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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="Maroon" title="c1">X</font> is <font color="Olive" title="b3">D</font> <a href="fomodel4.html#V14" title="FOMODEL4:attr.14">-inconsistent</a>  &amp; <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> 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="Maroon" title="c1">X</font> is <font color="Olive" title="b2">D</font> <a href="fomodel4.html#V14" title="FOMODEL4:attr.14">-inconsistent</a>  &amp; <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> 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="Maroon" title="c1">X</font> is <font color="Olive" title="b1">D</font> <a href="fomodel4.html#V14" title="FOMODEL4:attr.14">-inconsistent</a>  &amp; <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> 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="c1">X</font> is <font color="Maroon" title="c4">D</font> <a href="fomodel4.html#V14" title="FOMODEL4:attr.14">-inconsistent</a>  &amp; <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> 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">N</font> =  <a href="fomodel2.html#K1" title="FOMODEL2:func.1">TheNorSymbOf</a> <font color="Maroon" title="c2">S</font>;<br/>
<span class="kw">assume </span><a NAME="E1:177"/>
<font color="Maroon" title="c1">X</font> 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"> (  not <font color="Maroon" title="c4">D</font> is  <a href="fomodel4.html#V6" title="FOMODEL4:attr.6">isotone</a>  or  not  <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> or  not  <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> 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">consider </span><font color="Maroon" title="c6">phi1</font>, <font color="Maroon" title="c7">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="E3:177"/><span class="lab"><font color="Green" title="E99">B0</font></span>: 
( <font color="Maroon" title="c6">phi1</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>  &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="c6">phi1</font></span>)</span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c7">phi2</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#D65" target="_self" title="FOMODEL4:def.65">DefInc</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c8">psi</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="c6">phi1</font></span>)</span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c7">phi2</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="c2">S</font> ;<br/>
<span class="kw">consider </span><font color="Maroon" title="c9">H</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> , <font color="Maroon" title="c10">m</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><span class="kw"> such that </span><br/><a NAME="E6:177"/><span class="lab"><font color="Green" title="E100">B1</font></span>: 
( <font color="Maroon" title="c9">H</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">X</font> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c9">H</font>,<font color="Maroon" title="c6">phi1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> is <font color="Maroon" title="c10">m</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="txt" href="#E3:177"><span class="lab"><font color="Green" title="E99">B0</font></span></a>, <a class="ref" href="fomodel4.html#D62" target="_self" title="FOMODEL4:def.62">DefProvable3</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c11">K</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> , <font color="Maroon" title="c12">n</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><span class="kw"> such that </span><br/><a NAME="E8:177"/><span class="lab"><font color="Green" title="E101">B2</font></span>: 
( <font color="Maroon" title="c11">K</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">X</font> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c11">K</font>,<font color="Maroon" title="c8">psi</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> is <font color="Maroon" title="c12">n</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="txt" href="#E3:177"><span class="lab"><font color="Green" title="E99">B0</font></span></a>, <a class="ref" href="fomodel4.html#D62" target="_self" title="FOMODEL4:def.62">DefProvable3</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c13">HHH</font> = <font color="Maroon" title="c9">H</font>, <font color="Maroon" title="c14">KKK</font> = <font color="Maroon" title="c11">K</font> as   <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="txt" href="#E6:177"><span class="lab"><font color="Green" title="E100">B1</font></span></a>, <a class="txt" href="#E8:177"><span class="lab"><font color="Green" title="E101">B2</font></span></a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c15">sq1</font> = <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c9">H</font>,<font color="Maroon" title="c6">phi1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>, <font color="Maroon" title="c16">sq2</font> = <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c11">K</font>,<font color="Maroon" title="c8">psi</font></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="#E6:177"><span class="lab"><font color="Green" title="E100">B1</font></span></a>, <a class="txt" href="#E8:177"><span class="lab"><font color="Green" title="E101">B2</font></span></a></span>;<br/>
<a NAME="E11:177"/>
( <font color="Maroon" title="c9">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">sq1</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  &amp; <font color="Maroon" title="c11">K</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">sq2</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  )
 
<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/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c17">HH</font> = <font color="Maroon" title="c9">H</font>, <font color="Maroon" title="c18">KK</font> = <font color="Maroon" title="c11">K</font> 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="c19">J</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c17">HH</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c18">KK</font></span>)</span> <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">assume </span><a NAME="E14:177"/><span class="lab"><font color="Green" title="E102">B3</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">  <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="c20">DD</font> = <font color="Maroon" title="c4">D</font> as   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="fomodel4.html#V6" title="FOMODEL4:attr.6">isotone</a>  <a href="fomodel4.html#NM2" title="FOMODEL4:NM.2">RuleSet</a> of <font color="Maroon" title="c2">S</font> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c21">E1</font> =  <a href="fomodel4.html#K23" title="FOMODEL4:func.23">R1</a> <font color="Maroon" title="c2">S</font>, <font color="Maroon" title="c22">E8</font> =  <a href="fomodel4.html#K33" title="FOMODEL4:func.33">R8</a> <font color="Maroon" title="c2">S</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c20">DD</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:177"><span class="lab"><font color="Green" title="E102">B3</font></span></a></span>;<br/>
<a NAME="E17:177"/><span class="lab"><font color="Green" title="E103">B4</font></span>: 
( <font color="Maroon" title="c20">DD</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="c21">E1</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">DD</font> <a href="fomodel4.html#K41" title="FOMODEL4:func.41">null</a> <font color="Maroon" title="c21">E1</font> &amp; <font color="Maroon" title="c20">DD</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="c22">E8</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">DD</font> <a href="fomodel4.html#K41" title="FOMODEL4:func.41">null</a> <font color="Maroon" title="c22">E8</font> &amp; <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> is  <a href="fomodel4.html#V6" title="FOMODEL4:attr.6">isotone</a>  &amp; <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> is  <a href="fomodel4.html#V6" title="FOMODEL4:attr.6">isotone</a>  &amp;  not <font color="Maroon" title="c4">D</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  &amp; <font color="Maroon" title="c13">HHH</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c14">KKK</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">X</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:177"><span class="lab"><font color="Green" title="E102">B3</font></span></a></span>;<br/>
