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<span class="kw">let </span><font color="Maroon" title="c1">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#L1" title="AMI_1:struct.1">AMI-Struct</a> of <font color="Maroon" title="c1">N</font><br/> for <font color="Olive" title="b2">l</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><br/> for <font color="Olive" title="b3">p</font> being <font color="Olive">b<sub>2</sub></font> <a href="ami_1.html#V12" title="AMI_1:attr.12">-started</a>  <a href="ami_1.html#NM3" title="AMI_1:NM.3">PartState</a> of <font color="Olive" title="b1">S</font><br/> for <font color="Olive" title="b4">s</font> being  <a href="ami_1.html#NM3" title="AMI_1:NM.3">PartState</a> of <font color="Olive" title="b1">S</font>  st <font color="Olive" title="b3">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b4">s</font> holds <br/><font color="Olive" title="b4">s</font> is <font color="Olive" title="b2">l</font> <a href="ami_1.html#V12" title="AMI_1:attr.12">-started</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">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#L1" title="AMI_1:struct.1">AMI-Struct</a> of <font color="Maroon" title="c1">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">l</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><br/> for <font color="Olive" title="b2">p</font> being <font color="Olive">b<sub>1</sub></font> <a href="ami_1.html#V12" title="AMI_1:attr.12">-started</a>  <a href="ami_1.html#NM3" title="AMI_1:NM.3">PartState</a> of <font color="Maroon" title="c2">S</font><br/> for <font color="Olive" title="b3">s</font> being  <a href="ami_1.html#NM3" title="AMI_1:NM.3">PartState</a> of <font color="Maroon" title="c2">S</font>  st <font color="Olive" title="b2">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b3">s</font> holds <br/><font color="Olive" title="b3">s</font> is <font color="Olive" title="b1">l</font> <a href="ami_1.html#V12" title="AMI_1:attr.12">-started</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">l</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</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">p</font> being <font color="Maroon" title="c3">l</font> <a href="ami_1.html#V12" title="AMI_1:attr.12">-started</a>  <a href="ami_1.html#NM3" title="AMI_1:NM.3">PartState</a> of <font color="Maroon" title="c2">S</font><br/> for <font color="Olive" title="b2">s</font> being  <a href="ami_1.html#NM3" title="AMI_1:NM.3">PartState</a> of <font color="Maroon" title="c2">S</font>  st <font color="Olive" title="b1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">s</font> holds <br/><font color="Olive" title="b2">s</font> is <font color="Maroon" title="c3">l</font> <a href="ami_1.html#V12" title="AMI_1:attr.12">-started</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c4">p</font> be  <font color="Maroon" title="c3">l</font> <a href="ami_1.html#V12" title="AMI_1:attr.12">-started</a>  <a href="ami_1.html#NM3" title="AMI_1:NM.3">PartState</a> of <font color="Maroon" title="c2">S</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">s</font> being  <a href="ami_1.html#NM3" title="AMI_1:NM.3">PartState</a> of <font color="Maroon" title="c2">S</font>  st <font color="Maroon" title="c4">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">s</font> holds <br/><font color="Olive" title="b1">s</font> is <font color="Maroon" title="c3">l</font> <a href="ami_1.html#V12" title="AMI_1:attr.12">-started</a> </span><br/>







<a NAME="E1:183"/><span class="lab"><font color="Green" title="E49">A1</font></span>: 
 <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c2">S</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="ref" href="ami_1.html#D28" target="_self" title="AMI_1:def.28">Def41</a></span>;<br/>
<a NAME="E2:183"/><span class="lab"><font color="Green" title="E50">A2</font></span>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c4">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">l</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#D28" target="_self" title="AMI_1:def.28">Def41</a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c5">s</font> be   <a href="ami_1.html#NM3" title="AMI_1:NM.3">PartState</a> of <font color="Maroon" title="c2">S</font>; <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="c4">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">s</font> implies <font color="Maroon" title="c5">s</font> is <font color="Maroon" title="c3">l</font> <a href="ami_1.html#V12" title="AMI_1:attr.12">-started</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E3:183"/><span class="lab"><font color="Green" title="E51">Z</font></span>: 
<font color="Maroon" title="c4">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">s</font>
 ; <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="c5">s</font> is <font color="Maroon" title="c3">l</font> <a href="ami_1.html#V12" title="AMI_1:attr.12">-started</a> </span><br/>

<a NAME="E4:183"/><span class="kw">then </span>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c5">s</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T25" title="RELAT_1:th.25">RELAT_1:25</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:183"/>
 <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c2">S</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="c5">s</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:183"><span class="lab"><font color="Green" title="E49">A1</font></span></a></span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="ami_1.html#D28" target="_self" title="AMI_1:def.28">AMI_1:def 28</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">l</font></span><br/>

<span class="kw">thus </span><a NAME="E6:183"/>
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">l</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:183"><span class="lab"><font color="Green" title="E51">Z</font></span></a>, <a class="txt" href="#E2:183"><span class="lab"><font color="Green" title="E50">A2</font></span></a>, <a class="txt" href="#E1:183"><span class="lab"><font color="Green" title="E49">A1</font></span></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</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/>


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