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<span class="kw">let </span><font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c2">v</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">V</font>, <font color="Olive" title="b2">A</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Maroon" title="c2">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">V</font> &amp; <font color="Maroon" title="c1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">A</font> holds <br/> <a href="nomin_1.html#K4" title="NOMIN_1:func.4">ND_ex_1</a> (<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c1">a</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="nomin_1.html#K1" title="NOMIN_1:func.1">NDSS</a> (<font color="Olive" title="b1">V</font>,<font color="Olive" title="b2">A</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c3">V</font>, <font color="Maroon" title="c4">A</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"> ( <font color="Maroon" title="c2">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">V</font> &amp; <font color="Maroon" title="c1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">A</font> implies  <a href="nomin_1.html#K4" title="NOMIN_1:func.4">ND_ex_1</a> (<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c1">a</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="nomin_1.html#K1" title="NOMIN_1:func.1">NDSS</a> (<font color="Maroon" title="c3">V</font>,<font color="Maroon" title="c4">A</font>) )</span><br/>







<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:64"/><span class="lab"><font color="Green" title="E40">A1</font></span>: 
<font color="Maroon" title="c2">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">V</font>
 <span class="kw">and </span><br/><a NAME="E2:64"/><span class="lab"><font color="Green" title="E41">A2</font></span>: 
<font color="Maroon" title="c1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">A</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">  <a href="nomin_1.html#K4" title="NOMIN_1:func.4">ND_ex_1</a> (<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c1">a</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="nomin_1.html#K1" title="NOMIN_1:func.1">NDSS</a> (<font color="Maroon" title="c3">V</font>,<font color="Maroon" title="c4">A</font>)</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c5">V1</font> = <font color="Maroon" title="c3">V</font>, <font color="Maroon" title="c6">A1</font> = <font color="Maroon" title="c4">A</font> as   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:64"><span class="lab"><font color="Green" title="E40">A1</font></span></a>, <a class="txt" href="#E2:64"><span class="lab"><font color="Green" title="E41">A2</font></span></a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c7">v</font> = <font color="Maroon" title="c2">v</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c5">V1</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:64"><span class="lab"><font color="Green" title="E40">A1</font></span></a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c8">a</font> = <font color="Maroon" title="c1">a</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c6">A1</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:64"><span class="lab"><font color="Green" title="E41">A2</font></span></a></span>;<br/>
<a NAME="E6:64"/>
<font color="Maroon" title="c7">v</font> <a href="turing_1.html#K2" title="TURING_1:func.2">.--&gt;</a> <font color="Maroon" title="c8">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="nomin_1.html#K1" title="NOMIN_1:func.1">NDSS</a> (<font color="Maroon" title="c3">V</font>,<font color="Maroon" title="c4">A</font>)
 
;<br/>
<span class="kw">hence </span><a NAME="E7:64"/>
 <a href="nomin_1.html#K4" title="NOMIN_1:func.4">ND_ex_1</a> (<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c1">a</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="nomin_1.html#K1" title="NOMIN_1:func.1">NDSS</a> (<font color="Maroon" title="c3">V</font>,<font color="Maroon" title="c4">A</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"> verum</span><br/>


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