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<span class="kw">let </span><font color="Maroon" title="c1">m</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</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><br/>  for <font color="Olive" title="b4">SQ1</font>, <font color="Olive" title="b5">SQ2</font> being  <font color="Olive">b<sub>1</sub></font> <a href="fomodel4.html#V2" title="FOMODEL4:attr.2">-sequents-like</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b4">SQ1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b5">SQ2</font> &amp; <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>  ) holds <br/><span class="p1">(<span class="default">(<font color="Maroon" title="c1">m</font>,<font color="Olive" title="b2">D1</font>) <a href="fomodel4.html#K3" title="FOMODEL4:func.3">-derivables</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">SQ1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c1">m</font>,<font color="Olive" title="b3">D2</font>) <a href="fomodel4.html#K3" title="FOMODEL4:func.3">-derivables</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">SQ2</font></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">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="c2">S</font><br/>  for <font color="Olive" title="b3">SQ1</font>, <font color="Olive" title="b4">SQ2</font> being  <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>   st <font color="Olive" title="b3">SQ1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b4">SQ2</font> &amp; <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>  ) holds <br/><span class="p1">(<span class="default">(<font color="Maroon" title="c1">m</font>,<font color="Olive" title="b1">D1</font>) <a href="fomodel4.html#K3" title="FOMODEL4:func.3">-derivables</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">SQ1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c1">m</font>,<font color="Olive" title="b2">D2</font>) <a href="fomodel4.html#K3" title="FOMODEL4:func.3">-derivables</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">SQ2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">D1</font>, <font color="Maroon" title="c4">D2</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">SQ1</font>, <font color="Olive" title="b2">SQ2</font> being  <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>   st <font color="Olive" title="b1">SQ1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">SQ2</font> &amp; <font color="Maroon" title="c3">D1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">D2</font> &amp; ( <font color="Maroon" title="c4">D2</font> is  <a href="fomodel4.html#V6" title="FOMODEL4:attr.6">isotone</a>  or <font color="Maroon" title="c3">D1</font> is  <a href="fomodel4.html#V6" title="FOMODEL4:attr.6">isotone</a>  ) holds <br/><span class="p1">(<span class="default">(<font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c3">D1</font>) <a href="fomodel4.html#K3" title="FOMODEL4:func.3">-derivables</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">SQ1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c4">D2</font>) <a href="fomodel4.html#K3" title="FOMODEL4:func.3">-derivables</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">SQ2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">SQ1</font>, <font color="Maroon" title="c6">SQ2</font> be  <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> ; <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="c5">SQ1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">SQ2</font> &amp; <font color="Maroon" title="c3">D1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">D2</font> &amp; ( <font color="Maroon" title="c4">D2</font> is  <a href="fomodel4.html#V6" title="FOMODEL4:attr.6">isotone</a>  or <font color="Maroon" title="c3">D1</font> is  <a href="fomodel4.html#V6" title="FOMODEL4:attr.6">isotone</a>  ) implies <span class="p1">(<span class="default">(<font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c3">D1</font>) <a href="fomodel4.html#K3" title="FOMODEL4:func.3">-derivables</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">SQ1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c4">D2</font>) <a href="fomodel4.html#K3" title="FOMODEL4:func.3">-derivables</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">SQ2</font> )</span><br/>











<span class="kw">reconsider </span><font color="Maroon" title="c7">Seqts1</font> = <font color="Maroon" title="c5">SQ1</font>, <font color="Maroon" title="c8">Seqts2</font> = <font color="Maroon" title="c6">SQ2</font> as   <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> <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel4.html#D3" target="_self" title="FOMODEL4:def.3">DefSeqtLike2</a></span>;<br/>
<span class="kw">assume </span><a NAME="E2:63"/>
( <font color="Maroon" title="c5">SQ1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">SQ2</font> &amp; <font color="Maroon" title="c3">D1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">D2</font> &amp; ( <font color="Maroon" title="c4">D2</font> is  <a href="fomodel4.html#V6" title="FOMODEL4:attr.6">isotone</a>  or <font color="Maroon" title="c3">D1</font> is  <a href="fomodel4.html#V6" title="FOMODEL4:attr.6">isotone</a>  ) )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default">(<font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c3">D1</font>) <a href="fomodel4.html#K3" title="FOMODEL4:func.3">-derivables</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">SQ1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c4">D2</font>) <a href="fomodel4.html#K3" title="FOMODEL4:func.3">-derivables</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">SQ2</font></span><br/>

<a NAME="E3:63"/><span class="kw">then </span>
<span class="p1">(<span class="default">(<font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c3">D1</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="c7">Seqts1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c4">D2</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="c8">Seqts2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="fomodel4.html#E31"><span class="lab"><font color="Green" title="E26">Lm15</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:63"/>
<span class="p1">(<span class="default">(<font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c3">D1</font>) <a href="fomodel4.html#K3" title="FOMODEL4:func.3">-derivables</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">SQ1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c4">D2</font>) <a href="fomodel4.html#K3" title="FOMODEL4:func.3">-derivables</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">SQ2</font>
 ; <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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