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

<span class="kw">let </span><font color="Maroon" title="c4">F</font> be   <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="relat_1.html#V4" title="RELAT_1:attr.4">-defined</a>   the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <font color="Maroon" title="c3">S</font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">F</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  implies <font color="Maroon" title="c4">F</font> is  <a href="ami_wstd.html#V5" title="AMI_WSTD:attr.5">lower</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:40_1_1"/><span class="lab"><font color="Green" title="E24">F</font></span>: 
<font color="Maroon" title="c4">F</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"> <font color="Maroon" title="c4">F</font> is  <a href="ami_wstd.html#V5" title="AMI_WSTD:attr.5">lower</a> </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> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="ami_wstd.html#D10" target="_self" title="AMI_WSTD:def.10">AMI_WSTD:def 10</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">l</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c4">F</font> implies  for <font color="Olive" title="b1">m</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>   st <font color="Olive" title="b1">m</font> <a href="ami_wstd.html#R1" title="AMI_WSTD:pred.1">&lt;=</a> <font color="Maroon" title="c5">l</font>,<font color="Maroon" title="c3">S</font> holds <br/><font color="Olive" title="b1">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c4">F</font> )</span><br/>

<span class="kw">assume </span><a NAME="E2:40_1_1"/>
<font color="Maroon" title="c5">l</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c4">F</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">m</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>   st <font color="Olive" title="b1">m</font> <a href="ami_wstd.html#R1" title="AMI_WSTD:pred.1">&lt;=</a> <font color="Maroon" title="c5">l</font>,<font color="Maroon" title="c3">S</font> holds <br/><font color="Olive" title="b1">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c4">F</font></span><br/>

<span class="kw">hence </span><a NAME="E3:40_1_1"/>
 for <font color="Olive" title="b1">m</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>   st <font color="Olive" title="b1">m</font> <a href="ami_wstd.html#R1" title="AMI_WSTD:pred.1">&lt;=</a> <font color="Maroon" title="c5">l</font>,<font color="Maroon" title="c3">S</font> holds <br/><font color="Olive" title="b1">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c4">F</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:40_1_1"><span class="lab"><font color="Green" title="E24">F</font></span></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>
