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<span class="kw">let </span><font color="Maroon" title="c1">U</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</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">  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">E</font> being   <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>   <a href="relat_2.html#V1" title="RELAT_2:attr.1">reflexive</a>  <a href="relset_1.html#NM2" title="RELSET_1:NM.2">Relation</a> of <font color="Maroon" title="c1">U</font><br/>  for <font color="Olive" title="b4">f</font> being    <a href="fomodel2.html#M2" title="FOMODEL2:mode.2">Interpreter</a> of <font color="Olive" title="b2">l</font>,<font color="Maroon" title="c1">U</font> holds  <font color="Olive" title="b4">f</font> is <font color="Olive" title="b3">E</font> <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">E</font> being   <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>   <a href="relat_2.html#V1" title="RELAT_2:attr.1">reflexive</a>  <a href="relset_1.html#NM2" title="RELSET_1:NM.2">Relation</a> of <font color="Maroon" title="c1">U</font><br/>  for <font color="Olive" title="b3">f</font> being    <a href="fomodel2.html#M2" title="FOMODEL2:mode.2">Interpreter</a> of <font color="Olive" title="b1">l</font>,<font color="Maroon" title="c1">U</font> holds  <font color="Olive" title="b3">f</font> is <font color="Olive" title="b2">E</font> <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">E</font> being   <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>   <a href="relat_2.html#V1" title="RELAT_2:attr.1">reflexive</a>  <a href="relset_1.html#NM2" title="RELSET_1:NM.2">Relation</a> of <font color="Maroon" title="c1">U</font><br/>  for <font color="Olive" title="b2">f</font> being    <a href="fomodel2.html#M2" title="FOMODEL2:mode.2">Interpreter</a> of <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">U</font> holds  <font color="Olive" title="b2">f</font> is <font color="Olive" title="b1">E</font> <a href="fomodel3.html#V2" title="FOMODEL3:attr.2">-respecting</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c4">E</font> be   <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>   <a href="relat_2.html#V1" title="RELAT_2:attr.1">reflexive</a>  <a href="relset_1.html#NM2" title="RELSET_1:NM.2">Relation</a> of <font color="Maroon" title="c1">U</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">f</font> being    <a href="fomodel2.html#M2" title="FOMODEL2:mode.2">Interpreter</a> of <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">U</font> holds  <font color="Olive" title="b1">f</font> is <font color="Maroon" title="c4">E</font> <a href="fomodel3.html#V2" title="FOMODEL3:attr.2">-respecting</a> </span><br/>







<span class="kw">reconsider </span><font color="Maroon" title="c5">m</font> =  <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K19" title="FOMODEL1:func.19">ar</a> <font color="Maroon" title="c3">l</font></span>)</span> as   <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">zero</a>  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> ;<br/>
<span class="kw">let </span><font color="Maroon" title="c6">f</font> be    <a href="fomodel2.html#M2" title="FOMODEL2:mode.2">Interpreter</a> of <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">U</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="c6">f</font> is <font color="Maroon" title="c4">E</font> <a href="fomodel3.html#V2" title="FOMODEL3:attr.2">-respecting</a> </span><br/>

<a NAME="E2:112"/>
<font color="Maroon" title="c5">m</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c1">U</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel0.html#T10" title="FOMODEL0:th.10">FOMODEL0:10</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c7">ff</font> = <font color="Maroon" title="c6">f</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<font color="Maroon" title="c1">U</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel2.html#D2" title="FOMODEL2:def.2">FOMODEL2:def 2</a></span>;<br/>
<a NAME="E4:112"/>
 <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <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"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<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/>
<a NAME="E5:112"/><span class="kw">then </span>
<font color="Maroon" title="c7">ff</font> is <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<font color="Maroon" title="c4">E</font> <a href="fomodel3.html#V1" title="FOMODEL3:attr.1">-respecting</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="fomodel4.html#E100"><span class="lab"><font color="Green" title="E81">Lm49</font></span></a></span>;<br/>
<a NAME="E6:112"/><span class="kw">then </span>
<font color="Maroon" title="c6">f</font> is <font color="Maroon" title="c5">m</font> <a href="fomodel3.html#K10" title="FOMODEL3:func.10">-placesOf</a> <font color="Maroon" title="c4">E</font>,<font color="Maroon" title="c4">E</font> <a href="fomodel3.html#V1" title="FOMODEL3:attr.1">-respecting</a> 
 
;<br/>
<span class="kw">hence </span><a NAME="E7:112"/>
<font color="Maroon" title="c6">f</font> is <font color="Maroon" title="c4">E</font> <a href="fomodel3.html#V2" title="FOMODEL3:attr.2">-respecting</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel3.html#D10" title="FOMODEL3:def.10">FOMODEL3:def 10</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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