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<b>let </b><font color="Maroon" title="c1">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">N</font> being <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> <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#L1" title="AMI_1:struct.1">AMI-Struct</a> of <font color="Maroon" title="c1">IL</font>,<font color="Olive" title="b1">N</font><br/> for <font color="Olive" title="b3">p</font> being  <a href="ami_1.html#NM7" title="AMI_1:NM.7">PartState</a> of <font color="Olive" title="b2">S</font> holds <br/> ( <font color="Olive" title="b3">p</font> is <a href="ami_1.html#V16" title="AMI_1:attr.16">data-only</a> iff  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Olive" title="b3">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_1.html#K15" title="AMI_1:func.15">Data-Locations</a> <font color="Olive" title="b2">S</font> )</span><br/><b>let </b><font color="Maroon" title="c2">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">S</font> being non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="ami_1.html#L1" title="AMI_1:struct.1">AMI-Struct</a> of <font color="Maroon" title="c1">IL</font>,<font color="Maroon" title="c2">N</font><br/> for <font color="Olive" title="b2">p</font> being  <a href="ami_1.html#NM7" title="AMI_1:NM.7">PartState</a> of <font color="Olive" title="b1">S</font> holds <br/> ( <font color="Olive" title="b2">p</font> is <a href="ami_1.html#V16" title="AMI_1:attr.16">data-only</a> iff  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Olive" title="b2">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_1.html#K15" title="AMI_1:func.15">Data-Locations</a> <font color="Olive" title="b1">S</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#L1" title="AMI_1:struct.1">AMI-Struct</a> of <font color="Maroon" title="c1">IL</font>,<font color="Maroon" title="c2">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">p</font> being  <a href="ami_1.html#NM7" title="AMI_1:NM.7">PartState</a> of <font color="Maroon" title="c3">S</font> holds <br/> ( <font color="Olive" title="b1">p</font> is <a href="ami_1.html#V16" title="AMI_1:attr.16">data-only</a> iff  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Olive" title="b1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_1.html#K15" title="AMI_1:func.15">Data-Locations</a> <font color="Maroon" title="c3">S</font> )</span><br/><b>let </b><font color="Maroon" title="c4">p</font> be   <a href="ami_1.html#NM7" title="AMI_1:NM.7">PartState</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"> ( <font color="Maroon" title="c4">p</font> is <a href="ami_1.html#V16" title="AMI_1:attr.16">data-only</a> iff  <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="ami_1.html#K15" title="AMI_1:func.15">Data-Locations</a> <font color="Maroon" title="c3">S</font> )</span><br/>







<b>thus </b><a NAME="E1:199"/>
( <font color="Maroon" title="c4">p</font> is <a href="ami_1.html#V16" title="AMI_1:attr.16">data-only</a> implies  <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="ami_1.html#K15" title="AMI_1:func.15">Data-Locations</a> <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"> (  <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="ami_1.html#K15" title="AMI_1:func.15">Data-Locations</a> <font color="Maroon" title="c3">S</font> implies <font color="Maroon" title="c4">p</font> is <a href="ami_1.html#V16" title="AMI_1:attr.16">data-only</a> )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="199_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:199_1"/>
 <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#R1" title="XBOOLE_0:pred.1">misses</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c3">S</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c1">IL</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D50" target="_self" title="AMI_1:def.50">AMI_1:def 50</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <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="ami_1.html#K15" title="AMI_1:func.15">Data-Locations</a> <font color="Maroon" title="c3">S</font></span><br/>

<b>hence </b><a NAME="E2:199_1"/>
 <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="ami_1.html#K15" title="AMI_1:func.15">Data-Locations</a> <font color="Maroon" title="c3">S</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T86" title="XBOOLE_1:th.86">XBOOLE_1:86</a>, <a class="ref" href="ami_1.html#T80" target="_self" title="AMI_1:th.80">Th80</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E2:199"/>
 <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="ami_1.html#K15" title="AMI_1:func.15">Data-Locations</a> <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"> <font color="Maroon" title="c4">p</font> is <a href="ami_1.html#V16" title="AMI_1:attr.16">data-only</a></span><br/>

<b>hence </b><a NAME="E3:199"/>
 <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#R1" title="XBOOLE_0:pred.1">misses</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c3">S</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c1">IL</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T106" title="XBOOLE_1:th.106">XBOOLE_1:106</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D50" target="_self" title="AMI_1:def.50">AMI_1:def 50</a> <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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