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<span class="kw">set </span><font color="Maroon" title="c2">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="c3">SSS</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="c4">T</font> =  <a href="fomodel1.html#K5" title="FOMODEL1:func.5">TermSymbolsOf</a> <font color="Maroon" title="c1">S</font>;<br/>
<span class="kw">let </span><font color="Maroon" title="c5">s</font> be   <a href="fomodel1.html#V10" title="FOMODEL1:attr.10">ofAtomicFormula</a>  <a href="fomodel1.html#NM1" title="FOMODEL1:NM.1">Element</a> of <font color="Maroon" title="c1">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c5">s</font> is  <a href="fomodel1.html#V7" title="FOMODEL1:attr.7">relational</a>  implies <font color="Maroon" title="c5">s</font> is  <a href="fomodel1.html#V8" title="FOMODEL1:attr.8">termal</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:93_1_1"/>
 not <font color="Maroon" title="c5">s</font> is  <a href="fomodel1.html#V7" title="FOMODEL1:attr.7">relational</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">s</font> is  <a href="fomodel1.html#V8" title="FOMODEL1:attr.8">termal</a> </span><br/>

<a NAME="E2:93_1_1"/><span class="kw">then </span>
( <font color="Maroon" title="c5">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> &amp;  not <font color="Maroon" title="c5">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="fomodel1.html#K4" title="FOMODEL1:func.4">RelSymbolsOf</a> <font color="Maroon" title="c1">S</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel1.html#D17" target="_self" title="FOMODEL1:def.17">DefRelational</a>, <a class="ref" href="fomodel1.html#D20" target="_self" title="FOMODEL1:def.20">DefOfAtomicFormula</a></span>;<br/>
<a NAME="E3:93_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <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#K4" title="FOMODEL1:func.4">RelSymbolsOf</a> <font color="Maroon" title="c1">S</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>;<br/>
<a NAME="E4:93_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="fomodel1.html#K5" title="FOMODEL1:func.5">TermSymbolsOf</a> <font color="Maroon" title="c1">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel1.html#T11" target="_self" title="FOMODEL1:th.11">Th11</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:93_1_1"/>
<font color="Maroon" title="c5">s</font> is  <a href="fomodel1.html#V8" title="FOMODEL1:attr.8">termal</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel1.html#D18" target="_self" title="FOMODEL1:def.18">DefTermal0</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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