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<span class="kw">let </span><font color="Maroon" title="c1">y</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">D</font> being   <a href="fomodel4.html#NM2" title="FOMODEL4:NM.2">RuleSet</a> of <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b3">Seqts</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Olive" title="b1">S</font> <a href="fomodel4.html#K1" title="FOMODEL4:func.1">-sequents</a></span>)</span>  st <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">y</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> is <font color="Olive" title="b3">Seqts</font>,<font color="Olive" title="b2">D</font> <a href="fomodel4.html#V3" title="FOMODEL4:attr.3">-derivable</a>  holds <br/> ex <font color="Olive" title="b4">mm</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <font color="Maroon" title="c1">y</font> is <font color="Olive" title="b4">mm</font>,<font color="Olive" title="b3">Seqts</font>,<font color="Olive" title="b2">D</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</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">D</font> being   <a href="fomodel4.html#NM2" title="FOMODEL4:NM.2">RuleSet</a> of <font color="Maroon" title="c2">S</font><br/>  for <font color="Olive" title="b2">Seqts</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="fomodel4.html#K1" title="FOMODEL4:func.1">-sequents</a></span>)</span>  st <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">y</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> is <font color="Olive" title="b2">Seqts</font>,<font color="Olive" title="b1">D</font> <a href="fomodel4.html#V3" title="FOMODEL4:attr.3">-derivable</a>  holds <br/> ex <font color="Olive" title="b3">mm</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <font color="Maroon" title="c1">y</font> is <font color="Olive" title="b3">mm</font>,<font color="Olive" title="b2">Seqts</font>,<font color="Olive" title="b1">D</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">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">  for <font color="Olive" title="b1">Seqts</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="fomodel4.html#K1" title="FOMODEL4:func.1">-sequents</a></span>)</span>  st <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">y</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> is <font color="Olive" title="b1">Seqts</font>,<font color="Maroon" title="c3">D</font> <a href="fomodel4.html#V3" title="FOMODEL4:attr.3">-derivable</a>  holds <br/> ex <font color="Olive" title="b2">mm</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <font color="Maroon" title="c1">y</font> is <font color="Olive" title="b2">mm</font>,<font color="Olive" title="b1">Seqts</font>,<font color="Maroon" title="c3">D</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c4">Seqts</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="fomodel4.html#K1" title="FOMODEL4:func.1">-sequents</a></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">y</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> is <font color="Maroon" title="c4">Seqts</font>,<font color="Maroon" title="c3">D</font> <a href="fomodel4.html#V3" title="FOMODEL4:attr.3">-derivable</a>  implies  ex <font color="Olive" title="b1">mm</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <font color="Maroon" title="c1">y</font> is <font color="Olive" title="b1">mm</font>,<font color="Maroon" title="c4">Seqts</font>,<font color="Maroon" title="c3">D</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</a>  )</span><br/>







<span class="kw">set </span><font color="Maroon" title="c5">X</font> = <font color="Maroon" title="c4">Seqts</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">Q</font> = <font color="Maroon" title="c2">S</font> <a href="fomodel4.html#K1" title="FOMODEL4:func.1">-sequents</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">O</font> =  <a href="fomodel4.html#K2" title="FOMODEL4:func.2">OneStep</a> <font color="Maroon" title="c3">D</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">I</font> = <font color="Maroon" title="c3">D</font> <a href="fomodel4.html#K4" title="FOMODEL4:func.4">-iterators</a> ;<br/>
<span class="kw">assume </span><a NAME="E1:56"/>
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">y</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> is <font color="Maroon" title="c4">Seqts</font>,<font color="Maroon" title="c3">D</font> <a href="fomodel4.html#V3" title="FOMODEL4:attr.3">-derivable</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">mm</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <font color="Maroon" title="c1">y</font> is <font color="Olive" title="b1">mm</font>,<font color="Maroon" title="c4">Seqts</font>,<font color="Maroon" title="c3">D</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</a> </span><br/>

<a NAME="E2:56"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">y</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="fomodel4.html#K2" title="FOMODEL4:func.2">OneStep</a> <font color="Maroon" title="c3">D</font></span>)</span> <a href="lang1.html#K13" title="LANG1:func.13">[*]</a></span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">Seqts</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="ref" href="fomodel4.html#D6" target="_self" title="FOMODEL4:def.6">DefDerivable</a></span>;<br/>
<a NAME="E3:56"/><span class="kw">then </span>
