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<span class="kw">let </span><font color="Maroon" title="c1">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">S</font> being   <a href="fomodel1.html#NM2" title="FOMODEL1:NM.2">Language</a><br/>  for <font color="Olive" title="b2">phi</font> being   <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="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b3">D</font> being   <a href="fomodel4.html#NM2" title="FOMODEL4:NM.2">RuleSet</a> of <font color="Olive" title="b1">S</font>  st <font color="Olive" title="b3">D</font> is  <a href="fomodel4.html#V6" title="FOMODEL4:attr.6">isotone</a>  &amp;  <a href="fomodel4.html#K23" title="FOMODEL4:func.23">R1</a> <font color="Olive" title="b1">S</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b3">D</font> &amp;  <a href="fomodel4.html#K33" title="FOMODEL4:func.33">R8</a> <font color="Olive" title="b1">S</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b3">D</font> &amp; <font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b2">phi</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> is <font color="Olive" title="b3">D</font> <a href="fomodel4.html#V14" title="FOMODEL4:attr.14">-inconsistent</a>  holds <br/> <a href="fomodel2.html#K38" title="FOMODEL2:func.38">xnot</a> <font color="Olive" title="b2">phi</font> is <font color="Maroon" title="c1">X</font>,<font color="Olive" title="b3">D</font> <a href="fomodel4.html#V8" title="FOMODEL4:attr.8">-provable</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">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">  for <font color="Olive" title="b1">phi</font> being   <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="c2">S</font><br/>  for <font color="Olive" title="b2">D</font> being   <a href="fomodel4.html#NM2" title="FOMODEL4:NM.2">RuleSet</a> of <font color="Maroon" title="c2">S</font>  st <font color="Olive" title="b2">D</font> is  <a href="fomodel4.html#V6" title="FOMODEL4:attr.6">isotone</a>  &amp;  <a href="fomodel4.html#K23" title="FOMODEL4:func.23">R1</a> <font color="Maroon" title="c2">S</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">D</font> &amp;  <a href="fomodel4.html#K33" title="FOMODEL4:func.33">R8</a> <font color="Maroon" title="c2">S</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">D</font> &amp; <font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b1">phi</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> is <font color="Olive" title="b2">D</font> <a href="fomodel4.html#V14" title="FOMODEL4:attr.14">-inconsistent</a>  holds <br/> <a href="fomodel2.html#K38" title="FOMODEL2:func.38">xnot</a> <font color="Olive" title="b1">phi</font> is <font color="Maroon" title="c1">X</font>,<font color="Olive" title="b2">D</font> <a href="fomodel4.html#V8" title="FOMODEL4:attr.8">-provable</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">phi</font> be   <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="c2">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">D</font> being   <a href="fomodel4.html#NM2" title="FOMODEL4:NM.2">RuleSet</a> of <font color="Maroon" title="c2">S</font>  st <font color="Olive" title="b1">D</font> is  <a href="fomodel4.html#V6" title="FOMODEL4:attr.6">isotone</a>  &amp;  <a href="fomodel4.html#K23" title="FOMODEL4:func.23">R1</a> <font color="Maroon" title="c2">S</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">D</font> &amp;  <a href="fomodel4.html#K33" title="FOMODEL4:func.33">R8</a> <font color="Maroon" title="c2">S</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">D</font> &amp; <font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">phi</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> is <font color="Olive" title="b1">D</font> <a href="fomodel4.html#V14" title="FOMODEL4:attr.14">-inconsistent</a>  holds <br/> <a href="fomodel2.html#K38" title="FOMODEL2:func.38">xnot</a> <font color="Maroon" title="c3">phi</font> is <font color="Maroon" title="c1">X</font>,<font color="Olive" title="b1">D</font> <a href="fomodel4.html#V8" title="FOMODEL4:attr.8">-provable</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c4">D</font> be   <a href="fomodel4.html#NM2" title="FOMODEL4:NM.2">RuleSet</a> of <font color="Maroon" title="c2">S</font>; <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="c4">D</font> is  <a href="fomodel4.html#V6" title="FOMODEL4:attr.6">isotone</a>  &amp;  <a href="fomodel4.html#K23" title="FOMODEL4:func.23">R1</a> <font color="Maroon" title="c2">S</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">D</font> &amp;  <a href="fomodel4.html#K33" title="FOMODEL4:func.33">R8</a> <font color="Maroon" title="c2">S</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">D</font> &amp; <font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">phi</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> is <font color="Maroon" title="c4">D</font> <a href="fomodel4.html#V14" title="FOMODEL4:attr.14">-inconsistent</a>  implies  <a href="fomodel2.html#K38" title="FOMODEL2:func.38">xnot</a> <font color="Maroon" title="c3">phi</font> is <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c4">D</font> <a href="fomodel4.html#V8" title="FOMODEL4:attr.8">-provable</a>  )</span><br/>







<span class="kw">set </span><font color="Maroon" title="c5">XX</font> = <font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">phi</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">N</font> =  <a href="fomodel2.html#K1" title="FOMODEL2:func.1">TheNorSymbOf</a> <font color="Maroon" title="c2">S</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">G1</font> =  <a href="fomodel4.html#K23" title="FOMODEL4:func.23">R1</a> <font color="Maroon" title="c2">S</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">G8</font> =  <a href="fomodel4.html#K33" title="FOMODEL4:func.33">R8</a> <font color="Maroon" title="c2">S</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">E1</font> = <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#K23" title="FOMODEL4:func.23">R1</a> <font color="Maroon" title="c2">S</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">E8</font> = <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#K33" title="FOMODEL4:func.33">R8</a> <font color="Maroon" title="c2">S</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>;<br/>
