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

<a NAME="E1:7_1_1"/>
 for <font color="Olive" title="b1">z</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><a href="goedcpuc.html#K3" title="GOEDCPUC:func.3">Example_Formula_of</a> (<font color="Olive" title="b2">p</font>,<font color="Olive" title="b3">x</font>)</span>)</span> where <font color="Olive" title="b2">p</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">CQC-WFF</a> <font color="Maroon" title="c1">Al</font>, <font color="Olive" title="b3">x</font> is   <a href="qc_lang1.html#NM5" title="QC_LANG1:NM.5">bound_QC-variable</a> of <font color="Maroon" title="c1">Al</font> : verum </span> } </span>  holds <br/><font color="Olive" title="b1">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">CQC-WFF</a> <span class="p1">(<span class="default"><a href="goedcpuc.html#K1" title="GOEDCPUC:func.1">FCEx</a> <font color="Maroon" title="c1">Al</font></span>)</span>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="7_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c2">z</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</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"> ( <font color="Maroon" title="c2">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><a href="goedcpuc.html#K3" title="GOEDCPUC:func.3">Example_Formula_of</a> (<font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">x</font>)</span>)</span> where <font color="Olive" title="b1">p</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">CQC-WFF</a> <font color="Maroon" title="c1">Al</font>, <font color="Olive" title="b2">x</font> is   <a href="qc_lang1.html#NM5" title="QC_LANG1:NM.5">bound_QC-variable</a> of <font color="Maroon" title="c1">Al</font> : verum </span> } </span>  implies <font color="Maroon" title="c2">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">CQC-WFF</a> <span class="p1">(<span class="default"><a href="goedcpuc.html#K1" title="GOEDCPUC:func.1">FCEx</a> <font color="Maroon" title="c1">Al</font></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E1:7_1_1_1"/><span class="lab"><font color="Green" title="E4">A1</font></span>: 
<font color="Maroon" title="c2">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><a href="goedcpuc.html#K3" title="GOEDCPUC:func.3">Example_Formula_of</a> (<font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">x</font>)</span>)</span> where <font color="Olive" title="b1">p</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">CQC-WFF</a> <font color="Maroon" title="c1">Al</font>, <font color="Olive" title="b2">x</font> is   <a href="qc_lang1.html#NM5" title="QC_LANG1:NM.5">bound_QC-variable</a> of <font color="Maroon" title="c1">Al</font> : verum </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"> <font color="Maroon" title="c2">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">CQC-WFF</a> <span class="p1">(<span class="default"><a href="goedcpuc.html#K1" title="GOEDCPUC:func.1">FCEx</a> <font color="Maroon" title="c1">Al</font></span>)</span></span><br/>

<a NAME="E2:7_1_1_1"/>
 ex <font color="Olive" title="b1">p</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">CQC-WFF</a> <font color="Maroon" title="c1">Al</font> ex <font color="Olive" title="b2">x</font> being   <a href="qc_lang1.html#NM5" title="QC_LANG1:NM.5">bound_QC-variable</a> of <font color="Maroon" title="c1">Al</font> st <font color="Maroon" title="c2">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="goedcpuc.html#K3" title="GOEDCPUC:func.3">Example_Formula_of</a> (<font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">x</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:7_1_1_1"><span class="lab"><font color="Green" title="E4">A1</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:7_1_1_1"/>
<font color="Maroon" title="c2">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">CQC-WFF</a> <span class="p1">(<span class="default"><a href="goedcpuc.html#K1" title="GOEDCPUC:func.1">FCEx</a> <font color="Maroon" title="c1">Al</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"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E2:7_1_1"/>
<span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><a href="goedcpuc.html#K3" title="GOEDCPUC:func.3">Example_Formula_of</a> (<font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">x</font>)</span>)</span> where <font color="Olive" title="b1">p</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">CQC-WFF</a> <font color="Maroon" title="c1">Al</font>, <font color="Olive" title="b2">x</font> is   <a href="qc_lang1.html#NM5" title="QC_LANG1:NM.5">bound_QC-variable</a> of <font color="Maroon" title="c1">Al</font> : verum </span> } </span>  is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="cqc_lang.html#K3" title="CQC_LANG:func.3">CQC-WFF</a> <span class="p2">(<span class="default"><a href="goedcpuc.html#K1" title="GOEDCPUC:func.1">FCEx</a> <font color="Maroon" title="c1">Al</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D3" onmouseover="rs('tarski/D3')" onmouseout="rh()">TARSKI:def 3</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>