<font color="Maroon" title="c1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="fomodel4.html#K2" title="FOMODEL4:func.2">OneStep</a> <font color="Maroon" title="c3">D</font></span>)</span> <a href="lang1.html#K13" title="LANG1:func.13">[*]</a></span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">Seqts</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="ref" href="zfmisc_1.html#T31" title="ZFMISC_1:th.31">ZFMISC_1:31</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c9">Y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E5:56"/><span class="lab"><font color="Green" title="E21">B0</font></span>: 
( <font color="Maroon" title="c1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">Y</font> &amp; <font color="Maroon" title="c9">Y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="fomodel4.html#K2" title="FOMODEL4:func.2">OneStep</a> <font color="Maroon" title="c3">D</font></span>)</span> <a href="lang1.html#K13" title="LANG1:func.13">[*]</a></span>)</span> <a href="relset_1.html#K7" title="RELSET_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="c4">Seqts</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="tarski.html#D4" title="TARSKI:def.4">TARSKI:def 4</a></span>;<br/>
<a NAME="E6:56"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="fomodel4.html#K2" title="FOMODEL4:func.2">OneStep</a> <font color="Maroon" title="c3">D</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="fomodel4.html#K2" title="FOMODEL4:func.2">OneStep</a> <font color="Maroon" title="c3">D</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="fomodel4.html#E7"><span class="lab"><font color="Green" title="E6">Lm4</font></span></a></span>;<br/>
<a NAME="E7:56"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="fomodel4.html#K2" title="FOMODEL4:func.2">OneStep</a> <font color="Maroon" title="c3">D</font></span>)</span> <a href="lang1.html#K13" title="LANG1:func.13">[*]</a>  <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">D</font> <a href="fomodel4.html#K4" title="FOMODEL4:func.4">-iterators</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel0.html#T17" title="FOMODEL0:th.17">FOMODEL0:17</a></span>;<br/>
<a NAME="E8:56"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="fomodel4.html#K2" title="FOMODEL4:func.2">OneStep</a> <font color="Maroon" title="c3">D</font></span>)</span> <a href="lang1.html#K13" title="LANG1:func.13">[*]</a></span>)</span> <a href="relset_1.html#K7" title="RELSET_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="c4">Seqts</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>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b1">R</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">Seqts</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> where <font color="Olive" title="b1">R</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1"><a href="mcart_1.html#K12" title="MCART_1:func.12">[:</a><span class="default"><span class="p2">(<span class="default"><a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="fomodel4.html#K1" title="FOMODEL4:func.1">-sequents</a></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="fomodel4.html#K1" title="FOMODEL4:func.1">-sequents</a></span>)</span></span>)</span></span><a href="mcart_1.html#K12" title="MCART_1:func.12">:]</a></span> : <font color="Olive" title="b1">R</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">D</font> <a href="fomodel4.html#K4" title="FOMODEL4:func.4">-iterators</a>  </span> } </span> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relset_2.html#T34" title="RELSET_2:th.34">RELSET_2:34</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c10">Z</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E10:56"/><span class="lab"><font color="Green" title="E22">B1</font></span>: 
( <font color="Maroon" title="c9">Y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">Z</font> &amp; <font color="Maroon" title="c10">Z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b1">R</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">Seqts</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> where <font color="Olive" title="b1">R</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1"><a href="mcart_1.html#K12" title="MCART_1:func.12">[:</a><span class="default"><span class="p2">(<span class="default"><a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="fomodel4.html#K1" title="FOMODEL4:func.1">-sequents</a></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="fomodel4.html#K1" title="FOMODEL4:func.1">-sequents</a></span>)</span></span>)</span></span><a href="mcart_1.html#K12" title="MCART_1:func.12">:]</a></span> : <font color="Olive" title="b1">R</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">D</font> <a href="fomodel4.html#K4" title="FOMODEL4:func.4">-iterators</a>  </span> } </span>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:56"><span class="lab"><font color="Green" title="E21">B0</font></span></a>, <a class="ref" href="tarski.html#D4" title="TARSKI:def.4">TARSKI:def 4</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c11">f</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1"><a href="mcart_1.html#K12" title="MCART_1:func.12">[:</a><span class="default"><span class="p2">(<span class="default"><a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="fomodel4.html#K1" title="FOMODEL4:func.1">-sequents</a></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="fomodel4.html#K1" title="FOMODEL4:func.1">-sequents</a></span>)</span></span>)</span></span><a href="mcart_1.html#K12" title="MCART_1:func.12">:]</a></span><span class="kw"> such that </span><br/><a NAME="E12:56"/><span class="lab"><font color="Green" title="E23">B2</font></span>: 
