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<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ) <b>-&gt; </b>   <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of  <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  =  <a href="ami_3.html#K12" title="AMI_3:func.12">il.</a> <font color="Maroon">c<sub>1</sub></font>;<br/>
<a NAME="E1:57_1_1"/><i><font color="Green" title="E49">A1</font></i>: 
for <font color="Olive" title="b1">k</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  holds  <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">k</font>) is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> 
 
;<br/>
<b>consider </b><font color="Maroon" title="c1">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> , <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> <b> such that </b><br/><a NAME="E3:57_1_1"/><i><font color="Green" title="E50">A2</font></i>: 
for <font color="Olive" title="b1">k</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  holds  <font color="Maroon" title="c1">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">k</font>)
 <b>from </b><i><a class="ref" href="funct_2.html#S9" title="FUNCT_2:sch.9">FUNCT_2:sch 9</a>(<a class="txt" href="ami_6.html#E1:57_1_1"><i><font color="Green" title="E49">A1</font></i></a>);<br/></i>
<b>reconsider </b><font color="Maroon" title="c2">f</font> = <font color="Maroon" title="c1">f</font> as    <a href="ami_1.html#M6" title="AMI_1:mode.6">IL-Function</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> , <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  <b>by </b><i><a class="ref" href="ami_1.html#D36" title="AMI_1:def.36">AMI_1:def 36</a></i>;<br/>
<a NAME="E5:57_1_1"/>
( <font color="Maroon" title="c2">f</font> is <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a> &amp; ( for <font color="Olive" title="b1">k</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  holds <br/> ( <font color="Maroon" title="c2">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">k</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K3" title="AMISTD_1:func.3">SUCC</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="ami_1.html#K26" title="AMI_1:func.26">.</a> <font color="Olive" title="b1">k</font></span>)</span> &amp; ( for <font color="Olive" title="b2">j</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>   st <font color="Maroon" title="c2">f</font> <a href="ami_1.html#K26" title="AMI_1:func.26">.</a> <font color="Olive" title="b2">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K3" title="AMISTD_1:func.3">SUCC</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="ami_1.html#K26" title="AMI_1:func.26">.</a> <font color="Olive" title="b1">k</font></span>)</span> holds <br/><font color="Olive" title="b1">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">j</font> ) ) ) )
 
<b>by </b><i><a class="txt" href="ami_6.html#E3:57_1_1"><i><font color="Green" title="E50">A2</font></i></a>, <a class="ref" href="ami_6.html#T53" target="_self" title="AMI_6:th.53">Th53</a></i>;<br/>
<b>hence </b><a NAME="E6:57_1_1"/>
 <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  is <a href="amistd_1.html#V4" title="AMISTD_1:attr.4">standard</a>
 <b>by </b><i><a class="ref" href="amistd_1.html#T19" title="AMISTD_1:th.19">AMISTD_1:19</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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