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

<b>let </b><font color="Maroon" title="c1">IL</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</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">N</font> being <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="ami_1.html#V2" title="AMI_1:attr.2">stored-program</a> <a href="ami_1.html#V4" title="AMI_1:attr.4">halting</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="ami_1.html#V9" title="AMI_1:attr.9">realistic</a>  <a href="ami_1.html#L1" title="AMI_1:struct.1">AMI-Struct</a> of <font color="Maroon" title="c1">IL</font>,<font color="Olive" title="b1">N</font><br/> for <font color="Olive" title="b3">p</font> being  <a href="ami_1.html#NM8" title="AMI_1:NM.8">FinPartState</a> of <font color="Olive" title="b2">S</font> holds  <font color="Olive" title="b3">p</font> <a href="ami_1.html#R1" title="AMI_1:pred.1">computes</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><br/><b>let </b><font color="Maroon" title="c2">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#V4" title="AMI_1:attr.4">halting</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="ami_1.html#V9" title="AMI_1:attr.9">realistic</a>  <a href="ami_1.html#L1" title="AMI_1:struct.1">AMI-Struct</a> of <font color="Maroon" title="c1">IL</font>,<font color="Maroon" title="c2">N</font><br/> for <font color="Olive" title="b2">p</font> being  <a href="ami_1.html#NM8" title="AMI_1:NM.8">FinPartState</a> of <font color="Olive" title="b1">S</font> holds  <font color="Olive" title="b2">p</font> <a href="ami_1.html#R1" title="AMI_1:pred.1">computes</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><br/><b>let </b><font color="Maroon" title="c3">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#V4" title="AMI_1:attr.4">halting</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="ami_1.html#V9" title="AMI_1:attr.9">realistic</a>  <a href="ami_1.html#L1" title="AMI_1:struct.1">AMI-Struct</a> of <font color="Maroon" title="c1">IL</font>,<font color="Maroon" title="c2">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">p</font> being  <a href="ami_1.html#NM8" title="AMI_1:NM.8">FinPartState</a> of <font color="Maroon" title="c3">S</font> holds  <font color="Olive" title="b1">p</font> <a href="ami_1.html#R1" title="AMI_1:pred.1">computes</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><br/><b>let </b><font color="Maroon" title="c4">p</font> be   <a href="ami_1.html#NM8" title="AMI_1:NM.8">FinPartState</a> of <font color="Maroon" title="c3">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">p</font> <a href="ami_1.html#R1" title="AMI_1:pred.1">computes</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><br/><b>let </b><font color="Maroon" title="c5">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D29" target="_self" title="AMI_1:def.29">AMI_1:def 29</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies  ex <font color="Olive" title="b1">s</font> being  <a href="ami_1.html#NM8" title="AMI_1:NM.8">FinPartState</a> of <font color="Maroon" title="c3">S</font> st <br/>( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s</font> &amp; <font color="Maroon" title="c4">p</font> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <font color="Olive" title="b1">s</font> is   <a href="ami_1.html#NM9" title="AMI_1:NM.9">pre-program</a> of <font color="Maroon" title="c3">S</font> &amp; <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">s</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_1.html#K19" title="AMI_1:func.19">Result</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">p</font> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <font color="Olive" title="b1">s</font></span>)</span> ) )</span><br/>









<b>assume </b><a NAME="E1:86"/><i><font color="Green" title="E40">A1</font></i>: 
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">s</font> being  <a href="ami_1.html#NM8" title="AMI_1:NM.8">FinPartState</a> of <font color="Maroon" title="c3">S</font> st <br/>( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s</font> &amp; <font color="Maroon" title="c4">p</font> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <font color="Olive" title="b1">s</font> is   <a href="ami_1.html#NM9" title="AMI_1:NM.9">pre-program</a> of <font color="Maroon" title="c3">S</font> &amp; <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">s</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_1.html#K19" title="AMI_1:func.19">Result</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">p</font> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <font color="Olive" title="b1">s</font></span>)</span> )</span><br/>

<b>then reconsider </b><font color="Maroon" title="c6">x</font> = <font color="Maroon" title="c5">x</font> as   <a href="ami_1.html#NM8" title="AMI_1:NM.8">FinPartState</a> of <font color="Maroon" title="c3">S</font> ;<br/>
<b>take </b>
<font color="Maroon" title="c6">x</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">x</font> &amp; <font color="Maroon" title="c4">p</font> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <font color="Maroon" title="c6">x</font> is   <a href="ami_1.html#NM9" title="AMI_1:NM.9">pre-program</a> of <font color="Maroon" title="c3">S</font> &amp; <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_1.html#K19" title="AMI_1:func.19">Result</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">p</font> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <font color="Maroon" title="c6">x</font></span>)</span> )</span><br/>

<b>thus </b><a NAME="E3:86"/>
( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">x</font> &amp; <font color="Maroon" title="c4">p</font> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <font color="Maroon" title="c6">x</font> is   <a href="ami_1.html#NM9" title="AMI_1:NM.9">pre-program</a> of <font color="Maroon" title="c3">S</font> &amp; <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_1.html#K19" title="AMI_1:func.19">Result</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">p</font> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <font color="Maroon" title="c6">x</font></span>)</span> )
 <b>by </b><i><a class="txt" href="ami_1.html#E1:86"><i><font color="Green" title="E40">A1</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
