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<span class="kw">let </span><font color="Maroon" title="c1">nt</font> be   <a href="dtconstr.html#NM3" title="DTCONSTR:NM.3">NonTerminal</a> of <a href="scm_comp.html#K1" title="SCM_COMP:func.1">SCM-AE</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">nt</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> or <font color="Maroon" title="c1">nt</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,1</span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> or <font color="Maroon" title="c1">nt</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,2</span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> or <font color="Maroon" title="c1">nt</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,3</span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> or <font color="Maroon" title="c1">nt</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,4</span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> )</span><br/>

<span class="kw">consider </span><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E2:6"/><span class="lab"><font color="Green" title="E6">A1</font></span>: 
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> 1
 <span class="kw">and </span><br/><a NAME="E3:6"/><span class="lab"><font color="Green" title="E7">A2</font></span>: 
<font color="Maroon" title="c3">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> 5
 <span class="kw">and </span><br/><a NAME="E4:6"/><span class="lab"><font color="Green" title="E8">A3</font></span>: 
<font color="Maroon" title="c1">nt</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="scm_comp.html#E4"><span class="lab"><font color="Green" title="E4">Lm3</font></span></a>, <a class="ref" href="zfmisc_1.html#T84" title="ZFMISC_1:th.84">ZFMISC_1:84</a></span>;<br/>
<a NAME="E5:6"/><span class="lab"><font color="Green" title="E9">A4</font></span>: 
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:6"><span class="lab"><font color="Green" title="E6">A1</font></span></a>, <a class="ref" href="card_1.html#T49" title="CARD_1:th.49">CARD_1:49</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c4">n</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> <span class="kw"> such that </span><br/><a NAME="E7:6"/><span class="lab"><font color="Green" title="E10">A5</font></span>: 
<font color="Maroon" title="c3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">n</font>
 <span class="kw">and </span><br/><a NAME="E8:6"/><span class="lab"><font color="Green" title="E11">A6</font></span>: 
<font color="Maroon" title="c4">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 5
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:6"><span class="lab"><font color="Green" title="E7">A2</font></span></a>, <a class="txt" href="scm_comp.html#E2"><span class="lab"><font color="Green" title="E2">Lm2</font></span></a></span>;<br/>
<a NAME="E9:6"/>
5 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 
;<br/>
<a NAME="E10:6"/><span class="kw">then </span>
<font color="Maroon" title="c4">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 4
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:6"><span class="lab"><font color="Green" title="E11">A6</font></span></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/>
<span class="kw">hence </span><a NAME="E11:6"/>
( <font color="Maroon" title="c1">nt</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> or <font color="Maroon" title="c1">nt</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,1</span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> or <font color="Maroon" title="c1">nt</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,2</span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> or <font color="Maroon" title="c1">nt</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,3</span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> or <font color="Maroon" title="c1">nt</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,4</span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:6"><span class="lab"><font color="Green" title="E8">A3</font></span></a>, <a class="txt" href="#E5:6"><span class="lab"><font color="Green" title="E9">A4</font></span></a>, <a class="txt" href="#E7:6"><span class="lab"><font color="Green" title="E10">A5</font></span></a>, <a class="ref" href="nat_1.html#T28" title="NAT_1:th.28">NAT_1:28</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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