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<span class="kw">set </span><font color="Maroon" title="c4">X</font> = <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> (<font color="Maroon" title="c3">i</font>,<font color="Olive" title="b1">l</font>)</span>)</span> where <font color="Olive" title="b1">l</font> is   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> : verum </span> } </span> ;<br/>
<a NAME="E1:8_1_1"/>
<span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> (<font color="Maroon" title="c3">i</font>,<font color="Olive" title="b1">l</font>)</span>)</span> where <font color="Olive" title="b1">l</font> is   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> : verum </span> } </span>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="8_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c5">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" onmouseover="rs('tarski/D3')" onmouseout="rh()">TARSKI:def 3</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"> (  not <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> (<font color="Maroon" title="c3">i</font>,<font color="Olive" title="b1">l</font>)</span>)</span> where <font color="Olive" title="b1">l</font> is   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> : verum </span> } </span>  or <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> )</span><br/>

<span class="kw">assume </span><a NAME="E1:8_1_1_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> (<font color="Maroon" title="c3">i</font>,<font color="Olive" title="b1">l</font>)</span>)</span> where <font color="Olive" title="b1">l</font> is   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> : verum </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"> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a></span><br/>

<a NAME="E2:8_1_1_1"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">l</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> (<font color="Maroon" title="c3">i</font>,<font color="Olive" title="b1">l</font>)
 
;<br/>
<span class="kw">hence </span><a NAME="E3:8_1_1_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</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"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c5">X</font> = <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> (<font color="Maroon" title="c3">i</font>,<font color="Olive" title="b1">l</font>)</span>)</span> where <font color="Olive" title="b1">l</font> is   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> : verum </span> } </span>  as   <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> ;<br/>
<a NAME="E3:8_1_1"/>
 <a href="setfam_1.html#K6" title="SETFAM_1:func.6">meet</a> <font color="Maroon" title="c5">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> 
 
;<br/>
<span class="kw">hence </span><a NAME="E4:8_1_1"/>
 <a href="setfam_1.html#K1" title="SETFAM_1:func.1">meet</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> (<font color="Maroon" title="c3">i</font>,<font color="Olive" title="b1">l</font>)</span>)</span> where <font color="Olive" title="b1">l</font> is   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> : verum </span> } </span>  is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</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"> verum</span><br/>


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