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<a NAME="E1:118_1_1"/><span class="lab"><font color="Green" title="E45">A1</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c2">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/>
<a NAME="E2:118_1_1"/>
 <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <font color="Maroon" title="c1">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="c2">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="compos_1.html#D3" target="_self" title="COMPOS_1:def.3">Def7</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E4:118_1_1"/><span class="lab"><font color="Green" title="E46">A2</font></span>: 
<font color="Maroon" title="c4">x</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="c2">p</font>
 <span class="kw">and </span><br/><a NAME="E5:118_1_1"/><span class="lab"><font color="Green" title="E47">A3</font></span>: 
<font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</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="c1">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="E6:118_1_1"/><span class="lab"><font color="Green" title="E48">A4</font></span>: 
<font color="Maroon" title="c4">x</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> <span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">IncAddr</a> (<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">k</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:118_1_1"><span class="lab"><font color="Green" title="E46">A2</font></span></a>, <a class="ref" href="compos_1.html#D19" target="_self" title="COMPOS_1:def.19">Def40</a></span>;<br/>
<a NAME="E7:118_1_1"/><span class="lab"><font color="Green" title="E49">A5</font></span>: 
 <a href="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> (<span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">IncAddr</a> (<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">k</font>)</span>)</span>,<font color="Maroon" title="c3">k</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_1.html#K10" title="COMPOS_1:func.10">IncAddr</a> (<span class="p1">(<span class="default"><a href="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> (<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">k</font>)</span>)</span>,<font color="Maroon" title="c3">k</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="compos_1.html#T34" target="_self" title="COMPOS_1:th.34">Th121</a></span>;<br/>
<a NAME="E8:118_1_1"/><span class="lab"><font color="Green" title="E50">A6</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">IncAddr</a> (<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">k</font>)</span>)</span> <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">reconsider </span><font color="Maroon" title="c5">m</font> = <font color="Maroon" title="c4">x</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="txt" href="#E1:118_1_1"><span class="lab"><font color="Green" title="E45">A1</font></span></a>, <a class="txt" href="#E4:118_1_1"><span class="lab"><font color="Green" title="E46">A2</font></span></a></span>;<br/>
<span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">IncAddr</a> (<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">k</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">m</font> = 
 <a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c5">m</font></span>)</span>,<font color="Maroon" title="c3">k</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:118_1_1"><span class="lab"><font color="Green" title="E46">A2</font></span></a>, <a class="ref" href="compos_1.html#D19" target="_self" title="COMPOS_1:def.19">Def40</a></span>
<br/>.= 
 <a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<span class="p1">(<span class="default"><a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <font color="Maroon" title="c1">S</font></span>)</span>,<font color="Maroon" title="c3">k</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:118_1_1"><span class="lab"><font color="Green" title="E47">A3</font></span></a>, <a class="txt" href="#E4:118_1_1"><span class="lab"><font color="Green" title="E46">A2</font></span></a>, <a class="ref" href="partfun1.html#D6" title="PARTFUN1:def.6">PARTFUN1:def 6</a></span>
<br/>.= 
 <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <font color="Maroon" title="c1">S</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="compos_1.html#T11" target="_self" title="COMPOS_1:th.11">Th92</a></span>
;<br/>
<a NAME="E11:118_1_1"/><span class="kw">then </span>
 <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <font color="Maroon" title="c1">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> <span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">IncAddr</a> (<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">k</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:118_1_1"><span class="lab"><font color="Green" title="E48">A4</font></span></a>, <a class="ref" href="funct_1.html#T3" title="FUNCT_1:th.3">FUNCT_1:3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E12:118_1_1"/>
 <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <font color="Maroon" title="c1">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> <span class="p1">(<span class="default"><a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">k</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:118_1_1"><span class="lab"><font color="Green" title="E49">A5</font></span></a>, <a class="txt" href="#E8:118_1_1"><span class="lab"><font color="Green" title="E50">A6</font></span></a>, <a class="ref" href="valued_1.html#T26" title="VALUED_1:th.26">VALUED_1:26</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="compos_1.html#D3" target="_self" title="COMPOS_1:def.3">COMPOS_1:def 3</a> <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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