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<b>let </b><font color="Maroon" title="c6">s1</font>, <font color="Maroon" title="c7">s2</font> be   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <font color="Maroon" title="c3">S</font>;<br/>

<b>deffunc </b><font color="Maroon">H<sub>2</sub></font>(   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ,  <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <font color="Maroon" title="c3">S</font>) <b>-&gt; </b>  <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <font color="Maroon" title="c3">S</font> =  <a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> $2;<br/>
<b>given </b><font color="Maroon" title="c8">f1</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> , <a href="card_3.html#K4" title="CARD_3:func.4">product</a> the <a href="ami_1.html#U3" title="AMI_1:sel.3">Object-Kind</a> of <font color="Maroon" title="c3">S</font><b> such that </b><a NAME="E2:40_1_2"/><i><font color="Green" title="E14">G1</font></i>: 
<font color="Maroon" title="c6">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">f1</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">k</font>
 <b>and </b><br/><a NAME="E3:40_1_2"/><i><font color="Green" title="E15">G2</font></i>: 
<font color="Maroon" title="c8">f1</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s</font>
 <b>and </b><br/><a NAME="E4:40_1_2"/><i><font color="Green" title="E16">G3</font></i>: 
for <font color="Olive" title="b1">i</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds  <font color="Maroon" title="c8">f1</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Olive" title="b1">i</font>,<font color="Maroon" title="c8">f1</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Olive" title="b1">i</font>)
 ;<br/>

<b>given </b><font color="Maroon" title="c9">f2</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> , <a href="card_3.html#K4" title="CARD_3:func.4">product</a> the <a href="ami_1.html#U3" title="AMI_1:sel.3">Object-Kind</a> of <font color="Maroon" title="c3">S</font><b> such that </b><a NAME="E6:40_1_2"/><i><font color="Green" title="E17">H1</font></i>: 
<font color="Maroon" title="c7">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">f2</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">k</font>
 <b>and </b><br/><a NAME="E7:40_1_2"/><i><font color="Green" title="E18">H2</font></i>: 
<font color="Maroon" title="c9">f2</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s</font>
 <b>and </b><br/><a NAME="E8:40_1_2"/><i><font color="Green" title="E19">H3</font></i>: 
for <font color="Olive" title="b1">i</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds  <font color="Maroon" title="c9">f2</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Olive" title="b1">i</font>,<font color="Maroon" title="c9">f2</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Olive" title="b1">i</font>)
 ;<br/>

<a NAME="E9:40_1_2"/>
<font color="Maroon" title="c8">f1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c9">f2</font>
 
<b>from </b><i><a class="ref" href="nat_1.html#S16" title="NAT_1:sch.16">NAT_1:sch 16</a>(<a class="txt" href="ami_1.html#E3:40_1_2"><i><font color="Green" title="E15">G2</font></i></a>, <a class="txt" href="ami_1.html#E4:40_1_2"><i><font color="Green" title="E16">G3</font></i></a>, <a class="txt" href="ami_1.html#E7:40_1_2"><i><font color="Green" title="E18">H2</font></i></a>, <a class="txt" href="ami_1.html#E8:40_1_2"><i><font color="Green" title="E19">H3</font></i></a>);<br/></i>
<b>hence </b><a NAME="E10:40_1_2"/>
<font color="Maroon" title="c6">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">s2</font>
 <b>by </b><i><a class="txt" href="ami_1.html#E2:40_1_2"><i><font color="Green" title="E14">G1</font></i></a>, <a class="txt" href="ami_1.html#E6:40_1_2"><i><font color="Green" title="E17">H1</font></i></a></i>;<br/>


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