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<b>let </b><font color="Maroon" title="c1">m</font>, <font color="Maroon" title="c2">n</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c3">I</font> be  <a href="ami_1.html#V15" title="AMI_1:attr.15">programmed</a> <a href="ami_1.html#NM5" title="AMI_1:NM.5">FinPartState</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ;<br/>





<a NAME="E1:32"/><i><font color="Green" title="E25">A1</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K5" title="SCMFSA_4:func.5">IncAddr</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K5" title="SCMFSA_4:func.5">IncAddr</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c1">m</font></span>)</span>,<font color="Maroon" title="c2">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K5" title="SCMFSA_4:func.5">IncAddr</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c1">m</font></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa_4.html#D6" target="_self" title="SCMFSA_4:def.6">Def6</a></i>;<br/>
<a NAME="E2:32"/><i><font color="Green" title="E26">A2</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K5" title="SCMFSA_4:func.5">IncAddr</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c1">m</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c3">I</font>
 
<b>by </b><i><a class="ref" href="scmfsa_4.html#D6" target="_self" title="SCMFSA_4:def.6">Def6</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="32_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">l</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>assume </b><a NAME="E1:32_1"/><i><font color="Green" title="E27">A3</font></i>: 
 <a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <font color="Maroon" title="c4">l</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c3">I</font>
 ;<br/><b>then </b> <a href="ami_1.html#K30" title="AMI_1:func.30">pi</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K5" title="SCMFSA_4:func.5">IncAddr</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c1">m</font></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <font color="Maroon" title="c4">l</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmfsa_4.html#K5" title="SCMFSA_4:func.5">IncAddr</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c1">m</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <font color="Maroon" title="c4">l</font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa_4.html#E2:32"><i><font color="Green" title="E26">A2</font></i></a>, <a class="ref" href="ami_1.html#D47" title="AMI_1:def.47">AMI_1:def 47</a></i>
<br/>.= 
 <a href="scmfsa_4.html#K3" title="SCMFSA_4:func.3">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K30" title="AMI_1:func.30">pi</a> <font color="Maroon" title="c3">I</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <font color="Maroon" title="c4">l</font></span>)</span></span>)</span>,<font color="Maroon" title="c1">m</font>
<b>by </b><i><a class="txt" href="scmfsa_4.html#E1:32_1"><i><font color="Green" title="E27">A3</font></i></a>, <a class="ref" href="scmfsa_4.html#T24" target="_self" title="SCMFSA_4:th.24">Th24</a></i>
;<br/><b>hence </b><span class="p1">(<span class="default"><a href="scmfsa_4.html#K5" title="SCMFSA_4:func.5">IncAddr</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K5" title="SCMFSA_4:func.5">IncAddr</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c1">m</font></span>)</span>,<font color="Maroon" title="c2">n</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <font color="Maroon" title="c4">l</font></span>)</span> = 
 <a href="scmfsa_4.html#K3" title="SCMFSA_4:func.3">IncAddr</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K3" title="SCMFSA_4:func.3">IncAddr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K30" title="AMI_1:func.30">pi</a> <font color="Maroon" title="c3">I</font>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <font color="Maroon" title="c4">l</font></span>)</span></span>)</span>,<font color="Maroon" title="c1">m</font></span>)</span>,<font color="Maroon" title="c2">n</font>
<b>by </b><i><a class="txt" href="scmfsa_4.html#E2:32"><i><font color="Green" title="E26">A2</font></i></a>, <a class="txt" href="scmfsa_4.html#E1:32_1"><i><font color="Green" title="E27">A3</font></i></a>, <a class="ref" href="scmfsa_4.html#T24" target="_self" title="SCMFSA_4:th.24">Th24</a></i>
<br/>.= 
 <a href="scmfsa_4.html#K3" title="SCMFSA_4:func.3">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K30" title="AMI_1:func.30">pi</a> <font color="Maroon" title="c3">I</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <font color="Maroon" title="c4">l</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa_4.html#T23" target="_self" title="SCMFSA_4:th.23">Th23</a></i>
;<br/><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:32"/>
 <a href="scmfsa_4.html#K5" title="SCMFSA_4:func.5">IncAddr</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K5" title="SCMFSA_4:func.5">IncAddr</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c1">m</font></span>)</span>,<font color="Maroon" title="c2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_4.html#K5" title="SCMFSA_4:func.5">IncAddr</a> <font color="Maroon" title="c3">I</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa_4.html#E1:32"><i><font color="Green" title="E25">A1</font></i></a>, <a class="txt" href="scmfsa_4.html#E2:32"><i><font color="Green" title="E26">A2</font></i></a>, <a class="ref" href="scmfsa_4.html#D6" target="_self" title="SCMFSA_4:def.6">Def6</a></i>;<br/>


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