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<span class="kw">let </span><font color="Maroon" title="c3">Q</font> be   <a href="ltlaxio3.html#NM1" title="LTLAXIO3:NM.1">PNPair</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">X</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a> <a href="ltlaxio3.html#K1" title="LTLAXIO3:func.1">**</a></span>)</span>,<span class="p2">(<span class="default"><a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a> <a href="ltlaxio3.html#K1" title="LTLAXIO3:func.1">**</a></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>  st <font color="Maroon" title="c3">Q</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">X</font> holds <br/> <a href="ltlaxio4.html#K5" title="LTLAXIO4:func.5">comp</a> <font color="Maroon" title="c3">Q</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a>  <a href="ltlaxio4.html#K6" title="LTLAXIO4:func.6">comp</a> <font color="Olive" title="b1">X</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">X</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a> <a href="ltlaxio3.html#K1" title="LTLAXIO3:func.1">**</a></span>)</span>,<span class="p2">(<span class="default"><a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a> <a href="ltlaxio3.html#K1" title="LTLAXIO3:func.1">**</a></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</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"> ( <font color="Maroon" title="c3">Q</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c4">X</font> implies  <a href="ltlaxio4.html#K5" title="LTLAXIO4:func.5">comp</a> <font color="Maroon" title="c3">Q</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a>  <a href="ltlaxio4.html#K6" title="LTLAXIO4:func.6">comp</a> <font color="Maroon" title="c4">X</font> )</span><br/>



<span class="kw">assume </span><a NAME="E1:31"/>
<font color="Maroon" title="c3">Q</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c4">X</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="ltlaxio4.html#K5" title="LTLAXIO4:func.5">comp</a> <font color="Maroon" title="c3">Q</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a>  <a href="ltlaxio4.html#K6" title="LTLAXIO4:func.6">comp</a> <font color="Maroon" title="c4">X</font></span><br/>

<a NAME="E2:31"/><span class="kw">then </span><span class="lab"><font color="Green" title="E16">A1</font></span>: 
 <a href="ltlaxio4.html#K5" title="LTLAXIO4:func.5">comp</a> <font color="Maroon" title="c3">Q</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><a href="ltlaxio4.html#K5" title="LTLAXIO4:func.5">comp</a> <font color="Olive" title="b1">T</font></span>)</span> where <font color="Olive" title="b1">T</font> is   <a href="ltlaxio3.html#NM1" title="LTLAXIO3:NM.1">PNPair</a> : <font color="Olive" title="b1">T</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c4">X</font> </span> } </span> 
 
;<br/>
<span class="kw">let </span><font color="Maroon" title="c5">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="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ltlaxio4.html#K5" title="LTLAXIO4:func.5">comp</a> <font color="Maroon" title="c3">Q</font> or <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ltlaxio4.html#K6" title="LTLAXIO4:func.6">comp</a> <font color="Maroon" title="c4">X</font> )</span><br/>

<span class="kw">assume </span><a NAME="E3:31"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ltlaxio4.html#K5" title="LTLAXIO4:func.5">comp</a> <font color="Maroon" title="c3">Q</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="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ltlaxio4.html#K6" title="LTLAXIO4:func.6">comp</a> <font color="Maroon" title="c4">X</font></span><br/>

<span class="kw">hence </span><a NAME="E4:31"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ltlaxio4.html#K6" title="LTLAXIO4:func.6">comp</a> <font color="Maroon" title="c4">X</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:31"><span class="lab"><font color="Green" title="E16">A1</font></span></a>, <a class="ref" href="tarski.html#D4" onmouseover="rs('tarski/D4')" onmouseout="rh()">TARSKI:def 4</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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