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<a NAME="E1:24_1_1"/>
 <a href="scmnorm.html#K8" title="SCMNORM:func.8">ProgramPart</a> <font color="Maroon" title="c3">I</font> is <a href="scmnorm.html#V1" title="SCMNORM:attr.1">initial</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c4">m</font>, <font color="Maroon" title="c5">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <i><font color="Red">:: according to </font></i><a class="ref" href="scmnorm.html#D1" target="_self" title="SCMNORM:def.1">SCMNORM:def 1</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmnorm.html#K8" title="SCMNORM:func.8">ProgramPart</a> <font color="Maroon" title="c3">I</font></span>)</span> &amp; <font color="Maroon" title="c4">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c5">n</font> implies <font color="Maroon" title="c4">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmnorm.html#K8" title="SCMNORM:func.8">ProgramPart</a> <font color="Maroon" title="c3">I</font></span>)</span> )</span><br/>

<b>assume </b><b>that </b><br/><a NAME="E1:24_1_1_1"/><i><font color="Green" title="E2">A1</font></i>: 
<font color="Maroon" title="c5">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmnorm.html#K8" title="SCMNORM:func.8">ProgramPart</a> <font color="Maroon" title="c3">I</font></span>)</span>
 <b>and </b><br/><a NAME="E2:24_1_1_1"/><i><font color="Green" title="E3">A2</font></i>: 
<font color="Maroon" title="c4">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c5">n</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmnorm.html#K8" title="SCMNORM:func.8">ProgramPart</a> <font color="Maroon" title="c3">I</font></span>)</span></span><br/>

<a NAME="E3:24_1_1_1"/>
<font color="Maroon" title="c4">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 
<b>by </b><i><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></i>;<br/>
<a NAME="E4:24_1_1_1"/><b>then </b><i><font color="Green" title="E4">B</font></i>: 
<font color="Maroon" title="c4">m</font> is    <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of <font color="Maroon" title="c2">S</font>
 
<b>by </b><i><a class="ref" href="ami_1.html#D4" title="AMI_1:def.4">AMI_1:def 4</a></i>;<br/>
<a NAME="E5:24_1_1_1"/>
 <a href="scmnorm.html#K8" title="SCMNORM:func.8">ProgramPart</a> <font color="Maroon" title="c3">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">I</font>
 
<b>by </b><i><a class="ref" href="relat_1.html#T88" title="RELAT_1:th.88">RELAT_1:88</a></i>;<br/>
<a NAME="E6:24_1_1_1"/><b>then </b>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmnorm.html#K8" title="SCMNORM:func.8">ProgramPart</a> <font color="Maroon" title="c3">I</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">I</font>
 
<b>by </b><i><a class="ref" href="relat_1.html#T25" title="RELAT_1:th.25">RELAT_1:25</a></i>;<br/>
<a NAME="E7:24_1_1_1"/><b>then </b>
<font color="Maroon" title="c4">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">I</font>
 
<b>by </b><i><a class="txt" href="#E1:24_1_1_1"><i><font color="Green" title="E2">A1</font></i></a>, <a class="txt" href="#E2:24_1_1_1"><i><font color="Green" title="E3">A2</font></i></a>, <a class="ref" href="scmnorm.html#D1" target="_self" title="SCMNORM:def.1">Def1</a></i>;<br/>
<b>hence </b><a NAME="E8:24_1_1_1"/>
<font color="Maroon" title="c4">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmnorm.html#K8" title="SCMNORM:func.8">ProgramPart</a> <font color="Maroon" title="c3">I</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E4:24_1_1_1"><i><font color="Green" title="E4">B</font></i></a>, <a class="ref" href="ami_1.html#T106" title="AMI_1:th.106">AMI_1:106</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:24_1_1"/>
 <a href="scmnorm.html#K8" title="SCMNORM:func.8">ProgramPart</a> <font color="Maroon" title="c3">I</font> is  <a href="scmnorm.html#V1" title="SCMNORM:attr.1">initial</a> <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>
 ; <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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