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<span class="kw">set </span><font color="Maroon" title="c6">k</font> = <font color="Maroon" title="c4">T</font> <a href="trees_2.html#K5" title="TREES_2:func.5">|</a> <font color="Maroon" title="c5">t</font>;<br/>
<a NAME="E1:52_1_1"/><span class="lab"><font color="Green" title="E28">A1</font></span>: 
 <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">T</font> <a href="trees_2.html#K5" title="TREES_2:func.5">|</a> <font color="Maroon" title="c5">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c4">T</font></span>)</span> <a href="trees_1.html#K4" title="TREES_1:func.4">|</a> <font color="Maroon" title="c5">t</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="trees_2.html#D10" onmouseover="rs('trees_2/D10')" onmouseout="rh()">TREES_2:def 10</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E29">A2</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="52_1_1_1"><span class="kw">now </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">  for <font color="Olive" title="b1">u</font> being    <a href="trees_1.html#M1" title="TREES_1:mode.1">Element</a> of  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">T</font> <a href="trees_2.html#K5" title="TREES_2:func.5">|</a> <font color="Maroon" title="c5">t</font></span>)</span><br/>  for <font color="Olive" title="b2">w</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</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="Olive" title="b2">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">T</font> <a href="trees_2.html#K5" title="TREES_2:func.5">|</a> <font color="Maroon" title="c5">t</font></span>)</span> <a href="trees_2.html#K3" title="TREES_2:func.3">.</a> <font color="Olive" title="b1">u</font> holds <br/> <a href="trees_9.html#K2" title="TREES_9:func.2">succ</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">T</font> <a href="trees_2.html#K5" title="TREES_2:func.5">|</a> <font color="Maroon" title="c5">t</font></span>)</span>,<font color="Olive" title="b1">u</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the    <a href="ltlaxio4.html#M2" title="LTLAXIO4:mode.2">Enumeration</a> of  <a href="ltlaxio4.html#K9" title="LTLAXIO4:func.9">compn</a> <font color="Olive" title="b2">w</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c7">u</font> be    <a href="trees_1.html#M1" title="TREES_1:mode.1">Element</a> of  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">T</font> <a href="trees_2.html#K5" title="TREES_2:func.5">|</a> <font color="Maroon" title="c5">t</font></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">  for <font color="Olive" title="b1">w</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</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="Olive" title="b1">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">T</font> <a href="trees_2.html#K5" title="TREES_2:func.5">|</a> <font color="Maroon" title="c5">t</font></span>)</span> <a href="trees_2.html#K3" title="TREES_2:func.3">.</a> <font color="Maroon" title="c7">u</font> holds <br/> <a href="trees_9.html#K2" title="TREES_9:func.2">succ</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">T</font> <a href="trees_2.html#K5" title="TREES_2:func.5">|</a> <font color="Maroon" title="c5">t</font></span>)</span>,<font color="Maroon" title="c7">u</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the    <a href="ltlaxio4.html#M2" title="LTLAXIO4:mode.2">Enumeration</a> of  <a href="ltlaxio4.html#K9" title="LTLAXIO4:func.9">compn</a> <font color="Olive" title="b1">w</font></span><br/><span class="kw">reconsider </span><font color="Maroon" title="c8">tu</font> = <font color="Maroon" title="c5">t</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c7">u</font> as    <a href="trees_1.html#M1" title="TREES_1:mode.1">Element</a> of  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c4">T</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:52_1_1"><span class="lab"><font color="Green" title="E28">A1</font></span></a>, <a class="ref" href="trees_1.html#D6" onmouseover="rs('trees_1/D6')" onmouseout="rh()">TREES_1:def 6</a></span>;<br/><span class="kw">let </span><font color="Maroon" title="c9">w</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</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="c9">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">T</font> <a href="trees_2.html#K5" title="TREES_2:func.5">|</a> <font color="Maroon" title="c5">t</font></span>)</span> <a href="trees_2.html#K3" title="TREES_2:func.3">.