<span class="kw">assume </span><a NAME="E1:191"/><span class="lab"><font color="Green" title="E106">B10</font></span>: 
( <font color="Maroon" title="c4">D</font> is  <a href="fomodel4.html#V6" title="FOMODEL4:attr.6">isotone</a>  &amp;  <a href="fomodel4.html#K23" title="FOMODEL4:func.23">R1</a> <font color="Maroon" title="c2">S</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">D</font> &amp;  <a href="fomodel4.html#K33" title="FOMODEL4:func.33">R8</a> <font color="Maroon" title="c2">S</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">D</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="c1">X</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">phi</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> is <font color="Maroon" title="c4">D</font> <a href="fomodel4.html#V14" title="FOMODEL4:attr.14">-inconsistent</a>  or  <a href="fomodel2.html#K38" title="FOMODEL2:func.38">xnot</a> <font color="Maroon" title="c3">phi</font> is <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c4">D</font> <a href="fomodel4.html#V8" title="FOMODEL4:attr.8">-provable</a>  )</span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c11">F1</font> = <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#K23" title="FOMODEL4:func.23">R1</a> <font color="Maroon" title="c2">S</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>, <font color="Maroon" title="c12">F8</font> = <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#K33" title="FOMODEL4:func.33">R8</a> <font color="Maroon" title="c2">S</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c4">D</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/>
<span class="kw">assume </span><a NAME="E3:191"/>
<font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">phi</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> is <font color="Maroon" title="c4">D</font> <a href="fomodel4.html#V14" title="FOMODEL4:attr.14">-inconsistent</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="fomodel2.html#K38" title="FOMODEL2:func.38">xnot</a> <font color="Maroon" title="c3">phi</font> is <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c4">D</font> <a href="fomodel4.html#V8" title="FOMODEL4:attr.8">-provable</a> </span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c13">phi1</font>, <font color="Maroon" title="c14">phi2</font> being   <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="c2">S</font><span class="kw"> such that </span><br/><a NAME="E5:191"/><span class="lab"><font color="Green" title="E107">B0</font></span>: 
( <font color="Maroon" title="c13">phi1</font> is <font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">phi</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<font color="Maroon" title="c4">D</font> <a href="fomodel4.html#V8" title="FOMODEL4:attr.8">-provable</a>  &amp; <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#K1" title="FOMODEL2:func.1">TheNorSymbOf</a> <font color="Maroon" title="c2">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="c13">phi1</font></span>)</span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c14">phi2</font> is <font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">phi</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<font color="Maroon" title="c4">D</font> <a href="fomodel4.html#V8" title="FOMODEL4:attr.8">-provable</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel4.html#D65" target="_self" title="FOMODEL4:def.65">DefInc</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c15">nphi1</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#K1" title="FOMODEL2:func.1">TheNorSymbOf</a> <font color="Maroon" title="c2">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="c13">phi1</font></span>)</span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c14">phi2</font>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c16">H1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> , <font color="Maroon" title="c17">m1</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><span class="kw"> such that </span><br/><a NAME="E7:191"/><span class="lab"><font color="Green" title="E108">B1</font></span>: 
( <font color="Maroon" title="c16">H1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">phi</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c16">H1</font>,<font color="Maroon" title="c13">phi1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> is <font color="Maroon" title="c17">m1</font>, <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<font color="Maroon" title="c4">D</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel4.html#D62" target="_self" title="FOMODEL4:def.62">DefProvable3</a>, <a class="txt" href="#E5:191"><span class="lab"><font color="Green" title="E107">B0</font></span></a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c18">H2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> , <font color="Maroon" title="c19">m2</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><span class="kw"> such that </span><br/><a NAME="E9:191"/><span class="lab"><font color="Green" title="E109">B2</font></span>: 
