLE_0:func.6">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">X</font> implies <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="xtuple_0.html#K14" title="XTUPLE_0:func.14">proj2_4</a> <font color="Maroon" title="c5">X</font> )</span><br/>









<span class="kw">assume </span><a NAME="E1:51"/>
<span class="p1"><a href="xtuple_0.html#K6" title="XTUPLE_0:func.6">[</a><span class="default"><font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">x3</font></span><a href="xtuple_0.html#K6" title="XTUPLE_0:func.6">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">X</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="xtuple_0.html#K14" title="XTUPLE_0:func.14">proj2_4</a> <font color="Maroon" title="c5">X</font></span><br/>

<a NAME="E2:51"/><span class="kw">then </span>
<span class="p1"><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c1">x</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">x3</font></span><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">X</font>
 
;<br/>
<a NAME="E3:51"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c1">x</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="xtuple_0.html#K11" title="XTUPLE_0:func.11">proj1_3</a> <font color="Maroon" title="c5">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xtuple_0.html#T13" target="_self" onmouseover="rs('xtuple_0/T13')" onmouseout="rh()">Th13</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:51"/>
<font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="xtuple_0.html#K14" title="XTUPLE_0:func.14">proj2_4</a> <font color="Maroon" title="c5">X</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xtuple_0.html#D13" target="_self" onmouseover="rs('xtuple_0/D13')" onmouseout="rh()">Def13</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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