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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a> ;<br/>

<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="nat_1.html#NM1">Nat</a>] means for <font color="Olive">b<sub>1</sub></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">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">a<sub>1</sub></font> holds <br/><font color="Maroon">P<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>];<br/>
<a NAME="E1:17_1"/><i><font color="Green">E15</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[0]
 
<b>by </b><i><a class="txt" href="substut2.html#E1:17"><i><font color="Green">E13</font></i></a></i>;<br/>
<a NAME="E2:17_1"/><i><font color="Green">E16</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1]
 
<b>by </b><i><a class="txt" href="substut2.html#E2:17"><i><font color="Green">E14</font></i></a></i>;<br/>
<a NAME="E3:17_1"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>]
 
<b>from </b><i><a class="ref" href="nat_1.html#S1">NAT_1:sch 1</a>(<a class="txt" href="substut2.html#E1:17_1"><i><font color="Green">E15</font></i></a>, <a class="txt" href="substut2.html#E2:17_1"><i><font color="Green">E16</font></i></a>);<br/></i>
<a NAME="E4:17_1"/><b>then </b>
<font color="Maroon">S<sub>1</sub></font>[ <a href="cqc_sim1.html#K6">QuantNbr</a> <font color="Maroon">c<sub>1</sub></font>]
 
;<br/>
<b>hence </b><a NAME="E5:17_1"/>
<font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">c<sub>1</sub></font>]
 ;<br/>


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