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<b>let </b><font color="Maroon" title="c1">N</font> be  <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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">A</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#V7" title="AMI_1:attr.7">definite</a> <a href="amistd_1.html#V4" title="AMISTD_1:attr.4">standard</a>  <a href="ami_1.html#L1" title="AMI_1:struct.1">AMI-Struct</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,<font color="Maroon" title="c1">N</font><br/> for <font color="Olive" title="b2">I</font> being  <a href="ami_1.html#NM4" title="AMI_1:NM.4">Instruction</a> of <font color="Olive" title="b1">A</font><br/> for <font color="Olive" title="b3">s</font> being  <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <font color="Olive" title="b1">A</font><br/> for <font color="Olive" title="b4">o</font> being  <a href="ami_1.html#NM1" title="AMI_1:NM.1">Object</a> of <font color="Olive" title="b1">A</font><br/> for <font color="Olive" title="b5">w</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_1.html#K3" title="AMI_1:func.3">ObjectKind</a> <font color="Olive" title="b4">o</font>  st <font color="Olive" title="b2">I</font> is <a href="amistd_1.html#V5" title="AMISTD_1:attr.5">sequential</a> &amp; <font color="Olive" title="b4">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Olive" title="b1">A</font> holds <br/> <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Olive" title="b2">I</font>,<span class="p2">(<span class="default"><font color="Olive" title="b3">s</font> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Olive" title="b4">o</font>,<font color="Olive" title="b5">w</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Olive" title="b2">I</font>,<font color="Olive" title="b3">s</font></span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Olive" title="b4">o</font>,<font color="Olive" title="b5">w</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">A</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#V7" title="AMI_1:attr.7">definite</a> <a href="amistd_1.html#V4" title="AMISTD_1:attr.4">standard</a>  <a href="ami_1.html#L1" title="AMI_1:struct.1">AMI-Struct</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,<font color="Maroon" title="c1">N</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">I</font> being  <a href="ami_1.html#NM4" title="AMI_1:NM.4">Instruction</a> of <font color="Maroon" title="c2">A</font><br/> for <font color="Olive" title="b2">s</font> being  <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <font color="Maroon" title="c2">A</font><br/> for <font color="Olive" title="b3">o</font> being  <a href="ami_1.html#NM1" title="AMI_1:NM.1">Object</a> of <font color="Maroon" title="c2">A</font><br/> for <font color="Olive" title="b4">w</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_1.html#K3" title="AMI_1:func.3">ObjectKind</a> <font color="Olive" title="b3">o</font>  st <font color="Olive" title="b1">I</font> is <a href="amistd_1.html#V5" title="AMISTD_1:attr.5">sequential</a> &amp; <font color="Olive" title="b3">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c2">A</font> holds <br/> <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Olive" title="b1">I</font>,<span class="p2">(<span class="default"><font color="Olive" title="b2">s</font> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Olive" title="b3">o</font>,<font color="Olive" title="b4">w</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Olive" title="b1">I</font>,<font color="Olive" title="b2">s</font></span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Olive" title="b3">o</font>,<font color="Olive" title="b4">w</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c3">I</font> be   <a href="ami_1.html#NM4" title="AMI_1:NM.4">Instruction</a> of <font color="Maroon" title="c2">A</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">s</font> being  <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <font color="Maroon" title="c2">A</font><br/> for <font color="Olive" title="b2">o</font> being  <a href="ami_1.html#NM1" title="AMI_1:NM.1">Object</a> of <font color="Maroon" title="c2">A</font><br/> for <font color="Olive" title="b3">w</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_1.html#K3" title="AMI_1:func.3">ObjectKind</a> <font color="Olive" title="b2">o</font>  st <font color="Maroon" title="c3">I</font> is <a href="amistd_1.html#V5" title="AMISTD_1:attr.5">sequential</a> &amp; <font color="Olive" title="b2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c2">A</font> holds <br/> <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">I</font>,<span class="p2">(<span class="default"><font color="Olive" title="b1">s</font> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Olive" title="b2">o</font>,<font color="Olive" title="b3">w</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">I</font>,<font color="Olive" title="b1">s</font></span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Olive" title="b2">o</font>,<font color="Olive" title="b3">w</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c4">s</font> be   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <font color="Maroon" title="c2">A</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">o</font> being  <a href="ami_1.html#NM1" title="AMI_1:NM.1">Object</a> of <font color="Maroon" title="c2">A</font><br/> for <font color="Olive" title="b2">w</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_1.html#K3" title="AMI_1:func.3">ObjectKind</a> <font color="Olive" title="b1">o</font>  st <font color="Maroon" title="c3">I</font> is <a href="amistd_1.html#V5" title="AMISTD_1:attr.5">sequential</a> &amp; <font color="Olive" title="b1">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c2">A</font> holds <br/> <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">I</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Olive" title="b1">o</font>,<font color="Olive" title="b2">w</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">s</font></span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Olive" title="b1">o</font>,<font color="Olive" title="b2">w</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c5">o</font> be   <a href="ami_1.html#NM1" title="AMI_1:NM.1">Object</a> of <font color="Maroon" title="c2">A</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">w</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_1.html#K3" title="AMI_1:func.3">ObjectKind</a> <font color="Maroon" title="c5">o</font>  st <font color="Maroon" title="c3">I</font> is <a href="amistd_1.html#V5" title="AMISTD_1:attr.5">sequential</a> &amp; <font color="Maroon" title="c5">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c2">A</font> holds <br/> <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">I</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c5">o</font>,<font color="Olive" title="b1">w</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">s</font></span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c5">o</font>,<font color="Olive" title="b1">w</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c6">w</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_1.html#K3" title="AMI_1:func.3">ObjectKind</a> <font color="Maroon" title="c5">o</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">I</font> is <a href="amistd_1.html#V5" title="AMISTD_1:attr.5">sequential</a> &amp; <font color="Maroon" title="c5">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c2">A</font> implies  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">I</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">w</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">s</font></span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">w</font></span>)</span> )</span><br/>











<b>assume </b><b>that </b><br/><a NAME="E1:5"/><i><font color="Green" title="E3">A1</font></i>: 
<font color="Maroon" title="c3">I</font> is <a href="amistd_1.html#V5" title="AMISTD_1:attr.5">sequential</a>
 <b>and </b><br/><a NAME="E2:5"/><i><font color="Green" title="E4">A2</font></i>: 
<font color="Maroon" title="c5">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c2">A</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">I</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">w</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">s</font></span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">w</font></span>)</span></span><br/>

<b>thus </b> <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">I</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">w</font></span>)</span></span>)</span> = 
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">s</font></span>)</span>
<b>by </b><i><a class="txt" href="#E1:5"><i><font color="Green" title="E3">A1</font></i></a>, <a class="txt" href="#E2:5"><i><font color="Green" title="E4">A2</font></i></a>, <a class="ref" href="ami_7.html#T6" target="_self" title="AMI_7:th.6">Th6</a></i>
<br/>.= 
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">s</font></span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">w</font></span>)</span>
<b>by </b><i><a class="txt" href="#E2:5"><i><font color="Green" title="E4">A2</font></i></a>, <a class="ref" href="funct_7.html#T34" title="FUNCT_7:th.34">FUNCT_7:34</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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