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<span class="kw">let </span><font color="Maroon" title="c1">F</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">A</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <font color="Maroon" title="c1">F</font><br/>  for <font color="Olive" title="b2">J</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  holds   <a href="hallmar1.html#K1" title="HALLMAR1:func.1">union</a> (<font color="Olive" title="b1">A</font>,<font color="Olive" title="b2">J</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">F</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">A</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <font color="Maroon" title="c1">F</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">  for <font color="Olive" title="b1">J</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  holds   <a href="hallmar1.html#K1" title="HALLMAR1:func.1">union</a> (<font color="Maroon" title="c2">A</font>,<font color="Olive" title="b1">J</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">F</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">J</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">  <a href="hallmar1.html#K1" title="HALLMAR1:func.1">union</a> (<font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">J</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">F</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" onmouseover="rs('tarski/D3')" onmouseout="rh()">TARSKI:def 3</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"> (  not <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="hallmar1.html#K1" title="HALLMAR1:func.1">union</a> (<font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">J</font>) or <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">F</font> )</span><br/>







<span class="kw">assume </span><a NAME="E1:8"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="hallmar1.html#K1" title="HALLMAR1:func.1">union</a> (<font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">J</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"> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">F</font></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">j</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <span class="kw"> such that </span><br/><a NAME="E3:8"/>
<font color="Maroon" title="c5">j</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c3">J</font>
 <span class="kw">and </span><br/><a NAME="E4:8"/><span class="lab"><font color="Green" title="E5">A1</font></span>: 
<font color="Maroon" title="c5">j</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">A</font>
 <span class="kw">and </span><br/><a NAME="E5:8"/><span class="lab"><font color="Green" title="E6">A2</font></span>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="hallmar1.html#D1" target="_self" onmouseover="rs('hallmar1/D1')" onmouseout="rh()">Def1</a></span>;<br/>
<a NAME="E6:8"/>
(  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <font color="Maroon" title="c1">F</font> &amp; <font color="Maroon" title="c2">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c2">A</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:8"><span class="lab"><font color="Green" title="E5">A1</font></span></a>, <a class="ref" href="finseq_1.html#D4" onmouseover="rs('finseq_1/D4')" onmouseout="rh()">FINSEQ_1:def 4</a>, <a class="ref" href="funct_1.html#T3" onmouseover="rs('funct_1/T3')" onmouseout="rh()">FUNCT_1:3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:8"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">F</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:8"><span class="lab"><font color="Green" title="E6">A2</font></span></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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