( <font color="Maroon" title="c18">H2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">phi</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c18">H2</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><span class="p5">(<span class="default"><a href="fomodel2.html#K1" title="FOMODEL2:func.1">TheNorSymbOf</a> <font color="Maroon" title="c2">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="c13">phi1</font></span>)</span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c14">phi2</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> is <font color="Maroon" title="c19">m2</font>, <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<font color="Maroon" title="c4">D</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel4.html#D62" target="_self" title="FOMODEL4:def.62">DefProvable3</a>, <a class="txt" href="#E5:191"><span class="lab"><font color="Green" title="E107">B0</font></span></a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c20">seqt1</font> = <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c16">H1</font>,<font color="Maroon" title="c13">phi1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>, <font color="Maroon" title="c21">seqt2</font> = <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c18">H2</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><span class="p5">(<span class="default"><a href="fomodel2.html#K1" title="FOMODEL2:func.1">TheNorSymbOf</a> <font color="Maroon" title="c2">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="c13">phi1</font></span>)</span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c14">phi2</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> as  <font color="Maroon" title="c2">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>  <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:191"><span class="lab"><font color="Green" title="E108">B1</font></span></a>, <a class="txt" href="#E9:191"><span class="lab"><font color="Green" title="E109">B2</font></span></a></span>;<br/>
<a NAME="E11:191"/>
( <span class="p1">(<span class="default"><font color="Maroon" title="c20">seqt1</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> <font color="Maroon" title="c16">H1</font> <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="c21">seqt2</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> <font color="Maroon" title="c18">H2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 
;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c22">H11</font> = <font color="Maroon" title="c16">H1</font>, <font color="Maroon" title="c23">H22</font> = <font color="Maroon" title="c18">H2</font> as  <font color="Maroon" title="c2">S</font> <a href="fomodel4.html#V13" title="FOMODEL4:attr.13">-premises-like</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">phi</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="txt" href="#E7:191"><span class="lab"><font color="Green" title="E108">B1</font></span></a>, <a class="txt" href="#E9:191"><span class="lab"><font color="Green" title="E109">B2</font></span></a>, <a class="ref" href="fomodel0.html#T29" title="FOMODEL0:th.29">FOMODEL0:29</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c24">H111</font> = <font color="Maroon" title="c22">H11</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">phi</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>, <font color="Maroon" title="c25">H222</font> = <font color="Maroon" title="c23">H22</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">phi</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> as  <font color="Maroon" title="c2">S</font> <a href="fomodel4.html#V13" title="FOMODEL4:attr.13">-premises-like</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T43" title="XBOOLE_1:th.43">XBOOLE_1:43</a></span>;<br/>
<a NAME="E14:191"/>
( <font color="Maroon" title="c22">H11</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c24">H111</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">H11</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">phi</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp; <font color="Maroon" title="c23">H22</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c25">H222</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">H22</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">phi</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="ref" href="xboole_1.html#T48" title="XBOOLE_1:th.48">XBOOLE_1:48</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c26">pH1</font> = <font color="Maroon" title="c22">H11</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c24">H111</font>, <font color="Maroon" title="c27">pH2</font> = <font color="Maroon" title="c23">H22</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c25">H222</font> as  <font color="Maroon" title="c2">S</font> <a href="fomodel4.html#V13" title="FOMODEL4:attr.13">-premises-like</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">phi</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c28">H</font> = <font color="Maroon" title="c22">H11</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c23">H22</font> as  <font color="Maroon" title="c2">S</font> <a href="fomodel4.html#V13" title="FOMODEL4:attr.13">-premises-like</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">phi</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c29">h</font> = <font color="Maroon" title="c28">H</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">phi</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> as  <font color="Maroon" title="c2">S</font> <a href="fomodel4.html#V13" title="FOMODEL4:attr.13">-premises-like</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T43" title="XBOOLE_1:th.43">XBOOLE_1:43</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c30">hp</font> = <font color="Maroon" title="c28">H</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">phi</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> as  <font color="Maroon" title="c2">S</font> <a href="fomodel4.html#V13" title="FOMODEL4:attr.13">-premises-like</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">phi</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c31">Phi</font> = <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">phi</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> as  <font color="Maroon" title="c2">S</font> <a href="fomodel4.html#V13" title="FOMODEL4:attr.13">-premises-like</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  ;<br/>
