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<span class="kw">let </span><font color="Maroon" title="c4">F</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="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <font color="Maroon" title="c3">S</font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  <a href="ami_1.html#NM4" title="AMI_1:NM.4">FinPartState</a> of ; <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">F</font> is  <a href="amistd_1.html#V7" title="AMISTD_1:attr.7">really-closed</a>  &amp; <font color="Maroon" title="c4">F</font> is  <a href="amistd_1.html#V9" title="AMISTD_1:attr.9">lower</a>  &amp; not <font color="Maroon" title="c4">F</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  implies <font color="Maroon" title="c4">F</font> is  <a href="amistd_1.html#V8" title="AMISTD_1:attr.8">para-closed</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:94_1_1"/><span class="lab"><font color="Green" title="E44">A1</font></span>: 
<font color="Maroon" title="c4">F</font> is  <a href="amistd_1.html#V7" title="AMISTD_1:attr.7">really-closed</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c4">F</font> is  <a href="amistd_1.html#V9" title="AMISTD_1:attr.9">lower</a>  or <font color="Maroon" title="c4">F</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  or <font color="Maroon" title="c4">F</font> is  <a href="amistd_1.html#V8" title="AMISTD_1:attr.8">para-closed</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E2:94_1_1"/>
( <font color="Maroon" title="c4">F</font> is  <a href="amistd_1.html#V9" title="AMISTD_1:attr.9">lower</a>  &amp; not <font color="Maroon" title="c4">F</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  )
 ; <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">F</font> is  <a href="amistd_1.html#V8" title="AMISTD_1:attr.8">para-closed</a> </span><br/>

<a NAME="E3:94_1_1"/><span class="kw">then </span>
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c3">S</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</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">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="amistd_1.html#T49" target="_self" title="AMISTD_1:th.49">Th49</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:94_1_1"/>
<font color="Maroon" title="c4">F</font> is  <a href="amistd_1.html#V8" title="AMISTD_1:attr.8">para-closed</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:94_1_1"><span class="lab"><font color="Green" title="E44">A1</font></span></a>, <a class="ref" href="amistd_1.html#T44" target="_self" title="AMISTD_1:th.44">Th44</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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