( <font color="Maroon" title="c10">Z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">f</font> <a href="relset_1.html#K7" title="RELSET_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="c4">Seqts</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp; <font color="Maroon" title="c11">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">D</font> <a href="fomodel4.html#K4" title="FOMODEL4:func.4">-iterators</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:56"><span class="lab"><font color="Green" title="E22">B1</font></span></a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c12">mm</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <span class="kw"> such that </span><br/><a NAME="E14:56"/><span class="lab"><font color="Green" title="E24">B3</font></span>: 
<font color="Maroon" title="c11">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_7.html#K9" title="FUNCT_7:func.9">iter</a> (<span class="p1">(<span class="default"><a href="fomodel4.html#K2" title="FOMODEL4:func.2">OneStep</a> <font color="Maroon" title="c3">D</font></span>)</span>,<font color="Maroon" title="c12">mm</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:56"><span class="lab"><font color="Green" title="E23">B2</font></span></a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c12">mm</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">y</font> is <font color="Maroon" title="c12">mm</font>,<font color="Maroon" title="c4">Seqts</font>,<font color="Maroon" title="c3">D</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</a> </span><br/>

<a NAME="E15:56"/>
 <a href="funct_7.html#K9" title="FUNCT_7:func.9">iter</a> (<span class="p1">(<span class="default"><a href="fomodel4.html#K2" title="FOMODEL4:func.2">OneStep</a> <font color="Maroon" title="c3">D</font></span>)</span>,<font color="Maroon" title="c12">mm</font>) is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="fomodel4.html#K1" title="FOMODEL4:func.1">-sequents</a></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="fomodel4.html#K1" title="FOMODEL4:func.1">-sequents</a></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_7.html#T83" title="FUNCT_7:th.83">FUNCT_7:83</a></span>;<br/>
<a NAME="E16:56"/><span class="kw">then </span><span class="lab"><font color="Green" title="E25">BB4</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="funct_7.html#K9" title="FUNCT_7:func.9">iter</a> (<span class="p2">(<span class="default"><a href="fomodel4.html#K2" title="FOMODEL4:func.2">OneStep</a> <font color="Maroon" title="c3">D</font></span>)</span>,<font color="Maroon" title="c12">mm</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="fomodel4.html#K1" title="FOMODEL4:func.1">-sequents</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E17:56"/>
( <font color="Maroon" title="c1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">Y</font> &amp; <font color="Maroon" title="c9">Y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K11" title="RELAT_1:func.11">Im</a> (<span class="p1">(<span class="default"><a href="funct_7.html#K9" title="FUNCT_7:func.9">iter</a> (<span class="p2">(<span class="default"><a href="fomodel4.html#K2" title="FOMODEL4:func.2">OneStep</a> <font color="Maroon" title="c3">D</font></span>)</span>,<font color="Maroon" title="c12">mm</font>)</span>)</span>,<font color="Maroon" title="c4">Seqts</font>) )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:56"><span class="lab"><font color="Green" title="E21">B0</font></span></a>, <a class="txt" href="#E10:56"><span class="lab"><font color="Green" title="E22">B1</font></span></a>, <a class="txt" href="#E14:56"><span class="lab"><font color="Green" title="E24">B3</font></span></a>, <a class="txt" href="#E12:56"><span class="lab"><font color="Green" title="E23">B2</font></span></a></span>;<br/>
<a NAME="E18:56"/><span class="kw">then </span>
( <font color="Maroon" title="c1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">Y</font> &amp; <font color="Maroon" title="c9">Y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="funct_7.html#K9" title="FUNCT_7:func.9">iter</a> (<span class="p4">(<span class="default"><a href="fomodel4.html#K2" title="FOMODEL4:func.2">OneStep</a> <font color="Maroon" title="c3">D</font></span>)</span>,<font color="Maroon" title="c12">mm</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">Seqts</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:56"><span class="lab"><font color="Green" title="E25">BB4</font></span></a>, <a class="ref" href="funct_1.html#T59" title="FUNCT_1:th.59">FUNCT_1:59</a></span>;<br/>
<a NAME="E19:56"/><span class="kw">then </span>
<font color="Maroon" title="c1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c12">mm</font>,<font color="Maroon" title="c3">D</font>) <a href="fomodel4.html#K3" title="FOMODEL4:func.3">-derivables</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">Seqts</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E20:56"/>
<font color="Maroon" title="c1">y</font> is <font color="Maroon" title="c12">mm</font>,<font color="Maroon" title="c4">Seqts</font>,<font color="Maroon" title="c3">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#D7" target="_self" title="FOMODEL4:def.7">DefDerivable3</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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