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<a NAME="E1:35_1_1"/>
 <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <font color="Maroon" title="c2">S</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">P</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="compos_1.html#D3" title="COMPOS_1:def.3">COMPOS_1:def 3</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">i</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E3:35_1_1"/><span class="lab"><font color="Green" title="E19">W1</font></span>: 
<font color="Maroon" title="c4">i</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">P</font>
 <span class="kw">and </span><br/><a NAME="E4:35_1_1"/><span class="lab"><font color="Green" title="E20">W2</font></span>: 
<font color="Maroon" title="c3">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <font color="Maroon" title="c2">S</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D3" title="FUNCT_1:def.3">FUNCT_1:def 3</a></span>;<br/>
<a NAME="E5:35_1_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">P</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D18" title="RELAT_1:def.18">RELAT_1:def 18</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c5">i</font> = <font color="Maroon" title="c4">i</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35_1_1"><span class="lab"><font color="Green" title="E19">W1</font></span></a></span>;<br/>
<span class="kw">take </span><font color="Maroon" title="c6">p</font> =  <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<font color="Maroon" title="c5">i</font>,<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"> ( <font color="Maroon" title="c6">p</font> is <font color="Maroon" title="c3">P</font> <a href="extpro_1.html#V4" title="EXTPRO_1:attr.4">-autonomic</a>  &amp; <font color="Maroon" title="c6">p</font> is <font color="Maroon" title="c3">P</font> <a href="extpro_1.html#V5" title="EXTPRO_1:attr.5">-halted</a>  &amp;  not <font color="Maroon" title="c6">p</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  )</span><br/>

<a NAME="E7:35_1_1"/>
<font color="Maroon" title="c5">i</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p1">(<span class="default"><a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <font color="Maroon" title="c2">S</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">P</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35_1_1"><span class="lab"><font color="Green" title="E19">W1</font></span></a>, <a class="txt" href="#E4:35_1_1"><span class="lab"><font color="Green" title="E20">W2</font></span></a>, <a class="ref" href="funct_4.html#T85" title="FUNCT_4:th.85">FUNCT_4:85</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:35_1_1"/>
( <font color="Maroon" title="c6">p</font> is <font color="Maroon" title="c3">P</font> <a href="extpro_1.html#V4" title="EXTPRO_1:attr.4">-autonomic</a>  &amp; <font color="Maroon" title="c6">p</font> is <font color="Maroon" title="c3">P</font> <a href="extpro_1.html#V5" title="EXTPRO_1:attr.5">-halted</a>  &amp;  not <font color="Maroon" title="c6">p</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T10" target="_self" title="EXTPRO_1:th.10">Th11</a>, <a class="ref" href="extpro_1.html#T12" target="_self" title="EXTPRO_1:th.12">Th13</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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