<a NAME="E18:177"/><span class="lab"><font color="Green" title="E104">B7</font></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="c19">J</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c19">J</font></span>)</span> <a href="fomodel0.html#K13" title="FOMODEL0:func.13">null</a> <span class="p3">(<span class="default"><font color="Maroon" title="c12">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span></span>)</span>,<font color="Maroon" title="c6">phi1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> is <font color="Maroon" title="c12">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1,<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"><font color="Maroon" title="c19">J</font>,<font color="Maroon" title="c6">phi1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</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>  &amp; <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="c19">J</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c19">J</font></span>)</span> <a href="fomodel0.html#K13" title="FOMODEL0:func.13">null</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">m</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span></span>)</span>,<font color="Maroon" title="c8">psi</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> is <font color="Maroon" title="c10">m</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1,<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"><font color="Maroon" title="c19">J</font>,<font color="Maroon" title="c8">psi</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</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="E19:177"/>
<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="c17">HH</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p3">(<span class="default"><font color="Maroon" title="c18">KK</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="c6">phi1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> is <font color="Maroon" title="c10">m</font> <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="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="fomodel4.html#E38"><span class="lab"><font color="Green" title="E33">Lm28</font></span></a>, <a class="txt" href="#E6:177"><span class="lab"><font color="Green" title="E100">B1</font></span></a>, <a class="txt" href="#E14:177"><span class="lab"><font color="Green" title="E102">B3</font></span></a></span>;<br/>
<a NAME="E20:177"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c19">J</font>,<font color="Maroon" title="c6">phi1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> is <font color="Maroon" title="c10">m</font> <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="txt" href="#E17:177"><span class="lab"><font color="Green" title="E103">B4</font></span></a>, <a class="ref" href="xboole_1.html#T4" title="XBOOLE_1:th.4">XBOOLE_1:4</a></span>;<br/>
<a NAME="E21:177"/><span class="kw">then </span><span class="lab"><font color="Green" title="E105">BB5</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c19">J</font>,<font color="Maroon" title="c6">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="c10">m</font> <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> <span class="p1">(<span class="default"><font color="Maroon" title="c12">n</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="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:177"><span class="lab"><font color="Green" title="E104">B7</font></span></a>, <a class="txt" href="#E17:177"><span class="lab"><font color="Green" title="E103">B4</font></span></a>, <a class="txt" href="fomodel4.html#E38"><span class="lab"><font color="Green" title="E33">Lm28</font></span></a></span>;<br/>
<a NAME="E22:177"/>
<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="c18">KK</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p3">(<span class="default"><font color="Maroon" title="c17">HH</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="c8">psi</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> is <font color="Maroon" title="c12">n</font> <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="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="fomodel4.html#E38"><span class="lab"><font color="Green" title="E33">Lm28</font></span></a>, <a class="txt" href="#E8:177"><span class="lab"><font color="Green" title="E101">B2</font></span></a>, <a class="txt" href="#E14:177"><span class="lab"><font color="Green" title="E102">B3</font></span></a></span>;<br/>
<a NAME="E23:177"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c19">J</font>,<font color="Maroon" title="c8">psi</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> is <font color="Maroon" title="c12">n</font> <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="txt" href="#E17:177"><span class="lab"><font color="Green" title="E103">B4</font></span></a>, <a class="ref" href="xboole_1.html#T4" title="XBOOLE_1:th.4">XBOOLE_1:4</a></span>;<br/>
<a NAME="E24:177"/><span class="kw">then </span><span class="lab"><font color="Green" title="E106">BB6</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c19">J</font>,<font color="Maroon" title="c8">psi</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> is <span class="p1">(<span class="default"><font color="Maroon" title="c12">n</font> <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> <span class="p1">(<span class="default"><font color="Maroon" title="c10">m</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="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:177"><span class="lab"><font color="Green" title="E104">B7</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="#E17:177"><span class="lab"><font color="Green" title="E103">B4</font></span></a></span>;<br/>
<a NAME="E25:177"/>
<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="c18">KK</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c17">HH</font></span>)</span> <a href="fomodel0.html#K13" title="FOMODEL0:func.13">null</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">phi1</font> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c7">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"><font color="Maroon" title="c19">J</font>,<font color="Maroon" title="c6">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"><font color="Maroon" title="c19">J</font>,<font color="Maroon" title="c8">psi</font></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="E26:177"/><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="c18">KK</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c17">HH</font></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 <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">m</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c12">n</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 2</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1,<span class="p1">(<span class="default"><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></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><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></span>)</span>,<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="fomodel4.html#E109"><span class="lab"><font color="Green" title="E88">Lm40</font></span></a>, <a class="txt" href="#E21:177"><span class="lab"><font color="Green" title="E105">BB5</font></span></a>, <a class="txt" href="#E24:177"><span class="lab"><font color="Green" title="E106">BB6</font></span></a>, <a class="txt" href="#E14:177"><span class="lab"><font color="Green" title="E102">B3</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E27:177"/>
 <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="txt" href="#E17:177"><span class="lab"><font color="Green" title="E103">B4</font></span></a>, <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/>


</div>
