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<span class="kw">let </span><font color="Maroon" title="c1">Y</font>, <font color="Maroon" title="c2">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">D1</font>, <font color="Olive" title="b3">D2</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="b2">D1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b3">D2</font> &amp; ( <font color="Olive" title="b3">D2</font> is  <a href="fomodel4.html#V6" title="FOMODEL4:attr.6">isotone</a>  or <font color="Olive" title="b2">D1</font> is  <a href="fomodel4.html#V6" title="FOMODEL4:attr.6">isotone</a>  ) &amp; <font color="Maroon" title="c1">Y</font> is <font color="Maroon" title="c2">X</font>,<font color="Olive" title="b2">D1</font> <a href="fomodel4.html#V3" title="FOMODEL4:attr.3">-derivable</a>  holds <br/><font color="Maroon" title="c1">Y</font> is <font color="Maroon" title="c2">X</font>,<font color="Olive" title="b3">D2</font> <a href="fomodel4.html#V3" title="FOMODEL4:attr.3">-derivable</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">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">D1</font>, <font color="Olive" title="b2">D2</font> being   <a href="fomodel4.html#NM2" title="FOMODEL4:NM.2">RuleSet</a> of <font color="Maroon" title="c3">S</font>  st <font color="Olive" title="b1">D1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">D2</font> &amp; ( <font color="Olive" title="b2">D2</font> is  <a href="fomodel4.html#V6" title="FOMODEL4:attr.6">isotone</a>  or <font color="Olive" title="b1">D1</font> is  <a href="fomodel4.html#V6" title="FOMODEL4:attr.6">isotone</a>  ) &amp; <font color="Maroon" title="c1">Y</font> is <font color="Maroon" title="c2">X</font>,<font color="Olive" title="b1">D1</font> <a href="fomodel4.html#V3" title="FOMODEL4:attr.3">-derivable</a>  holds <br/><font color="Maroon" title="c1">Y</font> is <font color="Maroon" title="c2">X</font>,<font color="Olive" title="b2">D2</font> <a href="fomodel4.html#V3" title="FOMODEL4:attr.3">-derivable</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c4">D1</font>, <font color="Maroon" title="c5">D2</font> be   <a href="fomodel4.html#NM2" title="FOMODEL4:NM.2">RuleSet</a> of <font color="Maroon" title="c3">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">D1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">D2</font> &amp; ( <font color="Maroon" title="c5">D2</font> is  <a href="fomodel4.html#V6" title="FOMODEL4:attr.6">isotone</a>  or <font color="Maroon" title="c4">D1</font> is  <a href="fomodel4.html#V6" title="FOMODEL4:attr.6">isotone</a>  ) &amp; <font color="Maroon" title="c1">Y</font> is <font color="Maroon" title="c2">X</font>,<font color="Maroon" title="c4">D1</font> <a href="fomodel4.html#V3" title="FOMODEL4:attr.3">-derivable</a>  implies <font color="Maroon" title="c1">Y</font> is <font color="Maroon" title="c2">X</font>,<font color="Maroon" title="c5">D2</font> <a href="fomodel4.html#V3" title="FOMODEL4:attr.3">-derivable</a>  )</span><br/>









<span class="kw">set </span><font color="Maroon" title="c6">O1</font> =  <a href="fomodel4.html#K2" title="FOMODEL4:func.2">OneStep</a> <font color="Maroon" title="c4">D1</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">O2</font> =  <a href="fomodel4.html#K2" title="FOMODEL4:func.2">OneStep</a> <font color="Maroon" title="c5">D2</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">Q</font> = <font color="Maroon" title="c3">S</font> <a href="fomodel4.html#K1" title="FOMODEL4:func.1">-sequents</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">LH</font> =  <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="c4">D1</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="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">X</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">RH</font> =  <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="c5">D2</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="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">X</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span>;<br/>
<span class="kw">assume </span><a NAME="E1:66"/>
( <font color="Maroon" title="c4">D1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">D2</font> &amp; ( <font color="Maroon" title="c5">D2</font> is  <a href="fomodel4.html#V6" title="FOMODEL4:attr.6">isotone</a>  or <font color="Maroon" title="c4">D1</font> is  <a href="fomodel4.html#V6" title="FOMODEL4:attr.6">isotone</a>  ) &amp; <font color="Maroon" title="c1">Y</font> is <font color="Maroon" title="c2">X</font>,<font color="Maroon" title="c4">D1</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"> <font color="Maroon" title="c1">Y</font> is <font color="Maroon" title="c2">X</font>,<font color="Maroon" title="c5">D2</font> <a href="fomodel4.html#V3" title="FOMODEL4:attr.3">-derivable</a> </span><br/>

<a NAME="E2:66"/><span class="kw">then </span>
(  <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="c4">D1</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="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">X</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</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="c5">D2</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="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">X</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> &amp; <font color="Maroon" title="c1">Y</font> <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="c4">D1</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="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">X</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</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>, <a class="txt" href="fomodel4.html#E34"><span class="lab"><font color="Green" title="E29">Lm19</font></span></a></span>;<br/>
<a NAME="E3:66"/><span class="kw">then </span>
<font color="Maroon" title="c1">Y</font> <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="c5">D2</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="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">X</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:66"/>
<font color="Maroon" title="c1">Y</font> is <font color="Maroon" title="c2">X</font>,<font color="Maroon" title="c5">D2</font> <a href="fomodel4.html#V3" title="FOMODEL4:attr.3">-derivable</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel4.html#D6" target="_self" title="FOMODEL4:def.6">DefDerivable</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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