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<span class="kw">set </span><font color="Maroon" title="c5">f</font> = (<font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c4">num</font>) <a href="fomodel4.html#K48" title="FOMODEL4:func.48">AddFormulasTo</a> <font color="Maroon" title="c1">X</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">XX</font> = (<font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c4">num</font>) <a href="fomodel4.html#K49" title="FOMODEL4:func.49">CompletionOf</a> <font color="Maroon" title="c1">X</font>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c7">ff</font> = (<font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c4">num</font>) <a href="fomodel4.html#K48" title="FOMODEL4:func.48">AddFormulasTo</a> <font color="Maroon" title="c1">X</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>,<span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c4">num</font>) <a href="fomodel4.html#K48" title="FOMODEL4:func.48">AddFormulasTo</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T6" title="FUNCT_2:th.6">FUNCT_2:6</a></span>;<br/>
<a NAME="E2:249_1_1"/>
<font color="Maroon" title="c7">ff</font> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <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">(<font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c4">num</font>) <a href="fomodel4.html#K48" title="FOMODEL4:func.48">AddFormulasTo</a> <font color="Maroon" title="c1">X</font></span>)</span>
 
;<br/>
<a NAME="E3:249_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default">(<font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c4">num</font>) <a href="fomodel4.html#K48" title="FOMODEL4:func.48">AddFormulasTo</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> (<font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c4">num</font>) <a href="fomodel4.html#K49" title="FOMODEL4:func.49">CompletionOf</a> <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T74" title="ZFMISC_1:th.74">ZFMISC_1:74</a></span>;<br/>
<a NAME="E4:249_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> (<font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c4">num</font>) <a href="fomodel4.html#K49" title="FOMODEL4:func.49">CompletionOf</a> <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel4.html#D74" target="_self" title="FOMODEL4:def.74">DefAdd2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:249_1_1"/>
 for <font color="Olive">b<sub>1</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">X</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c4">num</font>) <a href="fomodel4.html#K49" title="FOMODEL4:func.49">CompletionOf</a> <font color="Maroon" title="c1">X</font></span>)</span> holds <br/><font color="Olive">b<sub>1</sub></font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</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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