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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="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">S</font> being   <a href="compos_1.html#V3" title="COMPOS_1:attr.3">standard-ins</a>   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="memstr_0.html#V2" title="MEMSTR_0:attr.2">IC-Ins-separated</a>   <a href="extpro_1.html#V3" title="EXTPRO_1:attr.3">halting</a>   <a href="amistd_5.html#V3" title="AMISTD_5:attr.3">IC-recognized</a>   <a href="extpro_1.html#L1" title="EXTPRO_1:struct.1">AMI-Struct</a> of <font color="Maroon" title="c1">N</font><br/>  for <font color="Olive" title="b2">q</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="compos_1.html#U1" title="COMPOS_1:sel.1">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="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>   non  <a href="compos_1.html#V2" title="COMPOS_1:attr.2">halt-free</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><br/>  for <font color="Olive" title="b3">p</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <font color="Olive">b<sub>2</sub></font> <a href="extpro_1.html#V4" title="EXTPRO_1:attr.4">-autonomic</a>  <a href="memstr_0.html#NM4" title="MEMSTR_0:NM.4">FinPartState</a> of <font color="Olive" title="b1">S</font> holds   <a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a>  <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="Olive" title="b3">p</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">S</font> be   <a href="compos_1.html#V3" title="COMPOS_1:attr.3">standard-ins</a>   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="memstr_0.html#V2" title="MEMSTR_0:attr.2">IC-Ins-separated</a>   <a href="extpro_1.html#V3" title="EXTPRO_1:attr.3">halting</a>   <a href="amistd_5.html#V3" title="AMISTD_5:attr.3">IC-recognized</a>   <a href="extpro_1.html#L1" title="EXTPRO_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="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">q</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="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <font color="Maroon" title="c2">S</font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>   non  <a href="compos_1.html#V2" title="COMPOS_1:attr.2">halt-free</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><br/>  for <font color="Olive" title="b2">p</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <font color="Olive">b<sub>1</sub></font> <a href="extpro_1.html#V4" title="EXTPRO_1:attr.4">-autonomic</a>  <a href="memstr_0.html#NM4" title="MEMSTR_0:NM.4">FinPartState</a> of <font color="Maroon" title="c2">S</font> holds   <a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a>  <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="Olive" title="b2">p</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">q</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="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <font color="Maroon" title="c2">S</font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>   non  <a href="compos_1.html#V2" title="COMPOS_1:attr.2">halt-free</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">p</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <font color="Maroon" title="c3">q</font> <a href="extpro_1.html#V4" title="EXTPRO_1:attr.4">-autonomic</a>  <a href="memstr_0.html#NM4" title="MEMSTR_0:NM.4">FinPartState</a> of <font color="Maroon" title="c2">S</font> holds   <a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a>  <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="Olive" title="b1">p</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">p</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <font color="Maroon" title="c3">q</font> <a href="extpro_1.html#V4" title="EXTPRO_1:attr.4">-autonomic</a>  <a href="memstr_0.html#NM4" title="MEMSTR_0:NM.4">FinPartState</a> of <font color="Maroon" title="c2">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a>  <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><br/>







<a NAME="E1:18"/><span class="lab"><font color="Green" title="E9">A2</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">p</font> <a href="subset_1.html#R2" title="SUBSET_1:pred.2">meets</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="memstr_0.html#NK3" title="MEMSTR_0:NK.3">Data-Locations</a> </span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="memstr_0.html#T41" title="MEMSTR_0:th.41">MEMSTR_0:41</a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="18_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:18_1"/>
(  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">p</font> <a href="subset_1.html#R2" title="SUBSET_1:pred.2">meets</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> or  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">p</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="memstr_0.html#NK3" title="MEMSTR_0:NK.3">Data-Locations</a>  )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:18"><span class="lab"><font color="Green" title="E9">A2</font></span></a>, <a class="ref" href="xboole_1.html#T70" title="XBOOLE_1:th.70">XBOOLE_1:70</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="18_1_1"><span class="kw">suppose </span></a><a NAME="E1:18_1_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">p</font> <a href="subset_1.html#R2" title="SUBSET_1:pred.2">meets</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a>  <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><br/><div class="add"><span class="kw">hence </span><a NAME="E2:18_1_1"/>
 <a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a>  <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="zfmisc_1.html#T50" title="ZFMISC_1:th.50">ZFMISC_1:50</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="18_1_2"><span class="kw">suppose </span></a><a NAME="E1:18_1_2"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">p</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="memstr_0.html#NK3" title="MEMSTR_0:NK.3">Data-Locations</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a>  <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><br/><div class="add"><a NAME="E2:18_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">p</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="memstr_0.html#NK3" title="MEMSTR_0:NK.3">Data-Locations</a> </span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></span>;<br/><a NAME="E3:18_1_2"/><span class="kw">then </span>
 <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <font color="Maroon" title="c4">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T38" title="RELAT_1:th.38">RELAT_1:38</a>, <a class="ref" href="relat_1.html#T61" title="RELAT_1:th.61">RELAT_1:61</a></span>;<br/><span class="kw">hence </span><a NAME="E4:18_1_2"/>
 <a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a>  <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="amistd_5.html#T3" target="_self" title="AMISTD_5:th.3">Th3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

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