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<span class="kw">let </span><font color="Maroon" title="c1">S</font> be   <a href="fomodel1.html#NM2" title="FOMODEL1:NM.2">Language</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="fomodel1.html#K17" title="FOMODEL1:func.17">AtomicFormulaSymbolsOf</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K9" title="FOMODEL1:func.9">OwnSymbolsOf</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.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="fomodel1.html#K18" title="FOMODEL1:func.18">TheEqSymbOf</a> <font color="Maroon" title="c1">S</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span><br/>

<span class="kw">set </span><font color="Maroon" title="c2">o</font> =  the <a href="struct_0.html#U3" title="STRUCT_0:sel.3">OneF</a> of <font color="Maroon" title="c1">S</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c3">z</font> =  the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">ZeroF</a> of <font color="Maroon" title="c1">S</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">f</font> =  the <a href="fomodel1.html#U1" title="FOMODEL1:sel.1">adicity</a> of <font color="Maroon" title="c1">S</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">R</font> =  <a href="fomodel1.html#K4" title="FOMODEL1:func.4">RelSymbolsOf</a> <font color="Maroon" title="c1">S</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">O</font> =  <a href="fomodel1.html#K9" title="FOMODEL1:func.9">OwnSymbolsOf</a> <font color="Maroon" title="c1">S</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">SS</font> =  <a href="fomodel1.html#K15" title="FOMODEL1:func.15">AllSymbolsOf</a> <font color="Maroon" title="c1">S</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">e</font> =  <a href="fomodel1.html#K18" title="FOMODEL1:func.18">TheEqSymbOf</a> <font color="Maroon" title="c1">S</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">n</font> =  <a href="fomodel1.html#K8" title="FOMODEL1:func.8">TheNorSymbOf</a> <font color="Maroon" title="c1">S</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">A</font> =  <a href="fomodel1.html#K17" title="FOMODEL1:func.17">AtomicFormulaSymbolsOf</a> <font color="Maroon" title="c1">S</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c11">D</font> =  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"> the <a href="struct_0.html#U3" title="STRUCT_0:sel.3">OneF</a> of <font color="Maroon" title="c1">S</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>;<br/>
<a NAME="E1:91"/><span class="lab"><font color="Green" title="E31">Z0</font></span>: 
 <a href="fomodel1.html#K18" title="FOMODEL1:func.18">TheEqSymbOf</a> <font color="Maroon" title="c1">S</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="fomodel1.html#K17" title="FOMODEL1:func.17">AtomicFormulaSymbolsOf</a> <font color="Maroon" title="c1">S</font>
 
;<br/>
<span class="p1">(<span class="default"><a href="fomodel1.html#K17" title="FOMODEL1:func.17">AtomicFormulaSymbolsOf</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K9" title="FOMODEL1:func.9">OwnSymbolsOf</a> <font color="Maroon" title="c1">S</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="fomodel1.html#K17" title="FOMODEL1:func.17">AtomicFormulaSymbolsOf</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="fomodel1.html#K15" title="FOMODEL1:func.15">AllSymbolsOf</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p2">(<span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"> the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">ZeroF</a> of <font color="Maroon" title="c1">S</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"> the <a href="struct_0.html#U3" title="STRUCT_0:sel.3">OneF</a> of <font color="Maroon" title="c1">S</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="enumset1.html#T1" title="ENUMSET1:th.1">ENUMSET1:1</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="fomodel1.html#K17" title="FOMODEL1:func.17">AtomicFormulaSymbolsOf</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="fomodel1.html#K17" title="FOMODEL1:func.17">AtomicFormulaSymbolsOf</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"> the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">ZeroF</a> of <font color="Maroon" title="c1">S</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T41" title="XBOOLE_1:th.41">XBOOLE_1:41</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="fomodel1.html#K17" title="FOMODEL1:func.17">AtomicFormulaSymbolsOf</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2">(<span class="default"><a href="fomodel1.html#K17" title="FOMODEL1:func.17">AtomicFormulaSymbolsOf</a> <font color="Maroon" title="c1">S</font></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="fomodel1.html#K17" title="FOMODEL1:func.17">AtomicFormulaSymbolsOf</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"> the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">ZeroF</a> of <font color="Maroon" title="c1">S</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T52" title="XBOOLE_1:th.52">XBOOLE_1:52</a></span>
<br/>.= 
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"> the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">ZeroF</a> of <font color="Maroon" title="c1">S</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:91"><span class="lab"><font color="Green" title="E31">Z0</font></span></a>, <a class="ref" href="zfmisc_1.html#T46" title="ZFMISC_1:th.46">ZFMISC_1:46</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E3:91"/>
<span class="p1">(<span class="default"><a href="fomodel1.html#K17" title="FOMODEL1:func.17">AtomicFormulaSymbolsOf</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K9" title="FOMODEL1:func.9">OwnSymbolsOf</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.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="fomodel1.html#K18" title="FOMODEL1:func.18">TheEqSymbOf</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 class="txt" 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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