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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">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="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">f</font> being   <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of <font color="Olive" title="b2">A</font><br/> for <font color="Olive" title="b4">I</font> being  <a href="ami_1.html#NM4" title="AMI_1:NM.4">Instruction</a> of <font color="Olive" title="b2">A</font>  st ( for <font color="Olive" title="b5">s</font> being  <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <font color="Olive" title="b2">A</font><br/> for <font color="Olive" title="b6">p</font> being <a href="ami_1.html#V15" title="AMI_1:attr.15">programmed</a> <a href="ami_1.html#NM8" title="AMI_1:NM.8">FinPartState</a> of <font color="Olive" title="b2">A</font> holds   <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Olive" title="b4">I</font>,<span class="p1">(<span class="default"><font color="Olive" title="b5">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <font color="Olive" title="b6">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Olive" title="b4">I</font>,<font color="Olive" title="b5">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <font color="Olive" title="b6">p</font> ) holds <br/> not <font color="Olive" title="b3">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_7.html#K4" title="AMI_7:func.4">Out_U_Inp</a> <font color="Olive" title="b4">I</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">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="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">f</font> being   <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of <font color="Olive" title="b1">A</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="b1">A</font>  st ( for <font color="Olive" title="b4">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="b5">p</font> being <a href="ami_1.html#V15" title="AMI_1:attr.15">programmed</a> <a href="ami_1.html#NM8" title="AMI_1:NM.8">FinPartState</a> of <font color="Olive" title="b1">A</font> holds   <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Olive" title="b3">I</font>,<span class="p1">(<span class="default"><font color="Olive" title="b4">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <font color="Olive" title="b5">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Olive" title="b3">I</font>,<font color="Olive" title="b4">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <font color="Olive" title="b5">p</font> ) holds <br/> not <font color="Olive" title="b2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_7.html#K4" title="AMI_7:func.4">Out_U_Inp</a> <font color="Olive" title="b3">I</font></span><br/><b>let </b><font color="Maroon" title="c3">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="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">f</font> being   <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of <font color="Maroon" title="c3">A</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="Maroon" title="c3">A</font>  st ( 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="Maroon" title="c3">A</font><br/> for <font color="Olive" title="b4">p</font> being <a href="ami_1.html#V15" title="AMI_1:attr.15">programmed</a> <a href="ami_1.html#NM8" title="AMI_1:NM.8">FinPartState</a> of <font color="Maroon" title="c3">A</font> holds   <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Olive" title="b2">I</font>,<span class="p1">(<span class="default"><font color="Olive" title="b3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <font color="Olive" title="b4">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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>,<font color="Olive" title="b3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <font color="Olive" title="b4">p</font> ) holds <br/> not <font color="Olive" title="b1">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_7.html#K4" title="AMI_7:func.4">Out_U_Inp</a> <font color="Olive" title="b2">I</font></span><br/><b>let </b><font color="Maroon" title="c4">f</font> be    <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of <font color="Maroon" title="c3">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">I</font> being  <a href="ami_1.html#NM4" title="AMI_1:NM.4">Instruction</a> of <font color="Maroon" title="c3">A</font>  st ( 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="c3">A</font><br/> for <font color="Olive" title="b3">p</font> being <a href="ami_1.html#V15" title="AMI_1:attr.15">programmed</a> <a href="ami_1.html#NM8" title="AMI_1:NM.8">FinPartState</a> of <font color="Maroon" title="c3">A</font> holds   <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Olive" title="b1">I</font>,<span class="p1">(<span class="default"><font color="Olive" title="b2">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <font color="Olive" title="b3">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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>,<font color="Olive" title="b2">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <font color="Olive" title="b3">p</font> ) holds <br/> not <font color="Maroon" title="c4">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_7.html#K4" title="AMI_7:func.4">Out_U_Inp</a> <font color="Olive" title="b1">I</font></span><br/><b>let </b><font color="Maroon" title="c5">I</font> be   <a href="ami_1.html#NM4" title="AMI_1:NM.4">Instruction</a> of <font color="Maroon" title="c3">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="c3">A</font><br/> for <font color="Olive" title="b2">p</font> being <a href="ami_1.html#V15" title="AMI_1:attr.15">programmed</a> <a href="ami_1.html#NM8" title="AMI_1:NM.8">FinPartState</a> of <font color="Maroon" title="c3">A</font> holds   <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">I</font>,<span class="p1">(<span class="default"><font color="Olive" title="b1">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <font color="Olive" title="b2">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">I</font>,<font color="Olive" title="b1">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <font color="Olive" title="b2">p</font> ) implies  not <font color="Maroon" title="c4">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_7.html#K4" title="AMI_7:func.4">Out_U_Inp</a> <font color="Maroon" title="c5">I</font> )</span><br/>









