<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c2">k</font> be   <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">N</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <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> <br/>  for <font color="Olive" title="b2">S</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="memstr_0.html#V2" title="MEMSTR_0:attr.2">IC-Ins-separated</a>   <a href="ami_wstd.html#V2" title="AMI_WSTD:attr.2">weakly_standard</a>   <a href="extpro_1.html#L1" title="EXTPRO_1:struct.1">AMI-Struct</a> of <font color="Olive" title="b1">N</font><br/>  for <font color="Olive" title="b3">l</font> being    <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>  holds  <span class="p1">(<span class="default"><font color="Olive" title="b3">l</font> <a href="ami_wstd.html#K4" title="AMI_WSTD:func.4">+</a> (<font color="Maroon" title="c2">k</font>,<font color="Olive" title="b2">S</font>)</span>)</span> <a href="ami_wstd.html#K7" title="AMI_WSTD:func.7">-'</a> (<font color="Maroon" title="c2">k</font>,<font color="Olive" title="b2">S</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">l</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">N</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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="memstr_0.html#V2" title="MEMSTR_0:attr.2">IC-Ins-separated</a>   <a href="ami_wstd.html#V2" title="AMI_WSTD:attr.2">weakly_standard</a>   <a href="extpro_1.html#L1" title="EXTPRO_1:struct.1">AMI-Struct</a> of <font color="Maroon" title="c3">N</font><br/>  for <font color="Olive" title="b2">l</font> being    <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>  holds  <span class="p1">(<span class="default"><font color="Olive" title="b2">l</font> <a href="ami_wstd.html#K4" title="AMI_WSTD:func.4">+</a> (<font color="Maroon" title="c2">k</font>,<font color="Olive" title="b1">S</font>)</span>)</span> <a href="ami_wstd.html#K7" title="AMI_WSTD:func.7">-'</a> (<font color="Maroon" title="c2">k</font>,<font color="Olive" title="b1">S</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">l</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">S</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="memstr_0.html#V2" title="MEMSTR_0:attr.2">IC-Ins-separated</a>   <a href="ami_wstd.html#V2" title="AMI_WSTD:attr.2">weakly_standard</a>   <a href="extpro_1.html#L1" title="EXTPRO_1:struct.1">AMI-Struct</a> of <font color="Maroon" title="c3">N</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">l</font> being    <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>  holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">l</font> <a href="ami_wstd.html#K4" title="AMI_WSTD:func.4">+</a> (<font color="Maroon" title="c2">k</font>,<font color="Maroon" title="c4">S</font>)</span>)</span> <a href="ami_wstd.html#K7" title="AMI_WSTD:func.7">-'</a> (<font color="Maroon" title="c2">k</font>,<font color="Maroon" title="c4">S</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">l</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">l</font> be    <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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c5">l</font> <a href="ami_wstd.html#K4" title="AMI_WSTD:func.4">+</a> (<font color="Maroon" title="c2">k</font>,<font color="Maroon" title="c4">S</font>)</span>)</span> <a href="ami_wstd.html#K7" title="AMI_WSTD:func.7">-'</a> (<font color="Maroon" title="c2">k</font>,<font color="Maroon" title="c4">S</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">l</font></span><br/>







<span class="kw">thus </span><span class="p1">(<span class="default"><font color="Maroon" title="c5">l</font> <a href="ami_wstd.html#K4" title="AMI_WSTD:func.4">+</a> (<font color="Maroon" title="c2">k</font>,<font color="Maroon" title="c4">S</font>)</span>)</span> <a href="ami_wstd.html#K7" title="AMI_WSTD:func.7">-'</a> (<font color="Maroon" title="c2">k</font>,<font color="Maroon" title="c4">S</font>) = 
 <a href="ami_wstd.html#K1" title="AMI_WSTD:func.1">il.</a> (<font color="Maroon" title="c4">S</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_wstd.html#K3" title="AMI_WSTD:func.3">locnum</a> (<font color="Maroon" title="c5">l</font>,<font color="Maroon" title="c4">S</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c2">k</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c2">k</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_wstd.html#D5" target="_self" title="AMI_WSTD:def.5">Def13</a></span>
<br/>.= 
 <a href="ami_wstd.html#K1" title="AMI_WSTD:func.1">il.</a> (<font color="Maroon" title="c4">S</font>,<span class="p1">(<span class="default"><a href="ami_wstd.html#K3" title="AMI_WSTD:func.3">locnum</a> (<font color="Maroon" title="c5">l</font>,<font color="Maroon" title="c4">S</font>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_d.html#T34" title="NAT_D:th.34">NAT_D:34</a></span>
<br/>.= 
<font color="Maroon" title="c5">l</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_wstd.html#D5" target="_self" title="AMI_WSTD:def.5">Def13</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/>


</div>
