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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#L1" title="AMI_1:struct.1">AMI-Struct</a> of <font color="Maroon" title="c1">N</font><br/> for <font color="Olive" title="b2">p</font> being  <a href="ami_1.html#NM3" title="AMI_1:NM.3">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#V14" title="AMI_1:attr.14">data-only</a>  iff  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Olive" title="b2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">p</font> )</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#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">p</font> being  <a href="ami_1.html#NM3" title="AMI_1:NM.3">PartState</a> of <font color="Maroon" title="c2">S</font> holds <br/> ( <font color="Olive" title="b1">p</font> is  <a href="ami_1.html#V14" title="AMI_1:attr.14">data-only</a>  iff  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Olive" title="b1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">p</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">p</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="c3">p</font> is  <a href="ami_1.html#V14" title="AMI_1:attr.14">data-only</a>  iff  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c3">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">p</font> )</span><br/>





<span class="kw">thus </span><a NAME="E1:236"/>
( <font color="Maroon" title="c3">p</font> is  <a href="ami_1.html#V14" title="AMI_1:attr.14">data-only</a>  implies  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c3">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">p</font> )
  <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#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c3">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">p</font> implies <font color="Maroon" title="c3">p</font> is  <a href="ami_1.html#V14" title="AMI_1:attr.14">data-only</a>  )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="236_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:236_1"/>
<font color="Maroon" title="c3">p</font> is  <a href="ami_1.html#V14" title="AMI_1:attr.14">data-only</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#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c3">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">p</font></span><br/>

<a NAME="E2:236_1"/><span class="kw">then </span>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">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="c2">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T139" target="_self" title="AMI_1:th.139">Th139</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:236_1"/>
 <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c3">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">p</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T97" title="RELAT_1:th.97">RELAT_1:97</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/>


</div><span class="kw">end;</span></div>

<span class="kw">assume </span><a NAME="E2:236"/>
 <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c3">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">p</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="c3">p</font> is  <a href="ami_1.html#V14" title="AMI_1:attr.14">data-only</a> </span><br/>

<a NAME="E3:236"/><span class="kw">then </span>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">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="c2">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T87" title="RELAT_1:th.87">RELAT_1:87</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:236"/>
<font color="Maroon" title="c3">p</font> is  <a href="ami_1.html#V14" title="AMI_1:attr.14">data-only</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T139" target="_self" title="AMI_1:th.139">Th139</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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