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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="qc_lang1.html#NM3">bound_QC-variable</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="fraenkel.html#M2">Element</a> of  <a href="valuat_1.html#K2" target="_self">Valuations_in</a> <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a> ;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="valuat_1.html#M1" target="_self">interpretation</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>









<div><i><font color="Green">E23</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="35_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:35_1"/>
<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="valuat_1.html#R1" target="_self">|=</a>  <a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 ;<br/><a NAME="E2:35_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="valuat_1.html#K7" target="_self">FOR_ALL</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><a href="valuat_1.html#K12" target="_self">Valid</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a> 
 <b>by </b><i><a class="ref" href="valuat_1.html#T30" target="_self">Th30</a></i>;<br/><b>hence </b><a NAME="E3:35_1"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="fraenkel.html#M2">Element</a> of  <a href="valuat_1.html#K2" target="_self">Valuations_in</a> <font color="Maroon">c<sub>1</sub></font> st ( for <font color="Olive">b<sub>2</sub></font> being  <a href="qc_lang1.html#NM3">bound_QC-variable</a> st <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b<sub>2</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>2</sub></font> ) holds <br/><span class="p1">(<span class="default"><a href="valuat_1.html#K12" target="_self">Valid</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a> 
 <b>by </b><i><a class="ref" href="valuat_1.html#T8" target="_self">Th8</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="35_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:35_2"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="fraenkel.html#M2">Element</a> of  <a href="valuat_1.html#K2" target="_self">Valuations_in</a> <font color="Maroon">c<sub>1</sub></font> st ( for <font color="Olive">b<sub>2</sub></font> being  <a href="qc_lang1.html#NM3">bound_QC-variable</a> st <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b<sub>2</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>2</sub></font> ) holds <br/><span class="p1">(<span class="default"><a href="valuat_1.html#K12" target="_self">Valid</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a> 
 ;<br/><a NAME="E2:35_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="valuat_1.html#K7" target="_self">FOR_ALL</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><a href="valuat_1.html#K12" target="_self">Valid</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a> 
 <b>by </b><i><a class="ref" href="valuat_1.html#T8" target="_self">Th8</a></i>;<br/><b>hence </b><a NAME="E3:35_2"/>
<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="valuat_1.html#R1" target="_self">|=</a>  <a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="valuat_1.html#T30" target="_self">Th30</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:35"/>
( <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="valuat_1.html#R1" target="_self">|=</a>  <a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> iff for <font color="Olive">b<sub>1</sub></font> being   <a href="fraenkel.html#M2">Element</a> of  <a href="valuat_1.html#K2" target="_self">Valuations_in</a> <font color="Maroon">c<sub>1</sub></font> st ( for <font color="Olive">b<sub>2</sub></font> being  <a href="qc_lang1.html#NM3">bound_QC-variable</a> st <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b<sub>2</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>2</sub></font> ) holds <br/><span class="p1">(<span class="default"><a href="valuat_1.html#K12" target="_self">Valid</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  )
 <b>by </b><i><a class="txt" href="valuat_1.html#E1:35"><i><font color="Green">E23</font></i></a></i>;<br/>


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