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<span class="kw">set </span><font color="Maroon" title="c4">F</font> =  <a href="compos_1.html#K4" title="COMPOS_1:func.4">Stop</a> <font color="Maroon" title="c3">S</font>;<br/>
<span class="kw">let </span><font color="Maroon" title="c5">l</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="amistd_1.html#D9" target="_self" onmouseover="rs('amistd_1/D9')" onmouseout="rh()">AMISTD_1:def 9</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">l</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#K4" title="COMPOS_1:func.4">Stop</a> <font color="Maroon" title="c3">S</font></span>)</span> implies  <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="compos_1.html#K4" title="COMPOS_1:func.4">Stop</a> <font color="Maroon" title="c3">S</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c5">l</font></span>)</span>,<font color="Maroon" title="c5">l</font>) <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"><a href="compos_1.html#K4" title="COMPOS_1:func.4">Stop</a> <font color="Maroon" title="c3">S</font></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E1:39_1_1"/><span class="lab"><font color="Green" title="E16">A1</font></span>: 
<font color="Maroon" title="c5">l</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#K4" title="COMPOS_1:func.4">Stop</a> <font color="Maroon" title="c3">S</font></span>)</span>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="compos_1.html#K4" title="COMPOS_1:func.4">Stop</a> <font color="Maroon" title="c3">S</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c5">l</font></span>)</span>,<font color="Maroon" title="c5">l</font>) <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"><a href="compos_1.html#K4" title="COMPOS_1:func.4">Stop</a> <font color="Maroon" title="c3">S</font></span>)</span></span><br/>

<a NAME="E2:39_1_1"/><span class="lab"><font color="Green" title="E17">A3</font></span>: 
<font color="Maroon" title="c5">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:39_1_1"><span class="lab"><font color="Green" title="E16">A1</font></span></a>, <a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>;<br/>
<span class="p1">(<span class="default"><a href="compos_1.html#K4" title="COMPOS_1:func.4">Stop</a> <font color="Maroon" title="c3">S</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c5">l</font> = 
<span class="p1">(<span class="default"><a href="compos_1.html#K4" title="COMPOS_1:func.4">Stop</a> <font color="Maroon" title="c3">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">l</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:39_1_1"><span class="lab"><font color="Green" title="E16">A1</font></span></a>, <a class="ref" href="partfun1.html#D6" onmouseover="rs('partfun1/D6')" onmouseout="rh()">PARTFUN1:def 6</a></span>
<br/>.= 
 <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <font color="Maroon" title="c3">S</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:39_1_1"><span class="lab"><font color="Green" title="E17">A3</font></span></a></span>
;<br/>
<span class="kw">hence </span><a NAME="E4:39_1_1"/>
 <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="compos_1.html#K4" title="COMPOS_1:func.4">Stop</a> <font color="Maroon" title="c3">S</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c5">l</font></span>)</span>,<font color="Maroon" title="c5">l</font>) <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"><a href="compos_1.html#K4" title="COMPOS_1:func.4">Stop</a> <font color="Maroon" title="c3">S</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:39_1_1"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="ref" href="amistd_1.html#T2" target="_self" onmouseover="rs('amistd_1/T2')" onmouseout="rh()">Th2</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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