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<b>let </b><font color="Maroon" title="c1">N</font> be  <a href="setfam_1.html#V1" title="SETFAM_1:attr.1">with_non-empty_elements</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">S</font> being non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="ami_1.html#V2" title="AMI_1:attr.2">stored-program</a> <a href="ami_1.html#V5" title="AMI_1:attr.5">IC-Ins-separated</a> <a href="ami_1.html#V7" title="AMI_1:attr.7">definite</a> <a href="amistd_1.html#V4" title="AMISTD_1:attr.4">standard</a>  <a href="ami_1.html#L1" title="AMI_1:struct.1">AMI-Struct</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,<font color="Maroon" title="c1">N</font><br/> for <font color="Olive" title="b2">F</font> being   <a href="amistd_1.html#M1" title="AMISTD_1:mode.1">IL-Subset</a> of <font color="Olive" title="b1">S</font> holds   <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Olive" title="b2">F</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="wellord2.html#K2" title="WELLORD2:func.2">order_type_of</a> <span class="p1">(<span class="default"><a href="wellord2.html#K1" title="WELLORD2:func.1">RelIncl</a> <span class="p2">(<span class="default"><a href="amistd_3.html#K3" title="AMISTD_3:func.3">LocNums</a> <font color="Olive" title="b2">F</font></span>)</span></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">S</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="ami_1.html#V2" title="AMI_1:attr.2">stored-program</a> <a href="ami_1.html#V5" title="AMI_1:attr.5">IC-Ins-separated</a> <a href="ami_1.html#V7" title="AMI_1:attr.7">definite</a> <a href="amistd_1.html#V4" title="AMISTD_1:attr.4">standard</a>  <a href="ami_1.html#L1" title="AMI_1:struct.1">AMI-Struct</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,<font color="Maroon" title="c1">N</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">F</font> being   <a href="amistd_1.html#M1" title="AMISTD_1:mode.1">IL-Subset</a> of <font color="Maroon" title="c2">S</font> holds   <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Olive" title="b1">F</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="wellord2.html#K2" title="WELLORD2:func.2">order_type_of</a> <span class="p1">(<span class="default"><a href="wellord2.html#K1" title="WELLORD2:func.1">RelIncl</a> <span class="p2">(<span class="default"><a href="amistd_3.html#K3" title="AMISTD_3:func.3">LocNums</a> <font color="Olive" title="b1">F</font></span>)</span></span>)</span></span><br/><b>let </b><font color="Maroon" title="c3">F</font> be    <a href="amistd_1.html#M1" title="AMISTD_1:mode.1">IL-Subset</a> of <font color="Maroon" title="c2">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c3">F</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="wellord2.html#K2" title="WELLORD2:func.2">order_type_of</a> <span class="p1">(<span class="default"><a href="wellord2.html#K1" title="WELLORD2:func.1">RelIncl</a> <span class="p2">(<span class="default"><a href="amistd_3.html#K3" title="AMISTD_3:func.3">LocNums</a> <font color="Maroon" title="c3">F</font></span>)</span></span>)</span></span><br/>





<b>set </b><font color="Maroon" title="c4">X</font> =  <a href="amistd_3.html#K3" title="AMISTD_3:func.3">LocNums</a> <font color="Maroon" title="c3">F</font>;<br/>
<a NAME="E1:44"/><i><font color="Green" title="E23">A1</font></i>: 
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="amistd_3.html#K3" title="AMISTD_3:func.3">LocNums</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="wellord2.html#K2" title="WELLORD2:func.2">order_type_of</a> <span class="p2">(<span class="default"><a href="wellord2.html#K1" title="WELLORD2:func.1">RelIncl</a> <span class="p3">(<span class="default"><a href="amistd_3.html#K3" title="AMISTD_3:func.3">LocNums</a> <font color="Maroon" title="c3">F</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="card_5.html#T16" title="CARD_5:th.16">CARD_5:16</a></i>;<br/>
<a NAME="E2:44"/>
<font color="Maroon" title="c3">F</font>, <a href="amistd_3.html#K3" title="AMISTD_3:func.3">LocNums</a> <font color="Maroon" title="c3">F</font> <a href="wellord2.html#R2" title="WELLORD2:pred.2">are_equipotent</a> 
 
<b>by </b><i><a class="ref" href="amistd_3.html#T27" target="_self" title="AMISTD_3:th.27">Th27</a></i>;<br/>
<a NAME="E3:44"/><b>then </b>
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c3">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="amistd_3.html#K3" title="AMISTD_3:func.3">LocNums</a> <font color="Maroon" title="c3">F</font></span>)</span>
 
<b>by </b><i><a class="ref" href="card_1.html#T21" title="CARD_1:th.21">CARD_1:21</a></i>;<br/>
<b>hence </b><a NAME="E4:44"/>
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c3">F</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="wellord2.html#K2" title="WELLORD2:func.2">order_type_of</a> <span class="p1">(<span class="default"><a href="wellord2.html#K1" title="WELLORD2:func.1">RelIncl</a> <span class="p2">(<span class="default"><a href="amistd_3.html#K3" title="AMISTD_3:func.3">LocNums</a> <font color="Maroon" title="c3">F</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E1:44"><i><font color="Green" title="E23">A1</font></i></a>, <a class="ref" href="card_1.html#T24" title="CARD_1:th.24">CARD_1:24</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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