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<span class="kw">thus </span><a NAME="E1:171_1_1"/>
( <font color="Maroon" title="c3">s</font> <a href="ami_1.html#R3" title="AMI_1:pred.3">halts_at</a> <font color="Maroon" title="c4">l</font> implies <font color="Maroon" title="c3">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <font color="Maroon" title="c2">S</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#D42" target="_self" title="AMI_1:def.42">Def42</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <font color="Maroon" title="c2">S</font> implies <font color="Maroon" title="c3">s</font> <a href="ami_1.html#R3" title="AMI_1:pred.3">halts_at</a> <font color="Maroon" title="c4">l</font> )</span><br/>

<span class="kw">assume </span><a NAME="E2:171_1_1"/><span class="lab"><font color="Green" title="E43">Z</font></span>: 
<font color="Maroon" title="c3">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <font color="Maroon" title="c2">S</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">s</font> <a href="ami_1.html#R3" title="AMI_1:pred.3">halts_at</a> <font color="Maroon" title="c4">l</font></span><br/>

<a NAME="E3:171_1_1"/><span class="lab"><font color="Green" title="E44">A</font></span>: 
<font color="Maroon" title="c4">l</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <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#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></span>;<br/>
<a NAME="E4:171_1_1"/>
 <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">s</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D4" title="PARTFUN1:def.4">PARTFUN1:def 4</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:171_1_1"/>
<font color="Maroon" title="c4">l</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">s</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:171_1_1"><span class="lab"><font color="Green" title="E44">A</font></span></a></span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="ami_1.html#D42" target="_self" title="AMI_1:def.42">AMI_1:def 42</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <font color="Maroon" title="c2">S</font></span><br/>

<span class="kw">thus </span><a NAME="E6:171_1_1"/>
<font color="Maroon" title="c3">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <font color="Maroon" title="c2">S</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:171_1_1"><span class="lab"><font color="Green" title="E43">Z</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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