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<b>let </b><font color="Maroon">X</font> be   <a href="subset_1.html#NM2">Subset</a> of <a href="cqc_lang.html#K7">CQC-WFF</a> ;<br/>

<b>set </b><font color="Maroon">PX</font> = <span class="p1">{<span class="default"> <font color="Olive">p</font> where <font color="Olive">p</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a>  :  ex <font color="Olive">f</font> being   <a href="finseq_1.html#M2">FinSequence</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><a href="cqc_lang.html#K7">CQC-WFF</a> ,<a href="cqc_the1.html#K2" target="_self">Proof_Step_Kinds</a> </span><a href="zfmisc_1.html#K2">:]</a></span> st <br/>( <font color="Olive">f</font> <a href="cqc_the1.html#R2" target="_self">is_a_proof_wrt</a> <font color="Maroon">X</font> &amp;  <a href="cqc_the1.html#K3" target="_self">Effect</a> <font color="Olive">f</font> <a href="hidden.html#R1">=</a> <font color="Olive">p</font> ) </span>}</span> ;<br/>
<a NAME="E1:53"/><i><font color="Green">E29</font></i>: 
<span class="p1">{<span class="default"> <font color="Olive">p</font> where <font color="Olive">p</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a>  :  ex <font color="Olive">f</font> being   <a href="finseq_1.html#M2">FinSequence</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><a href="cqc_lang.html#K7">CQC-WFF</a> ,<a href="cqc_the1.html#K2" target="_self">Proof_Step_Kinds</a> </span><a href="zfmisc_1.html#K2">:]</a></span> st <br/>( <font color="Olive">f</font> <a href="cqc_the1.html#R2" target="_self">is_a_proof_wrt</a> <font color="Maroon">X</font> &amp;  <a href="cqc_the1.html#K3" target="_self">Effect</a> <font color="Olive">f</font> <a href="hidden.html#R1">=</a> <font color="Olive">p</font> ) </span>}</span>  <a href="tarski.html#R1">c=</a>  <a href="cqc_the1.html#K1" target="_self">Cn</a> <font color="Maroon">X</font>
 
<b>by </b><i/>;<br/>
<b>reconsider </b><font color="Maroon">PX</font> = <span class="p1">{<span class="default"> <font color="Olive">p</font> where <font color="Olive">p</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a>  :  ex <font color="Olive">f</font> being   <a href="finseq_1.html#M2">FinSequence</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><a href="cqc_lang.html#K7">CQC-WFF</a> ,<a href="cqc_the1.html#K2" target="_self">Proof_Step_Kinds</a> </span><a href="zfmisc_1.html#K2">:]</a></span> st <br/>( <font color="Olive">f</font> <a href="cqc_the1.html#R2" target="_self">is_a_proof_wrt</a> <font color="Maroon">X</font> &amp;  <a href="cqc_the1.html#K3" target="_self">Effect</a> <font color="Olive">f</font> <a href="hidden.html#R1">=</a> <font color="Olive">p</font> ) </span>}</span>  as   <a href="subset_1.html#NM2">Subset</a> of <a href="cqc_lang.html#K7">CQC-WFF</a>  <b>by </b><i/>;<br/>
<a NAME="E3:53"/>
( <font color="Maroon">X</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">PX</font> &amp; <font color="Maroon">PX</font> <a href="cqc_the1.html#NR1" target="_self">is_a_theory</a>  )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E4:53"/><b>then </b>
 <a href="cqc_the1.html#K1" target="_self">Cn</a> <font color="Maroon">X</font> <a href="tarski.html#R1">c=</a> <span class="p1">{<span class="default"> <font color="Olive">p</font> where <font color="Olive">p</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a>  :  ex <font color="Olive">f</font> being   <a href="finseq_1.html#M2">FinSequence</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><a href="cqc_lang.html#K7">CQC-WFF</a> ,<a href="cqc_the1.html#K2" target="_self">Proof_Step_Kinds</a> </span><a href="zfmisc_1.html#K2">:]</a></span> st <br/>( <font color="Olive">f</font> <a href="cqc_the1.html#R2" target="_self">is_a_proof_wrt</a> <font color="Maroon">X</font> &amp;  <a href="cqc_the1.html#K3" target="_self">Effect</a> <font color="Olive">f</font> <a href="hidden.html#R1">=</a> <font color="Olive">p</font> ) </span>}</span> 
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E5:53"/>
<span class="p1">{<span class="default"> <font color="Olive">p</font> where <font color="Olive">p</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a>  :  ex <font color="Olive">f</font> being   <a href="finseq_1.html#M2">FinSequence</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><a href="cqc_lang.html#K7">CQC-WFF</a> ,<a href="cqc_the1.html#K2" target="_self">Proof_Step_Kinds</a> </span><a href="zfmisc_1.html#K2">:]</a></span> st <br/>( <font color="Olive">f</font> <a href="cqc_the1.html#R2" target="_self">is_a_proof_wrt</a> <font color="Maroon">X</font> &amp;  <a href="cqc_the1.html#K3" target="_self">Effect</a> <font color="Olive">f</font> <a href="hidden.html#R1">=</a> <font color="Olive">p</font> ) </span>}</span>  <a href="hidden.html#R1">=</a>  <a href="cqc_the1.html#K1" target="_self">Cn</a> <font color="Maroon">X</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>


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