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<span class="kw">set </span><font color="Maroon" title="c4">f</font> = (<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U</font>) <a href="fomodel2.html#K22" title="FOMODEL2:func.22">-TruthEval</a> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c5">nn</font> = <font color="Maroon" title="c2">m</font> as    <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>  <span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal1.html#D12" title="ORDINAL1:def.12">ORDINAL1:def 12</a></span>;<br/>
<span class="kw">take </span>
<span class="p1">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U</font>) <a href="fomodel2.html#K22" title="FOMODEL2:func.22">-TruthEval</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c5">nn</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">mm</font> being    <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>   st <font color="Maroon" title="c2">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">mm</font> holds <br/><span class="p1">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U</font>) <a href="fomodel2.html#K22" title="FOMODEL2:func.22">-TruthEval</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c5">nn</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U</font>) <a href="fomodel2.html#K22" title="FOMODEL2:func.22">-TruthEval</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b1">mm</font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c6">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"> ( <font color="Maroon" title="c2">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">mm</font> implies <span class="p1">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U</font>) <a href="fomodel2.html#K22" title="FOMODEL2:func.22">-TruthEval</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c5">nn</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U</font>) <a href="fomodel2.html#K22" title="FOMODEL2:func.22">-TruthEval</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c6">mm</font> )</span><br/>

<span class="kw">assume </span><a NAME="E2:58_1_1"/>
<font color="Maroon" title="c2">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">mm</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">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U</font>) <a href="fomodel2.html#K22" title="FOMODEL2:func.22">-TruthEval</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c5">nn</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U</font>) <a href="fomodel2.html#K22" title="FOMODEL2:func.22">-TruthEval</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c6">mm</font></span><br/>

<span class="kw">hence </span><a NAME="E3:58_1_1"/>
<span class="p1">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U</font>) <a href="fomodel2.html#K22" title="FOMODEL2:func.22">-TruthEval</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c5">nn</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U</font>) <a href="fomodel2.html#K22" title="FOMODEL2:func.22">-TruthEval</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c6">mm</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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