</a> <font color="Maroon" title="c7">u</font> implies  <a href="trees_9.html#K2" title="TREES_9:func.2">succ</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">T</font> <a href="trees_2.html#K5" title="TREES_2:func.5">|</a> <font color="Maroon" title="c5">t</font></span>)</span>,<font color="Maroon" title="c7">u</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the    <a href="ltlaxio4.html#M2" title="LTLAXIO4:mode.2">Enumeration</a> of  <a href="ltlaxio4.html#K9" title="LTLAXIO4:func.9">compn</a> <font color="Maroon" title="c9">w</font> )</span><br/><span class="kw">assume </span><a NAME="E2:52_1_1_1"/>
<font color="Maroon" title="c9">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">T</font> <a href="trees_2.html#K5" title="TREES_2:func.5">|</a> <font color="Maroon" title="c5">t</font></span>)</span> <a href="trees_2.html#K3" title="TREES_2:func.3">.</a> <font color="Maroon" title="c7">u</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="trees_9.html#K2" title="TREES_9:func.2">succ</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">T</font> <a href="trees_2.html#K5" title="TREES_2:func.5">|</a> <font color="Maroon" title="c5">t</font></span>)</span>,<font color="Maroon" title="c7">u</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the    <a href="ltlaxio4.html#M2" title="LTLAXIO4:mode.2">Enumeration</a> of  <a href="ltlaxio4.html#K9" title="LTLAXIO4:func.9">compn</a> <font color="Maroon" title="c9">w</font></span><br/><a NAME="E3:52_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E30">A3</font></span>: 
<font color="Maroon" title="c9">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">T</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">t</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c7">u</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:52_1_1"><span class="lab"><font color="Green" title="E28">A1</font></span></a>, <a class="ref" href="trees_2.html#D10" onmouseover="rs('trees_2/D10')" onmouseout="rh()">TREES_2:def 10</a></span>;<br/><span class="kw">thus </span> <a href="trees_9.html#K2" title="TREES_9:func.2">succ</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">T</font> <a href="trees_2.html#K5" title="TREES_2:func.5">|</a> <font color="Maroon" title="c5">t</font></span>)</span>,<font color="Maroon" title="c7">u</font>) = 
 <a href="trees_9.html#K2" title="TREES_9:func.2">succ</a> (<font color="Maroon" title="c4">T</font>,<font color="Maroon" title="c8">tu</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="trees_9.html#T31" onmouseover="rs('trees_9/T31')" onmouseout="rh()">TREES_9:31</a></span>
<br/>.= 
 the    <a href="ltlaxio4.html#M2" title="LTLAXIO4:mode.2">Enumeration</a> of  <a href="ltlaxio4.html#K9" title="LTLAXIO4:func.9">compn</a> <font color="Maroon" title="c9">w</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ltlaxio4.html#D11" target="_self" onmouseover="rs('ltlaxio4/D11')" onmouseout="rh()">Def11</a>, <a class="txt" href="#E3:52_1_1_1"><span class="lab"><font color="Green" title="E30">A3</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/></div><span class="kw">end;</span></div>
<a NAME="E3:52_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">T</font> <a href="trees_2.html#K5" title="TREES_2:func.5">|</a> <font color="Maroon" title="c5">t</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">T</font> <a href="trees_2.html#K3" title="TREES_2:func.3">.</a> <font color="Maroon" title="c5">t</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="trees_9.html#T35" onmouseover="rs('trees_9/T35')" onmouseout="rh()">TREES_9:35</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:52_1_1"/>
<font color="Maroon" title="c4">T</font> <a href="trees_2.html#K5" title="TREES_2:func.5">|</a> <font color="Maroon" title="c5">t</font> is    <a href="ltlaxio4.html#M3" title="LTLAXIO4:mode.3">pnptree</a> of <font color="Maroon" title="c4">T</font> <a href="trees_2.html#K3" title="TREES_2:func.3">.</a> <font color="Maroon" title="c5">t</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:52_1_1"><span class="lab"><font color="Green" title="E29">A2</font></span></a>, <a class="ref" href="ltlaxio4.html#D11" target="_self" onmouseover="rs('ltlaxio4/D11')" onmouseout="rh()">Def11</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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