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<span class="kw">let </span><font color="Maroon" title="c1">i</font> be   <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">N</font> being non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="setfam_1.html#V1" title="SETFAM_1:attr.1">with_non-empty_elements</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <br/> for <font color="Olive" title="b2">S</font> being non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="ami_1.html#V2" title="AMI_1:attr.2">stored-program</a>   <a href="ami_1.html#V5" title="AMI_1:attr.5">IC-Ins-separated</a>   <a href="ami_1.html#V8" title="AMI_1:attr.8">definite</a>   <a href="ami_1.html#V13" title="AMI_1:attr.13">standard-ins</a>   <a href="amistd_1.html#V4" title="AMISTD_1:attr.4">standard</a>   <a href="amistd_2.html#V6" title="AMISTD_2:attr.6">regular</a>   <a href="ami_1.html#L1" title="AMI_1:struct.1">AMI-Struct</a> of <font color="Olive" title="b1">N</font><br/> for <font color="Olive" title="b3">p</font> being  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="relat_1.html#V4" title="RELAT_1:attr.4">-defined</a>  the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <font color="Olive">b<sub>2</sub></font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  <a href="ami_1.html#NM4" title="AMI_1:NM.4">FinPartState</a> of  holds   <a href="amistd_2.html#K9" title="AMISTD_2:func.9">Shift</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <font color="Olive" title="b3">p</font>,<font color="Maroon" title="c1">i</font></span>)</span>,<font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">Shift</a> <font color="Olive" title="b3">p</font>,<font color="Maroon" title="c1">i</font></span>)</span>,<font color="Maroon" title="c1">i</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">N</font> be  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="setfam_1.html#V1" title="SETFAM_1:attr.1">with_non-empty_elements</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">S</font> being non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="ami_1.html#V2" title="AMI_1:attr.2">stored-program</a>   <a href="ami_1.html#V5" title="AMI_1:attr.5">IC-Ins-separated</a>   <a href="ami_1.html#V8" title="AMI_1:attr.8">definite</a>   <a href="ami_1.html#V13" title="AMI_1:attr.13">standard-ins</a>   <a href="amistd_1.html#V4" title="AMISTD_1:attr.4">standard</a>   <a href="amistd_2.html#V6" title="AMISTD_2:attr.6">regular</a>   <a href="ami_1.html#L1" title="AMI_1:struct.1">AMI-Struct</a> of <font color="Maroon" title="c2">N</font><br/> for <font color="Olive" title="b2">p</font> being  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="relat_1.html#V4" title="RELAT_1:attr.4">-defined</a>  the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <font color="Olive">b<sub>1</sub></font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  <a href="ami_1.html#NM4" title="AMI_1:NM.4">FinPartState</a> of  holds   <a href="amistd_2.html#K9" title="AMISTD_2:func.9">Shift</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <font color="Olive" title="b2">p</font>,<font color="Maroon" title="c1">i</font></span>)</span>,<font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">Shift</a> <font color="Olive" title="b2">p</font>,<font color="Maroon" title="c1">i</font></span>)</span>,<font color="Maroon" title="c1">i</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">S</font> be  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="ami_1.html#V2" title="AMI_1:attr.2">stored-program</a>   <a href="ami_1.html#V5" title="AMI_1:attr.5">IC-Ins-separated</a>   <a href="ami_1.html#V8" title="AMI_1:attr.8">definite</a>   <a href="ami_1.html#V13" title="AMI_1:attr.13">standard-ins</a>   <a href="amistd_1.html#V4" title="AMISTD_1:attr.4">standard</a>   <a href="amistd_2.html#V6" title="AMISTD_2:attr.6">regular</a>   <a href="ami_1.html#L1" title="AMI_1:struct.1">AMI-Struct</a> of <font color="Maroon" title="c2">N</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">p</font> being  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="relat_1.html#V4" title="RELAT_1:attr.4">-defined</a>  the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <font color="Maroon" title="c3">S</font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  <a href="ami_1.html#NM4" title="AMI_1:NM.4">FinPartState</a> of  holds   <a href="amistd_2.html#K9" title="AMISTD_2:func.9">Shift</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <font color="Olive" title="b1">p</font>,<font color="Maroon" title="c1">i</font></span>)</span>,<font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">Shift</a> <font color="Olive" title="b1">p</font>,<font color="Maroon" title="c1">i</font></span>)</span>,<font color="Maroon" title="c1">i</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">p</font> be   <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="relat_1.html#V4" title="RELAT_1:attr.4">-defined</a>  the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <font color="Maroon" title="c3">S</font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  <a href="ami_1.html#NM4" title="AMI_1:NM.4">FinPartState</a> of ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="amistd_2.html#K9" title="AMISTD_2:func.9">Shift</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c1">i</font></span>)</span>,<font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">Shift</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c1">i</font></span>)</span>,<font color="Maroon" title="c1">i</font></span><br/>







<span class="kw">set </span><font color="Maroon" title="c5">f</font> =  <a href="amistd_2.html#K9" title="AMISTD_2:func.9">Shift</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c1">i</font></span>)</span>,<font color="Maroon" title="c1">i</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">g</font> =  <a href="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">Shift</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c1">i</font></span>)</span>,<font color="Maroon" title="c1">i</font>;<br/>
