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<span class="kw">let </span><font color="Maroon" title="c1">mm</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">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">U1</font>, <font color="Olive" title="b3">U2</font> being   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> <br/>  for <font color="Olive" title="b4">I1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Olive" title="b2">U1</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b5">I2</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Olive" title="b3">U2</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Olive" title="b1">S</font> holds   <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default">(<font color="Olive" title="b4">I1</font>,<font color="Maroon" title="c1">mm</font>) <a href="fomodel2.html#K24" title="FOMODEL2:func.24">-TruthEval</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default">(<font color="Olive" title="b5">I2</font>,<font color="Maroon" title="c1">mm</font>) <a href="fomodel2.html#K24" title="FOMODEL2:func.24">-TruthEval</a></span>)</span></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">U1</font>, <font color="Olive" title="b2">U2</font> being   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> <br/>  for <font color="Olive" title="b3">I1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Olive" title="b1">U1</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c2">S</font><br/>  for <font color="Olive" title="b4">I2</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Olive" title="b2">U2</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c2">S</font> holds   <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default">(<font color="Olive" title="b3">I1</font>,<font color="Maroon" title="c1">mm</font>) <a href="fomodel2.html#K24" title="FOMODEL2:func.24">-TruthEval</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default">(<font color="Olive" title="b4">I2</font>,<font color="Maroon" title="c1">mm</font>) <a href="fomodel2.html#K24" title="FOMODEL2:func.24">-TruthEval</a></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">U1</font>, <font color="Maroon" title="c4">U2</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">I1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c3">U1</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c2">S</font><br/>  for <font color="Olive" title="b2">I2</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c4">U2</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c2">S</font> holds   <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default">(<font color="Olive" title="b1">I1</font>,<font color="Maroon" title="c1">mm</font>) <a href="fomodel2.html#K24" title="FOMODEL2:func.24">-TruthEval</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default">(<font color="Olive" title="b2">I2</font>,<font color="Maroon" title="c1">mm</font>) <a href="fomodel2.html#K24" title="FOMODEL2:func.24">-TruthEval</a></span>)</span></span><br/>







<span class="kw">set </span><font color="Maroon" title="c5">II1</font> = <font color="Maroon" title="c3">U1</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c2">S</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">II2</font> = <font color="Maroon" title="c4">U2</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c2">S</font>;<br/>
<span class="kw">let </span><font color="Maroon" title="c7">I1</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c3">U1</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <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">I2</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c4">U2</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c2">S</font> holds   <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c7">I1</font>,<font color="Maroon" title="c1">mm</font>) <a href="fomodel2.html#K24" title="FOMODEL2:func.24">-TruthEval</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default">(<font color="Olive" title="b1">I2</font>,<font color="Maroon" title="c1">mm</font>) <a href="fomodel2.html#K24" title="FOMODEL2:func.24">-TruthEval</a></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c8">I2</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c4">U2</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <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">  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c7">I1</font>,<font color="Maroon" title="c1">mm</font>) <a href="fomodel2.html#K24" title="FOMODEL2:func.24">-TruthEval</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c8">I2</font>,<font color="Maroon" title="c1">mm</font>) <a href="fomodel2.html#K24" title="FOMODEL2:func.24">-TruthEval</a></span>)</span></span><br/>



<span class="kw">set </span><font color="Maroon" title="c9">f1</font> = (<font color="Maroon" title="c7">I1</font>,<font color="Maroon" title="c1">mm</font>) <a href="fomodel2.html#K24" title="FOMODEL2:func.24">-TruthEval</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">f2</font> = (<font color="Maroon" title="c8">I2</font>,<font color="Maroon" title="c1">mm</font>) <a href="fomodel2.html#K24" title="FOMODEL2:func.24">-TruthEval</a> ;<br/>
<a NAME="E1:67"/>
(  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c7">I1</font>,<font color="Maroon" title="c1">mm</font>) <a href="fomodel2.html#K24" title="FOMODEL2:func.24">-TruthEval</a></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c8">I2</font>,<font color="Maroon" title="c1">mm</font>) <a href="fomodel2.html#K24" title="FOMODEL2:func.24">-TruthEval</a></span>)</span> &amp;  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c8">I2</font>,<font color="Maroon" title="c1">mm</font>) <a href="fomodel2.html#K24" title="FOMODEL2:func.24">-TruthEval</a></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c7">I1</font>,<font color="Maroon" title="c1">mm</font>) <a href="fomodel2.html#K24" title="FOMODEL2:func.24">-TruthEval</a></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="fomodel2.html#E37"><span class="lab"><font color="Green" title="E30">Lm24</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:67"/>
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c7">I1</font>,<font color="Maroon" title="c1">mm</font>) <a href="fomodel2.html#K24" title="FOMODEL2:func.24">-TruthEval</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c8">I2</font>,<font color="Maroon" title="c1">mm</font>) <a href="fomodel2.html#K24" title="FOMODEL2:func.24">-TruthEval</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0: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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