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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">IL</font> being non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</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#V14" title="AMI_1:attr.14">standard-ins</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">IL</font>,<font color="Maroon" title="c1">N</font><br/> for <font color="Olive" title="b3">I</font> being  <a href="ami_1.html#NM4" title="AMI_1:NM.4">Instruction</a> of <font color="Olive" title="b2">S</font><br/> for <font color="Olive" title="b4">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <font color="Olive" title="b3">I</font></span>)</span> holds <br/><span class="p1">(<span class="default"><a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <font color="Olive" title="b3">I</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Olive" title="b3">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">x</font></span><br/><b>let </b><font color="Maroon" title="c2">IL</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</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">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#V14" title="AMI_1:attr.14">standard-ins</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">IL</font>,<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">S</font><br/> for <font color="Olive" title="b3">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <font color="Olive" title="b2">I</font></span>)</span> holds <br/><span class="p1">(<span class="default"><a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <font color="Olive" title="b2">I</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Olive" title="b2">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">x</font></span><br/><b>let </b><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#V14" title="AMI_1:attr.14">standard-ins</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">IL</font>,<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="c3">S</font><br/> for <font color="Olive" title="b2">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <font color="Olive" title="b1">I</font></span>)</span> holds <br/><span class="p1">(<span class="default"><a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <font color="Olive" title="b1">I</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Olive" title="b1">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">x</font></span><br/><b>let </b><font color="Maroon" title="c4">I</font> be   <a href="ami_1.html#NM4" title="AMI_1:NM.4">Instruction</a> of <font color="Maroon" title="c3">S</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">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <font color="Maroon" title="c4">I</font></span>)</span> holds <br/><span class="p1">(<span class="default"><a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font></span><br/><b>let </b><font color="Maroon" title="c5">x</font> be    <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"> ( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <font color="Maroon" title="c4">I</font></span>)</span> implies <span class="p1">(<span class="default"><a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font> )</span><br/>









<b>assume </b><a NAME="E1:132"/><i><font color="Green" title="E64">A1</font></i>: 
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <font color="Maroon" title="c4">I</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font></span><br/>

<a NAME="E2:132"/><i><font color="Green" title="E65">A2</font></i>: 
 <a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <font color="Maroon" title="c4">I</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <span class="p1">(<span class="default"><a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">I</font></span>)</span>
 
;<br/>
<i><font color="Green" title="E66">A3</font></i>:  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span> = 
 <a href="card_3.html#K9" title="CARD_3:func.9">DOM</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <span class="p2">(<span class="default"><a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="card_3.html#T92" title="CARD_3:th.92">CARD_3:92</a></i>
<br/>.= 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <font color="Maroon" title="c4">I</font></span>)</span>
<b>by </b><i><a class="txt" href="#E2:132"><i><font color="Green" title="E65">A2</font></i></a>, <a class="ref" href="card_3.html#D12" title="CARD_3:def.12">CARD_3:def 12</a></i>
;<br/>
<a NAME="E4:132"/>
<span class="p1">(<span class="default"><a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_3.html#K5" title="CARD_3:func.5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <span class="p2">(<span class="default"><a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c5">x</font>
 
<b>by </b><i><a class="txt" href="#E2:132"><i><font color="Green" title="E65">A2</font></i></a>, <a class="ref" href="card_3.html#D6" title="CARD_3:def.6">CARD_3:def 6</a></i>;<br/>
<b>hence </b><a NAME="E5:132"/>
<span class="p1">(<span class="default"><a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font>
 <b>by </b><i><a class="txt" href="#E1:132"><i><font color="Green" title="E64">A1</font></i></a>, <a class="txt" href="#E3:132"><i><font color="Green" title="E66">A3</font></i></a>, <a class="ref" href="card_3.html#T93" title="CARD_3:th.93">CARD_3:93</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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