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<span class="kw">set </span><font color="Maroon" title="c3">AF</font> =  <a href="fomodel2.html#K30" title="FOMODEL2:func.30">AllFormulasOf</a> <font color="Maroon" title="c1">S</font>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c4">Phi</font> =  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  as   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="fomodel2.html#K30" title="FOMODEL2:func.30">AllFormulasOf</a> <font color="Maroon" title="c1">S</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T2" onmouseover="rs('xboole_1/T2')" onmouseout="rh()">XBOOLE_1:2</a></span>;<br/>
<a NAME="E2:111_1_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">Phi</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">phi</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span>,<font color="Maroon" title="c2">phi</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> is 1, <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</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="fomodel4.html#K24" title="FOMODEL4:func.24">R#0</a> <font color="Maroon" title="c1">S</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="fomodel4.html#V5" title="FOMODEL4:attr.5">-derivable</a> 
 
;<br/>
<span class="kw">hence </span><a NAME="E3:111_1_1"/>
 for <font color="Olive">b<sub>1</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">phi</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<font color="Maroon" title="c2">phi</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> holds <br/><font color="Olive">b<sub>1</sub></font> is 1, <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</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="fomodel4.html#K24" title="FOMODEL4:func.24">R#0</a> <font color="Maroon" title="c1">S</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="fomodel4.html#V5" title="FOMODEL4:attr.5">-derivable</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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