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<span class="kw">let </span><font color="Maroon" title="c1">a1</font>, <font color="Maroon" title="c2">a2</font>, <font color="Maroon" title="c3">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="c3">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">V</font> &amp;  not <font color="Maroon" title="c3">v</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c1">a1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">A</font> &amp;  not <font color="Maroon" title="c3">v</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c2">a2</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">A</font> &amp; <font color="Maroon" title="c1">a1</font> is    <a href="nomin_1.html#M2" title="NOMIN_1:mode.2">TypeSCNominativeData</a> of <font color="Olive" title="b1">V</font>,<font color="Olive" title="b2">A</font> &amp; <font color="Maroon" title="c2">a2</font> is    <a href="nomin_1.html#M2" title="NOMIN_1:mode.2">TypeSCNominativeData</a> of <font color="Olive" title="b1">V</font>,<font color="Olive" title="b2">A</font> holds <br/> <a href="nomin_1.html#K16" title="NOMIN_1:func.16">global_overlapping</a> (<font color="Olive" title="b1">V</font>,<font color="Olive" title="b2">A</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">v</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c1">a1</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">v</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c2">a2</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c2">a2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">V</font>, <font color="Maroon" title="c5">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="c3">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">V</font> &amp;  not <font color="Maroon" title="c3">v</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c1">a1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c5">A</font> &amp;  not <font color="Maroon" title="c3">v</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c2">a2</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c5">A</font> &amp; <font color="Maroon" title="c1">a1</font> is    <a href="nomin_1.html#M2" title="NOMIN_1:mode.2">TypeSCNominativeData</a> of <font color="Maroon" title="c4">V</font>,<font color="Maroon" title="c5">A</font> &amp; <font color="Maroon" title="c2">a2</font> is    <a href="nomin_1.html#M2" title="NOMIN_1:mode.2">TypeSCNominativeData</a> of <font color="Maroon" title="c4">V</font>,<font color="Maroon" title="c5">A</font> implies  <a href="nomin_1.html#K16" title="NOMIN_1:func.16">global_overlapping</a> (<font color="Maroon" title="c4">V</font>,<font color="Maroon" title="c5">A</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">v</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c1">a1</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">v</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c2">a2</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c2">a2</font> )</span><br/>









<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:98"/><span class="lab"><font color="Green" title="E54">A1</font></span>: 
<font color="Maroon" title="c3">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">V</font>
 <span class="kw">and </span><br/><a NAME="E2:98"/><span class="lab"><font color="Green" title="E55">A2</font></span>: 
(  not <font color="Maroon" title="c3">v</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c1">a1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c5">A</font> &amp;  not <font color="Maroon" title="c3">v</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c2">a2</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c5">A</font> )
 <span class="kw">and </span><br/><a NAME="E3:98"/><span class="lab"><font color="Green" title="E56">A3</font></span>: 
( <font color="Maroon" title="c1">a1</font> is    <a href="nomin_1.html#M2" title="NOMIN_1:mode.2">TypeSCNominativeData</a> of <font color="Maroon" title="c4">V</font>,<font color="Maroon" title="c5">A</font> &amp; <font color="Maroon" title="c2">a2</font> is    <a href="nomin_1.html#M2" title="NOMIN_1:mode.2">TypeSCNominativeData</a> of <font color="Maroon" title="c4">V</font>,<font color="Maroon" title="c5">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="c4">V</font>,<font color="Maroon" title="c5">A</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">v</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c1">a1</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">v</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c2">a2</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c2">a2</font></span><br/>

<a NAME="E4:98"/>
(  <a href="nomin_1.html#K13" title="NOMIN_1:func.13">naming</a> (<font color="Maroon" title="c4">V</font>,<font color="Maroon" title="c5">A</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c1">a1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c1">a1</font> &amp;  <a href="nomin_1.html#K13" title="NOMIN_1:func.13">naming</a> (<font color="Maroon" title="c4">V</font>,<font color="Maroon" title="c5">A</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c2">a2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c2">a2</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:98"><span class="lab"><font color="Green" title="E54">A1</font></span></a>, <a class="txt" href="#E3:98"><span class="lab"><font color="Green" title="E56">A3</font></span></a>, <a class="ref" href="nomin_1.html#D13" target="_self" onmouseover="rs('nomin_1/D13')" onmouseout="rh()">Def13</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:98"/>
 <a href="nomin_1.html#K16" title="NOMIN_1:func.16">global_overlapping</a> (<font color="Maroon" title="c4">V</font>,<font color="Maroon" title="c5">A</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">v</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c1">a1</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">v</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c2">a2</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c2">a2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:98"><span class="lab"><font color="Green" title="E55">A2</font></span></a>, <a class="ref" href="nomin_1.html#T65" target="_self" onmouseover="rs('nomin_1/T65')" onmouseout="rh()">Th65</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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