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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">l</font> being   <a href="fomodel1.html#V4" title="FOMODEL1:attr.4">literal</a>  <a href="fomodel1.html#NM1" title="FOMODEL1:NM.1">Element</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 <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><span class="p2">(<span class="default"><a href="fomodel4.html#K22" title="FOMODEL4:func.22">R0</a> <font color="Olive" title="b1">S</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel4.html#K25" title="FOMODEL4:func.25">R3a</a> <font color="Olive" title="b1">S</font></span>)</span></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b3">D</font> &amp; <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><span class="p2">(<span class="default"><a href="fomodel4.html#K24" title="FOMODEL4:func.24">R2</a> <font color="Olive" title="b1">S</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel4.html#K26" title="FOMODEL4:func.26">R3b</a> <font color="Olive" title="b1">S</font></span>)</span></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b3">D</font> &amp; <font color="Maroon" title="c1">X</font> is <font color="Olive" title="b3">D</font> <a href="fomodel4.html#V10" title="FOMODEL4:attr.10">-expanded</a>  holds <br/><font color="Maroon" title="c1">X</font> <a href="fomodel3.html#K4" title="FOMODEL3:func.4">-freeInterpreter</a> <font color="Olive" title="b2">l</font> is (<font color="Maroon" title="c1">X</font>,<font color="Olive" title="b3">D</font>) <a href="fomodel4.html#K6" title="FOMODEL4:func.6">-termEq</a>  <a href="fomodel3.html#V2" title="FOMODEL3:attr.2">-respecting</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">l</font> being   <a href="fomodel1.html#V4" title="FOMODEL1:attr.4">literal</a>  <a href="fomodel1.html#NM1" title="FOMODEL1:NM.1">Element</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 <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><span class="p2">(<span class="default"><a href="fomodel4.html#K22" title="FOMODEL4:func.22">R0</a> <font color="Maroon" title="c2">S</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel4.html#K25" title="FOMODEL4:func.25">R3a</a> <font color="Maroon" title="c2">S</font></span>)</span></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">D</font> &amp; <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><span class="p2">(<span class="default"><a href="fomodel4.html#K24" title="FOMODEL4:func.24">R2</a> <font color="Maroon" title="c2">S</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel4.html#K26" title="FOMODEL4:func.26">R3b</a> <font color="Maroon" title="c2">S</font></span>)</span></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">D</font> &amp; <font color="Maroon" title="c1">X</font> is <font color="Olive" title="b2">D</font> <a href="fomodel4.html#V10" title="FOMODEL4:attr.10">-expanded</a>  holds <br/><font color="Maroon" title="c1">X</font> <a href="fomodel3.html#K4" title="FOMODEL3:func.4">-freeInterpreter</a> <font color="Olive" title="b1">l</font> is (<font color="Maroon" title="c1">X</font>,<font color="Olive" title="b2">D</font>) <a href="fomodel4.html#K6" title="FOMODEL4:func.6">-termEq</a>  <a href="fomodel3.html#V2" title="FOMODEL3:attr.2">-respecting</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">l</font> be   <a href="fomodel1.html#V4" title="FOMODEL1:attr.4">literal</a>  <a href="fomodel1.html#NM1" title="FOMODEL1:NM.1">Element</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 <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><span class="p2">(<span class="default"><a href="fomodel4.html#K22" title="FOMODEL4:func.22">R0</a> <font color="Maroon" title="c2">S</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel4.html#K25" title="FOMODEL4:func.25">R3a</a> <font color="Maroon" title="c2">S</font></span>)</span></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">D</font> &amp; <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><span class="p2">(<span class="default"><a href="fomodel4.html#K24" title="FOMODEL4:func.24">R2</a> <font color="Maroon" title="c2">S</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel4.html#K26" title="FOMODEL4:func.26">R3b</a> <font color="Maroon" title="c2">S</font></span>)</span></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">D</font> &amp; <font color="Maroon" title="c1">X</font> is <font color="Olive" title="b1">D</font> <a href="fomodel4.html#V10" title="FOMODEL4:attr.10">-expanded</a>  holds <br/><font color="Maroon" title="c1">X</font> <a href="fomodel3.html#K4" title="FOMODEL3:func.4">-freeInterpreter</a> <font color="Maroon" title="c3">l</font> is (<font color="Maroon" title="c1">X</font>,<font color="Olive" title="b1">D</font>) <a