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<span class="kw">let </span><font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c2">a1</font>, <font color="Maroon" title="c3">v</font>, <font color="Maroon" title="c4">v1</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 <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">v1</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">V</font> &amp; <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">a1</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">A</font> holds <br/> <a href="nomin_1.html#K8" title="NOMIN_1:func.8">ND_ex_3</a> (<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">v1</font>,<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">a1</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="c5">V</font>, <font color="Maroon" title="c6">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"> ( <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">v1</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">V</font> &amp; <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">a1</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">A</font> implies  <a href="nomin_1.html#K8" title="NOMIN_1:func.8">ND_ex_3</a> (<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">v1</font>,<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">a1</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="c5">V</font>,<font color="Maroon" title="c6">A</font>) )</span><br/>











<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:74"/><span class="lab"><font color="Green" title="E44">A1</font></span>: 
<span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">v1</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">V</font>
 <span class="kw">and </span><br/><a NAME="E2:74"/><span class="lab"><font color="Green" title="E45">A2</font></span>: 
<span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">a1</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">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#K8" title="NOMIN_1:func.8">ND_ex_3</a> (<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">v1</font>,<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">a1</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="c5">V</font>,<font color="Maroon" title="c6">A</font>)</span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="74_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:74_1"/>
( <font color="Maroon" title="c3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">v1</font> or <font color="Maroon" title="c3">v</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">v1</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="74_1_1"><span class="kw">suppose </span></a><a NAME="E1:74_1_1"/>
<font color="Maroon" title="c3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">v1</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#K8" title="NOMIN_1:func.8">ND_ex_3</a> (<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">v1</font>,<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">a1</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="c5">V</font>,<font color="Maroon" title="c6">A</font>)</span><br/><div class="add"><a NAME="E2:74_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E46">A3</font></span>: 
 <a href="nomin_1.html#K8" title="NOMIN_1:func.8">ND_ex_3</a> (<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">v1</font>,<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">a1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="nomin_1.html#K4" title="NOMIN_1:func.4">ND_ex_1</a> (<font color="Maroon" title="c4">v1</font>,<font color="Maroon" title="c2">a1</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T81" onmouseover="rs('funct_4/T81')" onmouseout="rh()">FUNCT_4:81</a></span>;<br/><a NAME="E3:74_1_1"/>
( <font color="Maroon" title="c4">v1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">V</font> &amp; <font color="Maroon" title="c2">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">A</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:74"><span class="lab"><font color="Green" title="E44">A1</font></span></a>, <a class="txt" href="#E2:74"><span class="lab"><font color="Green" title="E45">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#T32" onmouseover="rs('zfmisc_1/T32')" onmouseout="rh()">ZFMISC_1:32</a></span>;<br/><span class="kw">hence </span><a NAME="E4:74_1_1"/>
 <a href="nomin_1.html#K8" title="NOMIN_1:func.8">ND_ex_3</a> (<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">v1</font>,<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">a1</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="c5">V</font>,<font color="Maroon" title="c6">A</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:74_1_1"><span class="lab"><font color="Green" title="E46">A3</font></span></a>, <a class="ref" href="nomin_1.html#T45" target="_self" onmouseover="rs('nomin_1/T45')" onmouseout="rh()">Th45</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="74_1_2"><span class="kw">suppose </span></a><a NAME="E1:74_1_2"/>
<font color="Maroon" title="c3">v</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">v1</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#K8" title="NOMIN_1:func.8">ND_ex_3</a> (<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">v1</font>,<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">a1</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="c5">V</font>,<font color="Maroon" title="c6">A</font>)</span><br/><div class="add"><a NAME="E2:74_1_2"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">v</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="subset_1.html#R1" title="SUBSET_1:pred.1">misses</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">v1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T11" onmouseover="rs('zfmisc_1/T11')" onmouseout="rh()">ZFMISC_1:11</a></span>;<br/><a NAME="E3:74_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E46">A4</font></span>: 
 <a href="nomin_1.html#K4" title="NOMIN_1:func.4">ND_ex_1</a> (<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c1">a</font>) <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a>  <a href="nomin_1.html#K4" title="NOMIN_1:func.4">ND_ex_1</a> (<font color="Maroon" title="c4">v1</font>,<font color="Maroon" title="c2">a1</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T87" onmouseover="rs('funcop_1/T87')" onmouseout="rh()">FUNCOP_1:87</a></span>;<br/><a NAME="E4:74_1_2"/>
( <font color="Maroon" title="c3">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">V</font> &amp; <font color="Maroon" title="c4">v1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">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="c6">A</font> &amp; <font color="Maroon" title="c2">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">A</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:74"><span class="lab"><font color="Green" title="E44">A1</font></span></a>, <a class="txt" href="#E2:74"><span class="lab"><font color="Green" title="E45">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#T32" onmouseover="rs('zfmisc_1/T32')" onmouseout="rh()">ZFMISC_1:32</a></span>;<br/><a NAME="E5:74_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E47">A5</font></span>: 
(  <a href="nomin_1.html#K4" title="NOMIN_1:func.4">ND_ex_1</a> (<font color="Maroon" title="c3">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="c5">V</font>,<font color="Maroon" title="c6">A</font>) &amp;  <a href="nomin_1.html#K4" title="NOMIN_1:func.4">ND_ex_1</a> (<font color="Maroon" title="c4">v1</font>,<font color="Maroon" title="c2">a1</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="c5">V</font>,<font color="Maroon" title="c6">A</font>) )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nomin_1.html#T45" target="_self" onmouseover="rs('nomin_1/T45')" onmouseout="rh()">Th45</a></span>;<br/><a NAME="E6:74_1_2"/>
 <a href="nomin_1.html#K8" title="NOMIN_1:func.8">ND_ex_3</a> (<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">v1</font>,<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">a1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="nomin_1.html#K4" title="NOMIN_1:func.4">ND_ex_1</a> (<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c1">a</font>)</span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="nomin_1.html#K4" title="NOMIN_1:func.4">ND_ex_1</a> (<font color="Maroon" title="c4">v1</font>,<font color="Maroon" title="c2">a1</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:74_1_2"><span class="lab"><font color="Green" title="E46">A4</font></span></a>, <a class="ref" href="funct_4.html#T30" onmouseover="rs('funct_4/T30')" onmouseout="rh()">FUNCT_4:30</a></span>;<br/><span class="kw">hence </span><a NAME="E7:74_1_2"/>
 <a href="nomin_1.html#K8" title="NOMIN_1:func.8">ND_ex_3</a> (<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">v1</font>,<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">a1</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="c5">V</font>,<font color="Maroon" title="c6">A</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:74_1_2"><span class="lab"><font color="Green" title="E46">A4</font></span></a>, <a class="txt" href="#E5:74_1_2"><span class="lab"><font color="Green" title="E47">A5</font></span></a>, <a class="ref" href="nomin_1.html#T8" target="_self" onmouseover="rs('nomin_1/T8')" onmouseout="rh()">Th8</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/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

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