<?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> holds <br/> (  <a href="goedelcp.html#K2" title="GOEDELCP:func.2">Ex-bound_in</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K13" title="CQC_LANG:func.13">Ex</a> <font color="Olive" title="b1">x</font>,<font color="Maroon" title="c1">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x</font> &amp;  <a href="goedelcp.html#K3" title="GOEDELCP:func.3">Ex-the_scope_of</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K13" title="CQC_LANG:func.13">Ex</a> <font color="Olive" title="b1">x</font>,<font color="Maroon" title="c1">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">p</font> )</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"> (  <a href="goedelcp.html#K2" title="GOEDELCP:func.2">Ex-bound_in</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K13" title="CQC_LANG:func.13">Ex</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> &amp;  <a href="goedelcp.html#K3" title="GOEDELCP:func.3">Ex-the_scope_of</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K13" title="CQC_LANG:func.13">Ex</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">p</font> )</span><br/>



<a NAME="E1:27"/><i><font color="Green" title="E27">A1</font></i>: 
 <a href="cqc_lang.html#K13" title="CQC_LANG:func.13">Ex</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">p</font> is <a href="qc_lang2.html#V4" title="QC_LANG2:attr.4">existential</a>
 
<b>by </b><i><a class="ref" href="qc_lang2.html#D13" title="QC_LANG2:def.13">QC_LANG2:def 13</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c3">q</font> being   <a href="qc_lang1.html#NM8" title="QC_LANG1:NM.8">QC-formula</a><b> such that </b><br/><a NAME="E3:27"/><i><font color="Green" title="E28">A2</font></i>: 
 <a href="cqc_lang.html#K13" title="CQC_LANG:func.13">Ex</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang2.html#K5" title="QC_LANG2:func.5">Ex</a> <span class="p1">(<span class="default"><a href="goedelcp.html#K2" title="GOEDELCP:func.2">Ex-bound_in</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K13" title="CQC_LANG:func.13">Ex</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">p</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">q</font>
 <b>by </b><i><a class="ref" href="goedelcp.html#D4" target="_self" title="GOEDELCP:def.4">Def4</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c4">y</font> being   <a href="qc_lang1.html#NM3" title="QC_LANG1:NM.3">bound_QC-variable</a><b> such that </b><br/><a NAME="E5:27"/><i><font color="Green" title="E29">A3</font></i>: 
 <a href="cqc_lang.html#K13" title="CQC_LANG:func.13">Ex</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cqc_lang.html#K13" title="CQC_LANG:func.13">Ex</a> <font color="Maroon" title="c4">y</font>,<span class="p1">(<span class="default"><a href="goedelcp.html#K3" title="GOEDELCP:func.3">Ex-the_scope_of</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K13" title="CQC_LANG:func.13">Ex</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">p</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E1:27"><i><font color="Green" title="E27">A1</font></i></a>, <a class="ref" href="goedelcp.html#D5" target="_self" title="GOEDELCP:def.5">Def5</a></i>;<br/>
<b>thus </b><a NAME="E6:27"/>
(  <a href="goedelcp.html#K2" title="GOEDELCP:func.2">Ex-bound_in</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K13" title="CQC_LANG:func.13">Ex</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> &amp;  <a href="goedelcp.html#K3" title="GOEDELCP:func.3">Ex-the_scope_of</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K13" title="CQC_LANG:func.13">Ex</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">p</font> )
 <b>by </b><i><a class="txt" href="#E3:27"><i><font color="Green" title="E28">A2</font></i></a>, <a class="txt" href="#E5:27"><i><font color="Green" title="E29">A3</font></i></a>, <a class="ref" href="qc_lang2.html#T19" title="QC_LANG2:th.19">QC_LANG2:19</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>
