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<span class="kw">let </span><font color="Maroon" title="c1">V</font>, <font color="Maroon" title="c2">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">  for <font color="Olive" title="b1">D1</font>, <font color="Olive" title="b2">D2</font> being    <a href="nomin_1.html#M1" title="NOMIN_1:mode.1">NonatomicND</a> of <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font>  st  not <font color="Olive" title="b1">D1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">A</font> &amp;  not <font color="Olive" title="b2">D2</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">A</font> holds <br/> <a href="nomin_1.html#K16" title="NOMIN_1:func.16">global_overlapping</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font>,<font color="Olive" title="b1">D1</font>,<font color="Olive" title="b2">D2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">D2</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">D1</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b1">D1</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p3">(<span class="default"><a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b2">D2</font></span>)</span></span>)</span></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">D1</font>, <font color="Maroon" title="c4">D2</font> be    <a href="nomin_1.html#M1" title="NOMIN_1:mode.1">NonatomicND</a> of <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">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"> (  not <font color="Maroon" title="c3">D1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">A</font> &amp;  not <font color="Maroon" title="c4">D2</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">A</font> implies  <a href="nomin_1.html#K16" title="NOMIN_1:func.16">global_overlapping</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">D1</font>,<font color="Maroon" title="c4">D2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">D2</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">D1</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c3">D1</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p3">(<span class="default"><a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c4">D2</font></span>)</span></span>)</span></span>)</span> )</span><br/>







<a NAME="E1:95"/><span class="lab"><font color="Green" title="E53">A1</font></span>: 
<font color="Maroon" title="c3">D1</font> is    <a href="nomin_1.html#M2" title="NOMIN_1:mode.2">TypeSCNominativeData</a> of <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nomin_1.html#D6" target="_self" onmouseover="rs('nomin_1/D6')" onmouseout="rh()">Def6</a></span>;<br/>
<a NAME="E2:95"/><span class="lab"><font color="Green" title="E54">A2</font></span>: 
<font color="Maroon" title="c4">D2</font> is    <a href="nomin_1.html#M2" title="NOMIN_1:mode.2">TypeSCNominativeData</a> of <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nomin_1.html#D6" target="_self" onmouseover="rs('nomin_1/D6')" onmouseout="rh()">Def6</a></span>;<br/>
<span class="kw">assume </span><a NAME="E3:95"/>
(  not <font color="Maroon" title="c3">D1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">A</font> &amp;  not <font color="Maroon" title="c4">D2</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">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#K16" title="NOMIN_1:func.16">global_overlapping</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">D1</font>,<font color="Maroon" title="c4">D2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">D2</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">D1</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c3">D1</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p3">(<span class="default"><a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c4">D2</font></span>)</span></span>)</span></span>)</span></span><br/>

<a NAME="E4:95"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">f1</font>, <font color="Olive" title="b2">f2</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> st <br/>( <font color="Olive" title="b1">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">D1</font> &amp; <font color="Olive" title="b2">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">D2</font> &amp;  <a href="nomin_1.html#K16" title="NOMIN_1:func.16">global_overlapping</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">D1</font>,<font color="Maroon" title="c4">D2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f2</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">f1</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b1">f1</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p3">(<span class="default"><a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b2">f2</font></span>)</span></span>)</span></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:95"><span class="lab"><font color="Green" title="E53">A1</font></span></a>, <a class="txt" href="#E2:95"><span class="lab"><font color="Green" title="E54">A2</font></span></a>, <a class="ref" href="nomin_1.html#D16" target="_self" onmouseover="rs('nomin_1/D16')" onmouseout="rh()">Def16</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:95"/>
 <a href="nomin_1.html#K16" title="NOMIN_1:func.16">global_overlapping</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">D1</font>,<font color="Maroon" title="c4">D2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">D2</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">D1</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c3">D1</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p3">(<span class="default"><a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c4">D2</font></span>)</span></span>)</span></span>)</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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