<span class="kw">set </span><font color="Maroon" title="c32">M</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c17">m1</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c19">m2</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c33">hh</font> = <font color="Maroon" title="c29">h</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">phi</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> as  <font color="Maroon" title="c2">S</font> <a href="fomodel4.html#V13" title="FOMODEL4:attr.13">-premises-like</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c34">e</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="c2">S</font> as  <font color="Maroon" title="c2">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">set </span><font color="Maroon" title="c35">x</font> = <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c33">hh</font>,<font color="Maroon" title="c13">phi1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c36">y</font> = <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c33">hh</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><span class="p5">(<span class="default"><a href="fomodel2.html#K1" title="FOMODEL2:func.1">TheNorSymbOf</a> <font color="Maroon" title="c2">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="c13">phi1</font></span>)</span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c14">phi2</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>;<br/>
<a NAME="E22:191"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c22">H11</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p4">(<span class="default"><font color="Maroon" title="c23">H22</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c31">Phi</font></span>)</span></span>)</span> <a href="fomodel0.html#K13" title="FOMODEL0:func.13">null</a> <span class="p3">(<span class="default"><font color="Maroon" title="c19">m2</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span></span>)</span>,<font color="Maroon" title="c13">phi1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> is <font color="Maroon" title="c19">m2</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1,<span class="p1"><a href="lang1.html#K4" title="LANG1:func.4">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c22">H11</font>,<font color="Maroon" title="c13">phi1</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="lang1.html#K4" title="LANG1:func.4">}</a></span>,<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#K23" title="FOMODEL4:func.23">R1</a> <font color="Maroon" title="c2">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> 
 
;<br/>
<a NAME="E23:191"/><span class="kw">then </span>
<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="c22">H11</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p3">(<span class="default"><font color="Maroon" title="c23">H22</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">phi</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span></span>)</span>,<font color="Maroon" title="c13">phi1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> is <font color="Maroon" title="c17">m1</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c19">m2</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span>, <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<font color="Maroon" title="c4">D</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</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#K23" title="FOMODEL4:func.23">R1</a> <font color="Maroon" title="c2">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="#E7:191"><span class="lab"><font color="Green" title="E108">B1</font></span></a>, <a class="txt" href="fomodel4.html#E38"><span class="lab"><font color="Green" title="E33">Lm28</font></span></a>, <a class="txt" href="#E1:191"><span class="lab"><font color="Green" title="E106">B10</font></span></a></span>;<br/>
<a NAME="E24:191"/><span class="kw">then </span>
<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="c28">H</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="c3">phi</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span>,<font color="Maroon" title="c13">phi1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> is <span class="p1">(<span class="default"><font color="Maroon" title="c17">m1</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c19">m2</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1, <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<font color="Maroon" title="c4">D</font> <a href="fomodel4.html#K41" title="FOMODEL4:func.41">null</a> <font color="Maroon" title="c11">F1</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T4" title="XBOOLE_1:th.4">XBOOLE_1:4</a></span>;<br/>
<a NAME="E25:191"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c29">h</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c30">hp</font></span>)</span> <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="c3">phi</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span>,<font color="Maroon" title="c13">phi1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> is <span class="p1">(<span class="default"><font color="Maroon" title="c17">m1</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c19">m2</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1, <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<font color="Maroon" title="c4">D</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel0.html#T48" title="FOMODEL0:th.48">FOMODEL0:48</a></span>;<br/>
