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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   <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">s</font> being  <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <font color="Olive" title="b2">S</font><br/> for <font color="Olive" title="b4">p</font> being  <a href="ami_1.html#NM8" title="AMI_1:NM.8">FinPartState</a> of <font color="Olive" title="b2">S</font> holds  <font color="Olive" title="b3">s</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Olive" title="b4">p</font></span>)</span> is   <a href="ami_1.html#NM8" title="AMI_1:NM.8">FinPartState</a> of <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   <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">s</font> being  <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <font color="Olive" title="b1">S</font><br/> for <font color="Olive" title="b3">p</font> being  <a href="ami_1.html#NM8" title="AMI_1:NM.8">FinPartState</a> of <font color="Olive" title="b1">S</font> holds  <font color="Olive" title="b2">s</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Olive" title="b3">p</font></span>)</span> is   <a href="ami_1.html#NM8" title="AMI_1:NM.8">FinPartState</a> of <font color="Olive" title="b1">S</font></span><br/><b>let </b><font color="Maroon" title="c3">S</font> be    <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">s</font> being  <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <font color="Maroon" title="c3">S</font><br/> for <font color="Olive" title="b2">p</font> being  <a href="ami_1.html#NM8" title="AMI_1:NM.8">FinPartState</a> of <font color="Maroon" title="c3">S</font> holds  <font color="Olive" title="b1">s</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Olive" title="b2">p</font></span>)</span> is   <a href="ami_1.html#NM8" title="AMI_1:NM.8">FinPartState</a> of <font color="Maroon" title="c3">S</font></span><br/><b>let </b><font color="Maroon" title="c4">s</font> be   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</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"> for <font color="Olive" title="b1">p</font> being  <a href="ami_1.html#NM8" title="AMI_1:NM.8">FinPartState</a> of <font color="Maroon" title="c3">S</font> holds  <font color="Maroon" title="c4">s</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Olive" title="b1">p</font></span>)</span> is   <a href="ami_1.html#NM8" title="AMI_1:NM.8">FinPartState</a> of <font color="Maroon" title="c3">S</font></span><br/><b>let </b><font color="Maroon" title="c5">p</font> be   <a href="ami_1.html#NM8" title="AMI_1:NM.8">FinPartState</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">s</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c5">p</font></span>)</span> is   <a href="ami_1.html#NM8" title="AMI_1:NM.8">FinPartState</a> of <font color="Maroon" title="c3">S</font></span><br/>









<a NAME="E1:74"/><i><font color="Green" title="E34">A1</font></i>: 
(  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> the <a href="ami_1.html#U3" title="AMI_1:sel.3">Object-Kind</a> of <font color="Maroon" title="c3">S</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="card_3.html#K8" title="CARD_3:func.8">sproduct</a> the <a href="ami_1.html#U3" title="AMI_1:sel.3">Object-Kind</a> of <font color="Maroon" title="c3">S</font> &amp; <font color="Maroon" title="c4">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> the <a href="ami_1.html#U3" title="AMI_1:sel.3">Object-Kind</a> of <font color="Maroon" title="c3">S</font> )
 
<b>by </b><i><a class="ref" href="card_3.html#T67" title="CARD_3:th.67">CARD_3:67</a></i>;<br/>
<a NAME="E2:74"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c5">p</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c5">p</font></span>)</span>
 
<b>by </b><i><a class="ref" href="relat_1.html#T90" title="RELAT_1:th.90">RELAT_1:90</a></i>;<br/>
<b>hence </b><a NAME="E3:74"/>
<font color="Maroon" title="c4">s</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c5">p</font></span>)</span> is   <a href="ami_1.html#NM8" title="AMI_1:NM.8">FinPartState</a> of <font color="Maroon" title="c3">S</font>
 <b>by </b><i><a class="txt" href="#E1:74"><i><font color="Green" title="E34">A1</font></i></a>, <a class="ref" href="card_3.html#T81" title="CARD_3:th.81">CARD_3:81</a>, <a class="ref" href="finset_1.html#T29" title="FINSET_1:th.29">FINSET_1:29</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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