<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">p</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">x</font> being  <a href="qc_lang1.html#NM3" title="QC_LANG1:NM.3">bound_QC-variable</a><br/> for <font color="Olive" title="b2">A</font> being non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <br/> for <font color="Olive" title="b3">v</font>, <font color="Olive" title="b4">w</font> being   <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> <font color="Olive" title="b2">A</font><br/> for <font color="Olive" title="b5">a</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b2">A</font>  st <font color="Olive" title="b3">v</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b1">x</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b4">w</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b1">x</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b3">v</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">x</font> <a href="sublemma.html#K13" title="SUBLEMMA:func.13">|</a> <font color="Olive" title="b5">a</font></span>)</span></span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">w</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">x</font> <a href="sublemma.html#K13" title="SUBLEMMA:func.13">|</a> <font color="Olive" title="b5">a</font></span>)</span></span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">x</font> be   <a href="qc_lang1.html#NM3" title="QC_LANG1:NM.3">bound_QC-variable</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">A</font> being non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <br/> for <font color="Olive" title="b2">v</font>, <font color="Olive" title="b3">w</font> being   <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> <font color="Olive" title="b1">A</font><br/> for <font color="Olive" title="b4">a</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">A</font>  st <font color="Olive" title="b2">v</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b3">w</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b2">v</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sublemma.html#K13" title="SUBLEMMA:func.13">|</a> <font color="Olive" title="b4">a</font></span>)</span></span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">w</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sublemma.html#K13" title="SUBLEMMA:func.13">|</a> <font color="Olive" title="b4">a</font></span>)</span></span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c3">A</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">v</font>, <font color="Olive" title="b2">w</font> being   <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> <font color="Maroon" title="c3">A</font><br/> for <font color="Olive" title="b3">a</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">A</font>  st <font color="Olive" title="b1">v</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b2">w</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b1">v</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sublemma.html#K13" title="SUBLEMMA:func.13">|</a> <font color="Olive" title="b3">a</font></span>)</span></span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">w</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sublemma.html#K13" title="SUBLEMMA:func.13">|</a> <font color="Olive" title="b3">a</font></span>)</span></span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c4">v</font>, <font color="Maroon" title="c5">w</font> be    <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> <font color="Maroon" title="c3">A</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">a</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">A</font>  st <font color="Maroon" title="c4">v</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c5">w</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> holds <br/><span class="p1">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sublemma.html#K13" title="SUBLEMMA:func.13">|</a> <font color="Olive" title="b1">a</font></span>)</span></span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">w</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sublemma.html#K13" title="SUBLEMMA:func.13">|</a> <font color="Olive" title="b1">a</font></span>)</span></span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c6">a</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">A</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">v</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c5">w</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> implies <span class="p1">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sublemma.html#K13" title="SUBLEMMA:func.13">|</a> <font color="Maroon" title="c6">a</font></span>)</span></span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">w</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sublemma.html#K13" title="SUBLEMMA:func.13">|</a> <font color="Maroon" title="c6">a</font></span>)</span></span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span> )</span><br/>











<b>assume </b><a NAME="E1:85"/><i><font color="Green" title="E64">A1</font></i>: 
<font color="Maroon" title="c4">v</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c5">w</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sublemma.html#K13" title="SUBLEMMA:func.13">|</a> <font color="Maroon" title="c6">a</font></span>)</span></span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">w</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sublemma.html#K13" title="SUBLEMMA:func.13">|</a> <font color="Maroon" title="c6">a</font></span>)</span></span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span></span><br/>

<a NAME="E2:85"/><i><font color="Green" title="E65">B2</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">w</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sublemma.html#K13" title="SUBLEMMA:func.13">|</a> <font color="Maroon" title="c6">a</font></span>)</span></span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font>
 
<b>by </b><i><a class="ref" href="sublemma.html#T64" target="_self" title="SUBLEMMA:th.64">Th64</a></i>;<br/>
<a NAME="E3:85"/><b>then </b><i><font color="Green" title="E66">A2</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sublemma.html#K13" title="SUBLEMMA:func.13">|</a> <font color="Maroon" title="c6">a</font></span>)</span></span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">w</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sublemma.html#K13" title="SUBLEMMA:func.13">|</a> <font color="Maroon" title="c6">a</font></span>)</span></span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="sublemma.html#T64" target="_self" title="SUBLEMMA:th.64">Th64</a></i>;<br/>
<a NAME="E4:85"/>
for <font color="Olive" title="b1">b</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sublemma.html#K13" title="SUBLEMMA:func.13">|</a> <font color="Maroon" title="c6">a</font></span>)</span></span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sublemma.html#K13" title="SUBLEMMA:func.13">|</a> <font color="Maroon" title="c6">a</font></span>)</span></span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">w</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sublemma.html#K13" title="SUBLEMMA:func.13">|</a> <font color="Maroon" title="c6">a</font></span>)</span></span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">b</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="85_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c7">b</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c7">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sublemma.html#K13" title="SUBLEMMA:func.13">|</a> <font color="Maroon" title="c6">a</font></span>)</span></span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sublemma.html#K13" title="SUBLEMMA:func.13">|</a> <font color="Maroon" title="c6">a</font></span>)</span></span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">w</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sublemma.html#K13" title="SUBLEMMA:func.13">|</a> <font color="Maroon" title="c6">a</font></span>)</span></span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">b</font> )</span><br/>

