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<b>let </b><font color="Maroon">CX</font> be  <a href="henmodel.html#V1">Consistent</a> <a href="subset_1.html#NM2">Subset</a> of <a href="cqc_lang.html#K7">CQC-WFF</a> ;<br/><b>let </b><font color="Maroon">JH</font> be    <a href="henmodel.html#M1">Henkin_interpretation</a> of <font color="Maroon">CX</font>;<br/>



<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a> ] <b>means </b>( <font color="Maroon">CX</font> is <a href="goedelcp.html#V1" target="_self">negation_faithful</a> &amp; <font color="Maroon">CX</font> is <a href="goedelcp.html#V2" target="_self">with_examples</a> implies ( <font color="Maroon">JH</font>, <a href="henmodel.html#K4">valH</a>  <a href="valuat_1.html#R1">|=</a> <font color="Maroon">a<sub>1</sub></font> iff <font color="Maroon">CX</font> <a href="henmodel.html#R1">|-</a> <font color="Maroon">a<sub>1</sub></font> ) );<br/>
<a NAME="E1:16"/><i><font color="Green">E54</font></i>: 
for <font color="Olive">p</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a>   st  <a href="cqc_sim1.html#K6">QuantNbr</a> <font color="Olive">p</font> <a href="xxreal_0.html#R1">&lt;=</a> 0 holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive">p</font>]
 
<b>by </b><i/>;<br/>
<a NAME="E2:16"/><i><font color="Green">E55</font></i>: 
for <font color="Olive">k</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st ( for <font color="Olive">p</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a>   st  <a href="cqc_sim1.html#K6">QuantNbr</a> <font color="Olive">p</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">k</font> holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive">p</font>] ) holds <br/>for <font color="Olive">p</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a>   st  <a href="cqc_sim1.html#K6">QuantNbr</a> <font color="Olive">p</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">k</font> <a href="nat_1.html#K1">+</a> 1 holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive">p</font>]
 
<b>by </b><i/>;<br/>
<b>thus </b><a NAME="E3:16"/>
for <font color="Olive">p</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a>  holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">p</font>]
 <b>from </b><i><a class="ref" href="substut2.html#S2">SUBSTUT2:sch 2</a>(, );</i><br/>


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