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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">x</font>, <font color="Olive" title="b2">X</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <br/>  for <font color="Olive" title="b3">S</font> being   <a href="fomodel1.html#NM2" title="FOMODEL1:NM.2">Language</a><br/>  for <font color="Olive" title="b4">D1</font>, <font color="Olive" title="b5">D2</font> being   <a href="fomodel4.html#NM2" title="FOMODEL4:NM.2">RuleSet</a> of <font color="Olive" title="b3">S</font>  st <font color="Olive" title="b4">D1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b5">D2</font> &amp; ( <font color="Olive" title="b5">D2</font> is  <a href="fomodel4.html#V6" title="FOMODEL4:attr.6">isotone</a>  or <font color="Olive" title="b4">D1</font> is  <a href="fomodel4.html#V6" title="FOMODEL4:attr.6">isotone</a>  ) &amp; <font color="Olive" title="b1">x</font> is <font color="Maroon" title="c1">m</font>,<font color="Olive" title="b2">X</font>,<font color="Olive" title="b4">D1</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</a>  holds <br/><font color="Olive" title="b1">x</font> is <font color="Maroon" title="c1">m</font>,<font color="Olive" title="b2">X</font>,<font color="Olive" title="b5">D2</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">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="c2">x</font> is <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c3">X</font>,<font color="Olive" title="b2">D1</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</a>  holds <br/><font color="Maroon" title="c2">x</font> is <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c3">X</font>,<font color="Olive" title="b3">D2</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c4">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="c4">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="c2">x</font> is <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c3">X</font>,<font color="Olive" title="b1">D1</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</a>  holds <br/><font color="Maroon" title="c2">x</font> is <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c3">X</font>,<font color="Olive" title="b2">D2</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c5">D1</font>, <font color="Maroon" title="c6">D2</font> be   <a href="fomodel4.html#NM2" title="FOMODEL4:NM.2">RuleSet</a> of <font color="Maroon" title="c4">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="c5">D1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">D2</font> &amp; ( <font color="Maroon" title="c6">D2</font> is  <a href="fomodel4.html#V6" title="FOMODEL4:attr.6">isotone</a>  or <font color="Maroon" title="c5">D1</font> is  <a href="fomodel4.html#V6" title="FOMODEL4:attr.6">isotone</a>  ) &amp; <font color="Maroon" title="c2">x</font> is <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c5">D1</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</a>  implies <font color="Maroon" title="c2">x</font> is <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c6">D2</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</a>  )</span><br/>











<span class="kw">set </span><font color="Maroon" title="c7">f1</font> = (<font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c5">D1</font>) <a href="fomodel4.html#K3" title="FOMODEL4:func.3">-derivables</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">f2</font> = (<font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c6">D2</font>) <a href="fomodel4.html#K3" title="FOMODEL4:func.3">-derivables</a> ;<br/>
<span class="kw">assume </span><a NAME="E1:144"/>
( <font color="Maroon" title="c5">D1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">D2</font> &amp; ( <font color="Maroon" title="c6">D2</font> is  <a href="fomodel4.html#V6" title="FOMODEL4:attr.6">isotone</a>  or <font color="Maroon" title="c5">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"> (  not <font color="Maroon" title="c2">x</font> is <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c5">D1</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</a>  or <font color="Maroon" title="c2">x</font> is <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c6">D2</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</a>  )</span><br/>

<a NAME="E2:144"/><span class="kw">then </span><span class="lab"><font color="Green" title="E96">B0</font></span>: 
<span class="p1">(<span class="default">(<font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c5">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="c3">X</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="c6">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="c3">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="fomodel4.html#E33"><span class="lab"><font color="Green" title="E28">Lm17</font></span></a></span>;<br/>
<span class="kw">assume </span><a NAME="E3:144"/>
<font color="Maroon" title="c2">x</font> is <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c5">D1</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-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="c2">x</font> is <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c6">D2</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</a> </span><br/>

<a NAME="E4:144"/><span class="kw">then </span>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c5">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="c3">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel4.html#D7" target="_self" title="FOMODEL4:def.7">DefDerivable3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:144"/>
<font color="Maroon" title="c2">x</font> is <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c6">D2</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>, <a class="txt" href="#E2:144"><span class="lab"><font color="Green" title="E96">B0</font></span></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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