<b>assume </b><a NAME="E1:85_1"/><i><font color="Green" title="E67">A3</font></i>: 
<font color="Maroon" title="c7">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sublemma.html#K13" title="SUBLEMMA:func.13">|</a> <font color="Maroon" title="c6">a</font></span>)</span></span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sublemma.html#K13" title="SUBLEMMA:func.13">|</a> <font color="Maroon" title="c6">a</font></span>)</span></span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">w</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sublemma.html#K13" title="SUBLEMMA:func.13">|</a> <font color="Maroon" title="c6">a</font></span>)</span></span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">b</font></span><br/>

<a NAME="E2:85_1"/><i><font color="Green" title="E68">A4</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sublemma.html#K13" title="SUBLEMMA:func.13">|</a> <font color="Maroon" title="c6">a</font></span>)</span></span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sublemma.html#K13" title="SUBLEMMA:func.13">|</a> <font color="Maroon" title="c6">a</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">b</font>
 
<b>by </b><i><a class="txt" href="sublemma.html#E1:85_1"><i><font color="Green" title="E67">A3</font></i></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></i>;<br/>
<a NAME="E3:85_1"/><i><font color="Green" title="E69">A5</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">w</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sublemma.html#K13" title="SUBLEMMA:func.13">|</a> <font color="Maroon" title="c6">a</font></span>)</span></span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">w</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sublemma.html#K13" title="SUBLEMMA:func.13">|</a> <font color="Maroon" title="c6">a</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">b</font>
 