href="fomodel4.html#K6" title="FOMODEL4:func.6">-termEq</a>  <a href="fomodel3.html#V2" title="FOMODEL3:attr.2">-respecting</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"> ( <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><span class="p2">(<span class="default"><a href="fomodel4.html#K22" title="FOMODEL4:func.22">R0</a> <font color="Maroon" title="c2">S</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel4.html#K25" title="FOMODEL4:func.25">R3a</a> <font color="Maroon" title="c2">S</font></span>)</span></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">D</font> &amp; <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><span class="p2">(<span class="default"><a href="fomodel4.html#K24" title="FOMODEL4:func.24">R2</a> <font color="Maroon" title="c2">S</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel4.html#K26" title="FOMODEL4:func.26">R3b</a> <font color="Maroon" title="c2">S</font></span>)</span></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">D</font> &amp; <font color="Maroon" title="c1">X</font> is <font color="Maroon" title="c4">D</font> <a href="fomodel4.html#V10" title="FOMODEL4:attr.10">-expanded</a>  implies <font color="Maroon" title="c1">X</font> <a href="fomodel3.html#K4" title="FOMODEL3:func.4">-freeInterpreter</a> <font color="Maroon" title="c3">l</font> is (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c4">D</font>) <a href="fomodel4.html#K6" title="FOMODEL4:func.6">-termEq</a>  <a href="fomodel3.html#V2" title="FOMODEL3:attr.2">-respecting</a>  )</span><br/>







<span class="kw">set </span><font color="Maroon" title="c5">AT</font> =  <a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c2">S</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">I</font> = <font color="Maroon" title="c1">X</font> <a href="fomodel3.html#K4" title="FOMODEL3:func.4">-freeInterpreter</a> <font color="Maroon" title="c3">l</font>;<br/>
<span class="kw">assume </span><a NAME="E1:113"/>
( <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><span class="p2">(<span class="default"><a href="fomodel4.html#K22" title="FOMODEL4:func.22">R0</a> <font color="Maroon" title="c2">S</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel4.html#K25" title="FOMODEL4:func.25">R3a</a> <font color="Maroon" title="c2">S</font></span>)</span></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">D</font> &amp; <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><span class="p2">(<span class="default"><a href="fomodel4.html#K24" title="FOMODEL4:func.24">R2</a> <font color="Maroon" title="c2">S</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel4.html#K26" title="FOMODEL4:func.26">R3b</a> <font color="Maroon" title="c2">S</font></span>)</span></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">D</font> &amp; <font color="Maroon" title="c1">X</font> is <font color="Maroon" title="c4">D</font> <a href="fomodel4.html#V10" title="FOMODEL4:attr.10">-expanded</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">X</font> <a href="fomodel3.html#K4" title="FOMODEL3:func.4">-freeInterpreter</a> <font color="Maroon" title="c3">l</font> is (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c4">D</font>) <a href="fomodel4.html#K6" title="FOMODEL4:func.6">-termEq</a>  <a href="fomodel3.html#V2" title="FOMODEL3:attr.2">-respecting</a> </span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c7">R</font> = (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c4">D</font>) <a href="fomodel4.html#K6" title="FOMODEL4:func.6">-termEq</a>  as   <a href="eqrel_1.html#NM2" title="EQREL_1:NM.2">Equivalence_Relation</a> of <span class="p1">(<span class="default"><a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c2">S</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="fomodel4.html#E90"><span class="lab"><font color="Green" title="E72">Lm11</font></span></a></span>;<br/>
<a NAME="E3:113"/>
<font color="Maroon" title="c1">X</font> <a href="fomodel3.html#K4" title="FOMODEL3:func.4">-freeInterpreter</a> <font color="Maroon" title="c3">l</font> is <font color="Maroon" title="c7">R</font> <a href="fomodel3.html#V2" title="FOMODEL3:attr.2">-respecting</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="fomodel4.html#E101"><span class="lab"><font color="Green" title="E82">Lm50</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:113"/>
<font color="Maroon" title="c1">X</font> <a href="fomodel3.html#K4" title="FOMODEL3:func.4">-freeInterpreter</a> <font color="Maroon" title="c3">l</font> is (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c4">D</font>) <a href="fomodel4.html#K6" title="FOMODEL4:func.6">-termEq</a>  <a href="fomodel3.html#V2" title="FOMODEL3:attr.2">-respecting</a> 
 ; <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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