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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">v1</font>, <font color="Maroon" title="c4">v2</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">v1</font>,<font color="Maroon" title="c4">v2</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; <font color="Maroon" title="c3">v1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">v2</font> &amp;  not <font color="Maroon" title="c3">v1</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="c4">v2</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">v1</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="c4">v2</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="c4">v2</font>,<font color="Maroon" title="c3">v1</font>) <a href="funct_4.html#K6" title="FUNCT_4:func.6">--&gt;</a> (<font color="Maroon" title="c2">a2</font>,<font color="Maroon" title="c1">a1</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">v1</font>,<font color="Maroon" title="c4">v2</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; <font color="Maroon" title="c3">v1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">v2</font> &amp;  not <font color="Maroon" title="c3">v1</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="c6">A</font> &amp;  not <font color="Maroon" title="c4">v2</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="c6">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="c5">V</font>,<font color="Maroon" title="c6">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="c5">V</font>,<font color="Maroon" title="c6">A</font> implies  <a href="nomin_1.html#K16" title="NOMIN_1:func.16">global_overlapping</a> (<font color="Maroon" title="c5">V</font>,<font color="Maroon" title="c6">A</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">v1</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="c4">v2</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="c4">v2</font>,<font color="Maroon" title="c3">v1</font>) <a href="funct_4.html#K6" title="FUNCT_4:func.6">--&gt;</a> (<font color="Maroon" title="c2">a2</font>,<font color="Maroon" title="c1">a1</font>) )</span><br/>











<span class="kw">set </span><font color="Maroon" title="c7">D1</font> = <font color="Maroon" title="c3">v1</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c1">a1</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">D2</font> = <font color="Maroon" title="c4">v2</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c2">a2</font>;<br/>
<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:99"/><span class="lab"><font color="Green" title="E55">A1</font></span>: 
<span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c3">v1</font>,<font color="Maroon" title="c4">v2</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="E2:99"/><span class="lab"><font color="Green" title="E56">A2</font></span>: 
<font color="Maroon" title="c3">v1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">v2</font>
 <span class="kw">and </span><br/><a NAME="E3:99"/><span class="lab"><font color="Green" title="E57">A3</font></span>: 
(  not <font color="Maroon" title="c3">v1</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="c6">A</font> &amp;  not <font color="Maroon" title="c4">v2</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="c6">A</font> )
 <span class="kw">and </span><br/><a NAME="E4:99"/><span class="lab"><font color="Green" title="E58">A4</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="c5">V</font>,<font color="Maroon" title="c6">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="c5">V</font>,<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#K16" title="NOMIN_1:func.16">global_overlapping</a> (<font color="Maroon" title="c5">V</font>,<font color="Maroon" title="c6">A</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">v1</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="c4">v2</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="c4">v2</font>,<font color="Maroon" title="c3">v1</font>) <a href="funct_4.html#K6" title="FUNCT_4:func.6">--&gt;</a> (<font color="Maroon" title="c2">a2</font>,<font color="Maroon" title="c1">a1</font>)</span><br/>

<a NAME="E5:99"/>
( <font color="Maroon" title="c3">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="c4">v2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">V</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:99"><span class="lab"><font color="Green" title="E55">A1</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="E6:99"/><span class="kw">then </span><span class="lab"><font color="Green" title="E59">A5</font></span>: 
(  <a href="nomin_1.html#K13" title="NOMIN_1:func.13">naming</a> (<font color="Maroon" title="c5">V</font>,<font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c3">v1</font>,<font color="Maroon" title="c1">a1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v1</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="c5">V</font>,<font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c4">v2</font>,<font color="Maroon" title="c2">a2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">v2</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="#E4:99"><span class="lab"><font color="Green" title="E58">A4</font></span></a>, <a class="ref" href="nomin_1.html#D13" target="_self" onmouseover="rs('nomin_1/D13')" onmouseout="rh()">Def13</a></span>;<br/>
<a NAME="E7:99"/><span class="lab"><font color="Green" title="E60">A6</font></span>: 
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">v1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">v2</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">v1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:99"><span class="lab"><font color="Green" title="E56">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#T14" onmouseover="rs('zfmisc_1/T14')" onmouseout="rh()">ZFMISC_1:14</a></span>;<br/>
<a NAME="E8:99"/>
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">v1</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">v2</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:99"><span class="lab"><font color="Green" title="E56">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#T11" onmouseover="rs('zfmisc_1/T11')" onmouseout="rh()">ZFMISC_1:11</a></span>;<br/>
<span class="kw">hence </span>(<font color="Maroon" title="c4">v2</font>,<font color="Maroon" title="c3">v1</font>) <a href="funct_4.html#K6" title="FUNCT_4:func.6">--&gt;</a> (<font color="Maroon" title="c2">a2</font>,<font color="Maroon" title="c1">a1</font>) = 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">v2</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="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c1">a1</font></span>)</span> <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="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c1">a1</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">v2</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c2">a2</font></span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:99"><span class="lab"><font color="Green" title="E60">A6</font></span></a>, <a class="ref" href="funct_4.html#T30" onmouseover="rs('funct_4/T30')" onmouseout="rh()">FUNCT_4:30</a>, <a class="ref" href="partfun1.html#T56" onmouseover="rs('partfun1/T56')" onmouseout="rh()">PARTFUN1:56</a></span>
<br/>.= 
 <a href="nomin_1.html#K16" title="NOMIN_1:func.16">global_overlapping</a> (<font color="Maroon" title="c5">V</font>,<font color="Maroon" title="c6">A</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">v1</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="c4">v2</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c2">a2</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:99"><span class="lab"><font color="Green" title="E57">A3</font></span></a>, <a class="txt" href="#E6:99"><span class="lab"><font color="Green" title="E59">A5</font></span></a>, <a class="ref" href="nomin_1.html#T64" target="_self" onmouseover="rs('nomin_1/T64')" onmouseout="rh()">Th64</a></span>
;<br/> <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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