<a NAME="E1:153"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c1">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="amistd_2.html#D15" target="_self" title="AMISTD_2:def.15">Def15</a></span>;<br/>
<span class="kw">then </span> <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">Shift</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c1">i</font></span>)</span> = 
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c3">S</font>,<span class="p3">(<span class="default"><font color="Olive" title="b1">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">i</font></span>)</span></span>)</span> where <font color="Olive" title="b1">m</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  :  <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c3">S</font>,<font color="Olive" title="b1">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="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c1">i</font></span>)</span> </span>}</span> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="amistd_2.html#D16" target="_self" title="AMISTD_2:def.16">Def16</a></span>
<br/>.= 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c1">i</font></span>)</span>,<font color="Maroon" title="c1">i</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="amistd_2.html#D16" target="_self" title="AMISTD_2:def.16">Def16</a></span>
;<br/>
<a NAME="E3:153"/><span class="kw">then </span><span class="lab"><font color="Green" title="E72">A1</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c1">i</font></span>)</span>,<font color="Maroon" title="c1">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">Shift</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c1">i</font></span>)</span>,<font color="Maroon" title="c1">i</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="amistd_2.html#D15" target="_self" title="AMISTD_2:def.15">Def15</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="153_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c7">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c7">x</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="amistd_2.html#K9" title="AMISTD_2:func.9">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c1">i</font></span>)</span>,<font color="Maroon" title="c1">i</font></span>)</span> implies <span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c1">i</font></span>)</span>,<font color="Maroon" title="c1">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">Shift</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c1">i</font></span>)</span>,<font color="Maroon" title="c1">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font> )</span><br/><a NAME="E1:153_2"/><span class="lab"><font color="Green" title="E73">A2</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c1">i</font></span>)</span>,<font color="Maroon" title="c1">i</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D18" title="RELAT_1:def.18">RELAT_1:def 18</a></span>;<br/><span class="kw">assume </span><a NAME="E2:153_2"/><span class="lab"><font color="Green" title="E74">A3</font></span>: 
<font color="Maroon" title="c7">x</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="amistd_2.html#K9" title="AMISTD_2:func.9">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c1">i</font></span>)</span>,<font color="Maroon" title="c1">i</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c1">i</font></span>)</span>,<font color="Maroon" title="c1">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">Shift</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c1">i</font></span>)</span>,<font color="Maroon" title="c1">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font></span><br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c8">x9</font> = <font color="Maroon" title="c7">x</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:153_2"><span class="lab"><font color="Green" title="E73">A2</font></span></a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c9">xx</font> = <font color="Maroon" title="c8">x9</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ;<br/><a NAME="E5:153_2"/>
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c3">S</font>,<span class="p3">(<span class="default"><font color="Olive" title="b1">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">i</font></span>)</span></span>)</span> where <font color="Olive" title="b1">m</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  :  <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c3">S</font>,<font color="Olive" title="b1">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="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c1">i</font></span>)</span> </span>}</span> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:153_2"><span class="lab"><font color="Green" title="E74">A3</font></span></a>, <a class="ref" href="amistd_2.html#D16" target="_self" title="AMISTD_2:def.16">Def16</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c10">m</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <span class="kw"> such that </span><br/><a NAME="E7:153_2"/><span class="lab"><font color="Green" title="E75">A4</font></span>: 
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c3">S</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c10">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">i</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E8:153_2"/><span class="lab"><font color="Green" title="E76">A5</font></span>: 
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c3">S</font>,<font color="Maroon" title="c10">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="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c1">i</font></span>)</span>
 ;<br/><a NAME="E9:153_2"/><span class="lab"><font color="Green" title="E77">A6</font></span>: 
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c3">S</font>,<font color="Maroon" title="c10">m</font></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">S</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:153_2"><span class="lab"><font color="Green" title="E75">A4</font></span></a>, <a class="ref" href="amistd_1.html#D13" title="AMISTD_1:def.13">AMISTD_1:def 13</a></span>;<br/><a NAME="E10:153_2"/><span class="lab"><font color="Green" title="E78">A7</font></span>: 