<b>by </b><i><a class="txt" href="sublemma.html#E3:85"><i><font color="Green" title="E66">A2</font></i></a>, <a class="txt" href="sublemma.html#E1:85_1"><i><font color="Green" title="E67">A3</font></i></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></i>;<br/>
<div><i><font color="Green" title="E70">A6</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="85_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:85_1_1"/><i><font color="Green" title="E71">A7</font></i>: 
<font color="Maroon" title="c7">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">x</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sublemma.html#K13" title="SUBLEMMA:func.13">|</a> <font color="Maroon" title="c6">a</font></span>)</span></span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">w</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sublemma.html#K13" title="SUBLEMMA:func.13">|</a> <font color="Maroon" title="c6">a</font></span>)</span></span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">b</font></span><br/><a NAME="E2:85_1_1"/><b>then </b><i><font color="Green" title="E72">A8</font></i>: 
not <font color="Maroon" title="c7">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E3:85_1_1"/>
<font color="Maroon" title="c7">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font>
 <b>by </b><i><a class="txt" href="sublemma.html#E1:85_1"><i><font color="Green" title="E67">A3</font></i></a>, <a class="ref" href="sublemma.html#T64" target="_self" title="SUBLEMMA:th.64">Th64</a></i>;<br/><a NAME="E4:85_1_1"/><b>then </b><i><font color="Green" title="E73">A9</font></i>: 
<font color="Maroon" title="c7">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 <b>by </b><i><a class="txt" href="sublemma.html#E2:85_1_1"><i><font color="Green" title="E72">A8</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E5:85_1_1"/><b>then </b><i><font color="Green" title="E74">A10</font></i>: 
<font color="Maroon" title="c7">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="sublemma.html#T64" target="_self" title="SUBLEMMA:th.64">Th64</a></i>;<br/><a NAME="E6:85_1_1"/>
<font color="Maroon" title="c7">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">w</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="sublemma.html#E4:85_1_1"><i><font color="Green" title="E73">A9</font></i></a>, <a class="ref" href="sublemma.html#T64" target="_self" title="SUBLEMMA:th.64">Th64</a></i>;<br/><a NAME="E7:85_1_1"/><b>then </b><i><font color="Green" title="E75">A11</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">w</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">w</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">b</font>
 <b>by </b><i><a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></i>;<br/><a NAME="E8:85_1_1"/>
( <span class="p1">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sublemma.html#K13" title="SUBLEMMA:func.13">|</a> <font color="Maroon" title="c6">a</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">v</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">b</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c5">w</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sublemma.html#K13" title="SUBLEMMA:func.13">|</a> <font color="Maroon" title="c6">a</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">w</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">b</font> )
 <b>by </b><i><a class="txt" href="sublemma.html#E1:85_1_1"><i><font color="Green" title="E71">A7</font></i></a>, <a class="ref" href="sublemma.html#T49" target="_self" title="SUBLEMMA:th.49">Th49</a></i>;<br/><b>hence </b><a NAME="E9:85_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sublemma.html#K13" title="SUBLEMMA:func.13">|</a> <font color="Maroon" title="c6">a</font></span>)</span></span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">w</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sublemma.html#K13" title="SUBLEMMA:func.13">|</a> <font color="Maroon" title="c6">a</font></span>)</span></span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">b</font>
 <b>by </b><i><a class="txt" href="sublemma.html#E1:85"><i><font color="Green" title="E64">A1</font></i></a>, <a class="txt" href="sublemma.html#E2:85_1"><i><font color="Green" title="E68">A4</font></i></a>, <a class="txt" href="sublemma.html#E3:85_1"><i><font color="Green" title="E69">A5</font></i></a>, <a class="txt" href="sublemma.html#E5:85_1_1"><i><font color="Green" title="E74">A10</font></i></a>, <a class="txt" href="sublemma.html#E7:85_1_1"><i><font color="Green" title="E75">A11</font></i></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="85_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:85_1_2"/><i><font color="Green" title="E71">A12</font></i>: 
<font color="Maroon" title="c7">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sublemma.html#K13" title="SUBLEMMA:func.13">|</a> <font color="Maroon" title="c6">a</font></span>)</span></span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">w</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sublemma.html#K13" title="SUBLEMMA:func.13">|</a> <font color="Maroon" title="c6">a</font></span>)</span></span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">b</font></span><br/><a NAME="E2:85_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sublemma.html#K13" title="SUBLEMMA:func.13">|</a> <font color="Maroon" title="c6">a</font></span>)</span></span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sublemma.html#K13" title="SUBLEMMA:func.13">|</a> <font color="Maroon" title="c6">a</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">b</font>
 <b>by </b><i><a class="txt" href="sublemma.html#E1:85_1"><i><font color="Green" title="E67">A3</font></i></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></i>;<br/><a NAME="E3:85_1_2"/><b>then </b><i><font color="Green" title="E72">A13</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sublemma.html#K13" title="SUBLEMMA:func.13">|</a> <font color="Maroon" title="c6">a</font></span>)</span></span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">a</font>
 <b>by </b><i><a class="txt" href="sublemma.html#E1:85_1_2"><i><font color="Green" title="E71">A12</font></i></a>, <a class="ref" href="sublemma.html#T50" target="_self" title="SUBLEMMA:th.50">Th50</a></i>;<br/><a NAME="E4:85_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">w</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sublemma.html#K13" title="SUBLEMMA:func.13">|</a> <font color="Maroon" title="c6">a</font></span>)</span></span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">w</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sublemma.html#K13" title="SUBLEMMA:func.13">|</a> <font color="Maroon" title="c6">a</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">b</font>
 <b>by </b><i><a class="txt" href="sublemma.html#E3:85"><i><font color="Green" title="E66">A2</font></i></a>, <a class="txt" href="sublemma.html#E1:85_1"><i><font color="Green" title="E67">A3</font></i></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></i>;<br/><b>hence </b><a NAME="E5:85_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sublemma.html#K13" title="SUBLEMMA:func.13">|</a> <font color="Maroon" title="c6">a</font></span>)</span></span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">w</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sublemma.html#K13" title="SUBLEMMA:func.13">|</a> <font color="Maroon" title="c6">a</font></span>)</span></span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">b</font>
 <b>by </b><i><a class="txt" href="sublemma.html#E1:85_1_2"><i><font color="Green" title="E71">A12</font></i></a>, <a class="txt" href="sublemma.html#E3:85_1_2"><i><font color="Green" title="E72">A13</font></i></a>, <a class="ref" href="sublemma.html#T50" target="_self" title="SUBLEMMA:th.50">Th50</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:85_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sublemma.html#K13" title="SUBLEMMA:func.13">|</a> <font color="Maroon" title="c6">a</font></span>)</span></span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">w</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sublemma.html#K13" title="SUBLEMMA:func.13">|</a> <font color="Maroon" title="c6">a</font></span>)</span></span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">b</font>
 <b>by </b><i><a class="txt" href="sublemma.html#E4:85_1"><i><font color="Green" title="E70">A6</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E5:85"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sublemma.html#K13" title="SUBLEMMA:func.13">|</a> <font color="Maroon" title="c6">a</font></span>)</span></span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">w</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sublemma.html#K13" title="SUBLEMMA:func.13">|</a> <font color="Maroon" title="c6">a</font></span>)</span></span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c1">p</font></span>)</span>
 <b>by </b><i><a class="txt" href="sublemma.html#E2:85"><i><font color="Green" title="E65">B2</font></i></a>, <a class="ref" href="funct_1.html#T9" title="FUNCT_1:th.9">FUNCT_1:9</a>, <a class="ref" href="sublemma.html#T64" target="_self" title="SUBLEMMA:th.64">Th64</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
