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<span class="kw">set </span><font color="Maroon" title="c3">E</font> =  <a href="fomodel2.html#K34" title="FOMODEL2:func.34">TheEqSymbOf</a> <font color="Maroon" title="c1">S</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">SS</font> =  <a href="fomodel1.html#K1" title="FOMODEL1:func.1">AllSymbolsOf</a> <font color="Maroon" title="c1">S</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">T</font> = <font color="Maroon" title="c1">S</font> <a href="fomodel1.html#K39" title="FOMODEL1:func.39">-termsOfMaxDepth</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">C</font> = <font color="Maroon" title="c1">S</font> <a href="fomodel1.html#K21" title="FOMODEL1:func.21">-multiCat</a> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c7">phi</font> = <span class="p1">(<span class="default"><span class="p2"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="fomodel2.html#K34" title="FOMODEL2:func.34">TheEqSymbOf</a> <font color="Maroon" title="c1">S</font></span>)</span></span><a href="fomodel2.html#K31" title="FOMODEL2:func.31">*&gt;</a></span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c2">t</font></span>)</span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c2">t</font> as   <a href="fomodel2.html#V4" title="FOMODEL2:attr.4">wff</a>  <a href="fomodel1.html#NM3" title="FOMODEL1:NM.3">string</a> of <font color="Maroon" title="c1">S</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="fomodel4.html#E2"><span class="lab"><font color="Green" title="E2">Lm10</font></span></a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c8">Seqts</font> =  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">S</font> <a href="fomodel4.html#K1" title="FOMODEL4:func.1">-sequents</a></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T2" title="XBOOLE_1:th.2">XBOOLE_1:2</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c9">seqt</font> = <span class="p1"><a href="fomodel4.html#K7" title="FOMODEL4:func.7">[</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<font color="Maroon" title="c7">phi</font></span><a href="fomodel4.html#K7" title="FOMODEL4:func.7">]</a></span> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">S</font> <a href="fomodel4.html#K1" title="FOMODEL4:func.1">-sequents</a>  ;<br/>
<a NAME="E4:84_1_1"/>
( <font color="Maroon" title="c9">seqt</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  &amp; <font color="Maroon" title="c9">seqt</font> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="fomodel2.html#K34" title="FOMODEL2:func.34">TheEqSymbOf</a> <font color="Maroon" title="c1">S</font></span>)</span></span><a href="fomodel2.html#K31" title="FOMODEL2:func.31">*&gt;</a></span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c2">t</font></span>)</span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c2">t</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></span>;<br/>
<a NAME="E5:84_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c9">seqt</font> <a href="fomodel4.html#R3" title="FOMODEL4:pred.3">Rule2</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel4.html#D20" target="_self" title="FOMODEL4:def.20">Def2</a></span>;<br/>
<a NAME="E6:84_1_1"/><span class="kw">then </span>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c8">Seqts</font>,<font color="Maroon" title="c9">seqt</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="fomodel4.html#K10" title="FOMODEL4:func.10">P2</a> <font color="Maroon" title="c1">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel4.html#D33" target="_self" title="FOMODEL4:def.33">DefP2</a></span>;<br/>
<a NAME="E7:84_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c9">seqt</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="fomodel4.html#K24" title="FOMODEL4:func.24">R2</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">Seqts</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="fomodel4.html#E70"><span class="lab"><font color="Green" title="E65">Lm1</font></span></a></span>;<br/>
<a NAME="E8:84_1_1"/><span class="kw">then </span>
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c9">seqt</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="fomodel4.html#K24" title="FOMODEL4:func.24">R2</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">Seqts</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T31" title="ZFMISC_1:th.31">ZFMISC_1:31</a></span>;<br/>
<a NAME="E9:84_1_1"/><span class="kw">then </span>
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c9">seqt</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> is  <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">R2</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#V3" title="FOMODEL4:attr.3">-derivable</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="fomodel4.html#E36"><span class="lab"><font color="Green" title="E31">Lm9</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:84_1_1"/>
 for <font color="Olive">b<sub>1</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</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="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><span class="p0">(<span class="default"><a href="fomodel2.html#K34" title="FOMODEL2:func.34">TheEqSymbOf</a> <font color="Maroon" title="c1">S</font></span>)</span></span><a href="fomodel2.html#K31" title="FOMODEL2:func.31">*&gt;</a></span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c2">t</font></span>)</span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c2">t</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> holds <br/><font color="Olive">b<sub>1</sub></font> is <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">R2</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#V7" title="FOMODEL4:attr.7">-derivable</a> 
 ; <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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