<b>assume </b><a NAME="E1:40"/><i><font color="Green" title="E16">A1</font></i>: 
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="c3">A</font><br/> for <font color="Olive" title="b2">p</font> being <a href="ami_1.html#V15" title="AMI_1:attr.15">programmed</a> <a href="ami_1.html#NM8" title="AMI_1:NM.8">FinPartState</a> of <font color="Maroon" title="c3">A</font> holds   <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">I</font>,<span class="p1">(<span class="default"><font color="Olive" title="b1">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <font color="Olive" title="b2">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">I</font>,<font color="Olive" title="b1">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <font color="Olive" title="b2">p</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> not <font color="Maroon" title="c4">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_7.html#K4" title="AMI_7:func.4">Out_U_Inp</a> <font color="Maroon" title="c5">I</font></span><br/>

<b>assume </b><a NAME="E2:40"/>
<font color="Maroon" title="c4">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_7.html#K4" title="AMI_7:func.4">Out_U_Inp</a> <font color="Maroon" title="c5">I</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<b>then consider </b><font color="Maroon" title="c6">s</font> being   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <font color="Maroon" title="c3">A</font>, <font color="Maroon" title="c7">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="c4">f</font><b> such that </b><br/><a NAME="E4:40"/><i><font color="Green" title="E17">A2</font></i>: 
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">I</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c7">w</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">s</font></span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c7">w</font>
 <b>by </b><i><a class="ref" href="ami_7.html#D5" target="_self" title="AMI_7:def.5">Def5</a></i>;<br/>
<a NAME="E5:40"/><i><font color="Green" title="E18">A3</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">A</font>
 
<b>by </b><i><a class="ref" href="ami_1.html#T79" title="AMI_1:th.79">AMI_1:79</a></i>;<br/>
<a NAME="E6:40"/><i><font color="Green" title="E19">A4</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">A</font>
 
<b>by </b><i><a class="ref" href="ami_1.html#T79" title="AMI_1:th.79">AMI_1:79</a></i>;<br/>
<b>set </b><font color="Maroon" title="c8">p</font> = <font color="Maroon" title="c4">f</font> <a href="ami_1.html#K16" title="AMI_1:func.16">.--&gt;</a> <font color="Maroon" title="c7">w</font>;<br/>
<a NAME="E7:40"/><i><font color="Green" title="E20">A5</font></i>: 
<font color="Maroon" title="c4">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">IL</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="E8:40"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="ami_1.html#K16" title="AMI_1:func.16">.--&gt;</a> <font color="Maroon" title="c7">w</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>;<br/>
<a NAME="E9:40"/><b>then </b>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="ami_1.html#K16" title="AMI_1:func.16">.--&gt;</a> <font color="Maroon" title="c7">w</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">IL</font>
 
<b>by </b><i><a class="txt" href="#E7:40"><i><font color="Green" title="E20">A5</font></i></a>, <a class="ref" href="zfmisc_1.html#T37" title="ZFMISC_1:th.37">ZFMISC_1:37</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c9">p</font> = <font color="Maroon" title="c4">f</font> <a href="ami_1.html#K16" title="AMI_1:func.16">.--&gt;</a> <font color="Maroon" title="c7">w</font> as  <a href="ami_1.html#V15" title="AMI_1:attr.15">programmed</a> <a href="ami_1.html#NM8" title="AMI_1:NM.8">FinPartState</a> of <font color="Maroon" title="c3">A</font> <b>by </b><i><a class="ref" href="ami_1.html#D40" title="AMI_1:def.40">AMI_1:def 40</a></i>;<br/>
<a NAME="E11:40"/><i><font color="Green" title="E21">A6</font></i>: 
<font color="Maroon" title="c6">s</font> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c7">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <font color="Maroon" title="c9">p</font>
 
<b>by </b><i><a class="txt" href="#E5:40"><i><font color="Green" title="E18">A3</font></i></a>, <a class="ref" href="funct_7.html#D3" title="FUNCT_7:def.3">FUNCT_7:def 3</a></i>;<br/>
<a NAME="E12:40"/>
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">I</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <font color="Maroon" title="c9">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <font color="Maroon" title="c9">p</font>
 
<b>by </b><i><a class="txt" href="#E1:40"><i><font color="Green" title="E16">A1</font></i></a></i>;<br/>
<b>hence </b><a NAME="E13:40"/>
contradiction
 <b>by </b><i><a class="txt" href="#E4:40"><i><font color="Green" title="E17">A2</font></i></a>, <a class="txt" href="#E6:40"><i><font color="Green" title="E19">A4</font></i></a>, <a class="txt" href="#E11:40"><i><font color="Green" title="E21">A6</font></i></a>, <a class="ref" href="funct_7.html#D3" title="FUNCT_7:def.3">FUNCT_7:def 3</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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