<a NAME="E26:191"/><span class="kw">then </span><span class="lab"><font color="Green" title="E110">BB3</font></span>: 
<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="c29">h</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p3">(<span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">phi</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="fomodel4.html#K40" title="FOMODEL4:func.40">null</a> <font color="Maroon" title="c30">hp</font></span>)</span></span>)</span>,<font color="Maroon" title="c13">phi1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> is <span class="p1">(<span class="default"><font color="Maroon" title="c17">m1</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c19">m2</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1, <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<font color="Maroon" title="c4">D</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T4" title="XBOOLE_1:th.4">XBOOLE_1:4</a></span>;<br/>
<a NAME="E27:191"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c23">H22</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p4">(<span class="default"><font color="Maroon" title="c22">H11</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">phi</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span></span>)</span> <a href="fomodel0.html#K13" title="FOMODEL0:func.13">null</a> <span class="p3">(<span class="default"><font color="Maroon" title="c17">m1</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><span class="p5">(<span class="default"><a href="fomodel2.html#K1" title="FOMODEL2:func.1">TheNorSymbOf</a> <font color="Maroon" title="c2">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="c13">phi1</font></span>)</span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c14">phi2</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> is <font color="Maroon" title="c17">m1</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1,<span class="p1"><a href="lang1.html#K4" title="LANG1:func.4">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c23">H22</font>,<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#K1" title="FOMODEL2:func.1">TheNorSymbOf</a> <font color="Maroon" title="c2">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="c13">phi1</font></span>)</span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c14">phi2</font></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="lang1.html#K4" title="LANG1:func.4">}</a></span>,<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#K23" title="FOMODEL4:func.23">R1</a> <font color="Maroon" title="c2">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> 
 
;<br/>
<a NAME="E28:191"/><span class="kw">then </span>
<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="c23">H22</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p3">(<span class="default"><font color="Maroon" title="c22">H11</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">phi</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><span class="p5">(<span class="default"><a href="fomodel2.html#K1" title="FOMODEL2:func.1">TheNorSymbOf</a> <font color="Maroon" title="c2">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="c13">phi1</font></span>)</span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c14">phi2</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> is <font color="Maroon" title="c19">m2</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">m1</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span>, <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<font color="Maroon" title="c4">D</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</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#K23" title="FOMODEL4:func.23">R1</a> <font color="Maroon" title="c2">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="#E9:191"><span class="lab"><font color="Green" title="E109">B2</font></span></a>, <a class="txt" href="fomodel4.html#E38"><span class="lab"><font color="Green" title="E33">Lm28</font></span></a>, <a class="txt" href="#E1:191"><span class="lab"><font color="Green" title="E106">B10</font></span></a></span>;<br/>
<a NAME="E29:191"/><span class="kw">then </span>
<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="c28">H</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="c3">phi</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><span class="p5">(<span class="default"><a href="fomodel2.html#K1" title="FOMODEL2:func.1">TheNorSymbOf</a> <font color="Maroon" title="c2">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="c13">phi1</font></span>)</span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c14">phi2</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> is <span class="p1">(<span class="default"><font color="Maroon" title="c17">m1</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c19">m2</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1, <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<font color="Maroon" title="c4">D</font> <a href="fomodel4.html#K41" title="FOMODEL4:func.41">null</a> <font color="Maroon" title="c11">F1</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T4" title="XBOOLE_1:th.4">XBOOLE_1:4</a></span>;<br/>
