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<span class="kw">set </span><font color="Maroon" title="c5">Q</font> = <font color="Maroon" title="c1">S</font> <a href="fomodel4.html#K1" title="FOMODEL4:func.1">-sequents</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">psi</font> = (<font color="Maroon" title="c2">l</font>,<font color="Maroon" title="c3">t</font>) <a href="fomodel3.html#K37" title="FOMODEL3:func.37">SubstIn</a> <font color="Maroon" title="c4">phi</font>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c7">Sq</font> = <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"><span class="p3">(<span class="default">(<font color="Maroon" title="c2">l</font>,<font color="Maroon" title="c3">t</font>) <a href="fomodel3.html#K37" title="FOMODEL3:func.37">SubstIn</a> <font color="Maroon" title="c4">phi</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><span class="p3"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><font color="Maroon" title="c2">l</font></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="c4">phi</font></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> as  <font color="Maroon" title="c1">S</font> <a href="fomodel4.html#V1" title="FOMODEL4:attr.1">-sequent-like</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c8">SQ</font> = <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="fomodel0.html#K13" title="FOMODEL0:func.13">null</a> <font color="Maroon" title="c1">S</font> as  <font color="Maroon" title="c1">S</font> <a href="fomodel4.html#V2" title="FOMODEL4:attr.2">-sequents-like</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c9">seqt</font> = <font color="Maroon" title="c7">Sq</font> 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>  <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel4.html#D2" target="_self" title="FOMODEL4:def.2">DefSeqtLike</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c10">Seqts</font> = <font color="Maroon" title="c8">SQ</font> 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="fomodel4.html#D3" target="_self" title="FOMODEL4:def.3">DefSeqtLike2</a></span>;<br/>
<a NAME="E5:179_1_1"/>
( <span class="p1">(<span class="default"><font color="Maroon" title="c9">seqt</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a></span>)</span> <a href="xboole_0.html#K5" title="XBOOLE_0:func.5">\+\</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">(<font color="Maroon" title="c2">l</font>,<font color="Maroon" title="c3">t</font>) <a href="fomodel3.html#K37" title="FOMODEL3:func.37">SubstIn</a> <font color="Maroon" title="c4">phi</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c9">seqt</font> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a></span>)</span> <a href="xboole_0.html#K5" title="XBOOLE_0:func.5">\+\</a> <span class="p1">(<span class="default"><span class="p2"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><font color="Maroon" title="c2">l</font></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="c4">phi</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 
;<br/>
<a NAME="E6:179_1_1"/><span class="kw">then </span>
( <font color="Maroon" title="c10">Seqts</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c9">seqt</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <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">(<font color="Maroon" title="c2">l</font>,<font color="Maroon" title="c3">t</font>) <a href="fomodel3.html#K37" title="FOMODEL3:func.37">SubstIn</a> <font color="Maroon" title="c4">phi</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &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"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><font color="Maroon" title="c2">l</font></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="c4">phi</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel0.html#T29" title="FOMODEL0:th.29">FOMODEL0:29</a></span>;<br/>
<a NAME="E7:179_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c9">seqt</font> <a href="fomodel4.html#R8" title="FOMODEL4:pred.8">Rule4</a> <font color="Maroon" title="c10">Seqts</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel4.html#D25" target="_self" title="FOMODEL4:def.25">Def4</a></span>;<br/>
<a NAME="E8:179_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="c10">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#K15" title="FOMODEL4:func.15">P4</a> <font color="Maroon" title="c1">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel4.html#D38" target="_self" title="FOMODEL4:def.38">DefP4</a></span>;<br/>
<a NAME="E9:179_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c7">Sq</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="fomodel4.html#K29" title="FOMODEL4:func.29">R4</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">SQ</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel4.html#T2" target="_self" title="FOMODEL4:th.2">Th3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:179_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="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"><span class="p3">(<span class="default">(<font color="Maroon" title="c2">l</font>,<font color="Maroon" title="c3">t</font>) <a href="fomodel3.html#K37" title="FOMODEL3:func.37">SubstIn</a> <font color="Maroon" title="c4">phi</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><span class="p3"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><font color="Maroon" title="c2">l</font></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="c4">phi</font></span>)</span></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#K29" title="FOMODEL4:func.29">R4</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#V4" title="FOMODEL4:attr.4">-derivable</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="fomodel4.html#E111"><span class="lab"><font color="Green" title="E90">Lm22</font></span></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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