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c3">S</font>,<font color="Maroon" title="c10">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="c4">p</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:153_2"><span class="lab"><font color="Green" title="E76">A5</font></span></a>, <a class="ref" href="amistd_2.html#D15" target="_self" title="AMISTD_2:def.15">Def15</a></span>;<br/><a NAME="E11:153_2"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">Shift</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c1">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c3">S</font>,<span class="p3">(<span class="default"><font color="Olive" title="b1">mm</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">i</font></span>)</span></span>)</span> where <font color="Olive" title="b1">mm</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  :  <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c3">S</font>,<font color="Olive" title="b1">mm</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="c4">p</font> </span>}</span> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="amistd_2.html#D16" target="_self" title="AMISTD_2:def.16">Def16</a></span>;<br/><a NAME="E12:153_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E79">A8</font></span>: 
<font color="Maroon" title="c8">x9</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="amistd_2.html#K9" title="AMISTD_2:func.9">Shift</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c1">i</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:153_2"><span class="lab"><font color="Green" title="E75">A4</font></span></a>, <a class="txt" href="#E10:153_2"><span class="lab"><font color="Green" title="E78">A7</font></span></a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c11">mm</font> =  <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c3">S</font>,<font color="Maroon" title="c10">m</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ;<br/><span class="lab"><font color="Green" title="E80">A9</font></span>: <font color="Maroon" title="c4">p</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c11">mm</font> = 
<font color="Maroon" title="c4">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c3">S</font>,<font color="Maroon" title="c10">m</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:153_2"><span class="lab"><font color="Green" title="E78">A7</font></span></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">Shift</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c1">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c3">S</font>,<font color="Maroon" title="c10">m</font></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c3">S</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:153_2"><span class="lab"><font color="Green" title="E78">A7</font></span></a>, <a class="ref" href="amistd_2.html#T65" target="_self" title="AMISTD_2:th.65">Th65</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">Shift</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c1">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c3">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">i</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="amistd_1.html#D13" title="AMISTD_1:def.13">AMISTD_1:def 13</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">Shift</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c1">i</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c9">xx</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:153_2"><span class="lab"><font color="Green" title="E75">A4</font></span></a>, <a class="txt" href="#E12:153_2"><span class="lab"><font color="Green" title="E79">A8</font></span></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></span>
;<br/><span class="kw">thus </span><span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c1">i</font></span>)</span>,<font color="Maroon" title="c1">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font> = 
<span class="p1">(<span class="default"><a href="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c1">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c3">S</font>,<font color="Maroon" title="c10">m</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:153_2"><span class="lab"><font color="Green" title="E76">A5</font></span></a>, <a class="txt" href="#E9:153_2"><span class="lab"><font color="Green" title="E77">A6</font></span></a>, <a class="ref" href="amistd_2.html#T65" target="_self" title="AMISTD_2:th.65">Th65</a></span>
<br/>.= 
 <a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">Shift</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c1">i</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c9">xx</font></span>)</span>,<font color="Maroon" title="c1">i</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:153_2"><span class="lab"><font color="Green" title="E78">A7</font></span></a>, <a class="txt" href="#E14:153_2"><span class="lab"><font color="Green" title="E80">A9</font></span></a>, <a class="ref" href="amistd_2.html#T74" target="_self" title="AMISTD_2:th.74">Th74</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">Shift</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c1">i</font></span>)</span>,<font color="Maroon" title="c1">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:153_2"><span class="lab"><font color="Green" title="E79">A8</font></span></a>, <a class="ref" href="amistd_2.html#T74" target="_self" title="AMISTD_2:th.74">Th74</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E5:153"/>
 <a href="amistd_2.html#K9" title="AMISTD_2:func.9">Shift</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c1">i</font></span>)</span>,<font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">Shift</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c1">i</font></span>)</span>,<font color="Maroon" title="c1">i</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:153"><span class="lab"><font color="Green" title="E72">A1</font></span></a>, <a class="ref" href="funct_1.html#T9" title="FUNCT_1:th.9">FUNCT_1:9</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