<a NAME="E30:191"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c29">h</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c30">hp</font></span>)</span> <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="c3">phi</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><span class="p5">(<span class="default"><a href="fomodel2.html#K1" title="FOMODEL2:func.1">TheNorSymbOf</a> <font color="Maroon" title="c2">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="c13">phi1</font></span>)</span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c14">phi2</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> is <span class="p1">(<span class="default"><font color="Maroon" title="c17">m1</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c19">m2</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1, <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<font color="Maroon" title="c4">D</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel0.html#T48" title="FOMODEL0:th.48">FOMODEL0:48</a></span>;<br/>
<a NAME="E31:191"/><span class="kw">then </span><span class="lab"><font color="Green" title="E111">BB4</font></span>: 
<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="c29">h</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p3">(<span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">phi</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="fomodel4.html#K40" title="FOMODEL4:func.40">null</a> <font color="Maroon" title="c30">hp</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><span class="p5">(<span class="default"><a href="fomodel2.html#K1" title="FOMODEL2:func.1">TheNorSymbOf</a> <font color="Maroon" title="c2">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="c13">phi1</font></span>)</span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c14">phi2</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> is <span class="p1">(<span class="default"><font color="Maroon" title="c17">m1</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c19">m2</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1, <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<font color="Maroon" title="c4">D</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T4" title="XBOOLE_1:th.4">XBOOLE_1:4</a></span>;<br/>
<a NAME="E32:191"/>
<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="c29">h</font> <a href="fomodel0.html#K13" title="FOMODEL0:func.13">null</a> <span class="p3">(<span class="default"><font color="Maroon" title="c13">phi1</font> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c14">phi2</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel2.html#K38" title="FOMODEL2:func.38">xnot</a> <font color="Maroon" title="c3">phi</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> is 1,<span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c29">h</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">phi</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span>,<font color="Maroon" title="c13">phi1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c29">h</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">phi</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span>,<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#K1" title="FOMODEL2:func.1">TheNorSymbOf</a> <font color="Maroon" title="c2">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="c13">phi1</font></span>)</span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c14">phi2</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<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#K33" title="FOMODEL4:func.33">R8</a> <font color="Maroon" title="c2">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> 
 
;<br/>
<a NAME="E33:191"/><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="c29">h</font>,<span class="p2">(<span class="default"><a href="fomodel2.html#K38" title="FOMODEL2:func.38">xnot</a> <font color="Maroon" title="c3">phi</font></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> is <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c17">m1</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c19">m2</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1,<font color="Maroon" title="c34">e</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c34">e</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">D</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c4">D</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</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#K33" title="FOMODEL4:func.33">R8</a> <font color="Maroon" title="c2">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="#E26:191"><span class="lab"><font color="Green" title="E110">BB3</font></span></a>, <a class="txt" href="#E31:191"><span class="lab"><font color="Green" title="E111">BB4</font></span></a>, <a class="txt" href="fomodel4.html#E109"><span class="lab"><font color="Green" title="E88">Lm40</font></span></a>, <a class="txt" href="#E1:191"><span class="lab"><font color="Green" title="E106">B10</font></span></a></span>;<br/>
<a NAME="E34:191"/><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="c29">h</font>,<span class="p2">(<span class="default"><a href="fomodel2.html#K38" title="FOMODEL2:func.38">xnot</a> <font color="Maroon" title="c3">phi</font></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> is <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c17">m1</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c19">m2</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1, <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<font color="Maroon" title="c4">D</font> <a href="fomodel4.html#K41" title="FOMODEL4:func.41">null</a> <font color="Maroon" title="c12">F8</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</a> 
 
;<br/>
<span class="kw">hence </span><a NAME="E35:191"/>
 <a href="fomodel2.html#K38" title="FOMODEL2:func.38">xnot</a> <font color="Maroon" title="c3">phi</font> is <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c4">D</font> <a href="fomodel4.html#V8" title="FOMODEL4:attr.8">-provable</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel4.html#D62" target="_self" title="FOMODEL4:def.62">DefProvable3</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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