<?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#NM9" title="AMI_1:NM.9">pre-program</a> of <font color="Olive" title="b2">S</font><br/> for <font color="Olive" title="b4">F</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of  <a href="ami_1.html#K14" title="AMI_1:func.14">FinPartSt</a> <font color="Olive" title="b2">S</font>, <a href="ami_1.html#K14" title="AMI_1:func.14">FinPartSt</a> <font color="Olive" title="b2">S</font>  st <font color="Olive" title="b4">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p1">(<span class="default"><a href="ami_1.html#K19" title="AMI_1:func.19">Result</a> <font color="Olive" title="b3">p</font></span>)</span> holds <br/><font color="Olive" title="b3">p</font> is    <a href="ami_1.html#M4" title="AMI_1:mode.4">Program</a> of <font color="Olive" title="b4">F</font></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#NM9" title="AMI_1:NM.9">pre-program</a> of <font color="Olive" title="b1">S</font><br/> for <font color="Olive" title="b3">F</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of  <a href="ami_1.html#K14" title="AMI_1:func.14">FinPartSt</a> <font color="Olive" title="b1">S</font>, <a href="ami_1.html#K14" title="AMI_1:func.14">FinPartSt</a> <font color="Olive" title="b1">S</font>  st <font color="Olive" title="b3">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p1">(<span class="default"><a href="ami_1.html#K19" title="AMI_1:func.19">Result</a> <font color="Olive" title="b2">p</font></span>)</span> holds <br/><font color="Olive" title="b2">p</font> is    <a href="ami_1.html#M4" title="AMI_1:mode.4">Program</a> of <font color="Olive" title="b3">F</font></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#NM9" title="AMI_1:NM.9">pre-program</a> of <font color="Maroon" title="c3">S</font><br/> for <font color="Olive" title="b2">F</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of  <a href="ami_1.html#K14" title="AMI_1:func.14">FinPartSt</a> <font color="Maroon" title="c3">S</font>, <a href="ami_1.html#K14" title="AMI_1:func.14">FinPartSt</a> <font color="Maroon" title="c3">S</font>  st <font color="Olive" title="b2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p1">(<span class="default"><a href="ami_1.html#K19" title="AMI_1:func.19">Result</a> <font color="Olive" title="b1">p</font></span>)</span> holds <br/><font color="Olive" title="b1">p</font> is    <a href="ami_1.html#M4" title="AMI_1:mode.4">Program</a> of <font color="Olive" title="b2">F</font></span><br/><b>let </b><font color="Maroon" title="c4">p</font> be   <a href="ami_1.html#NM9" title="AMI_1:NM.9">pre-program</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"> for <font color="Olive" title="b1">F</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of  <a href="ami_1.html#K14" title="AMI_1:func.14">FinPartSt</a> <font color="Maroon" title="c3">S</font>, <a href="ami_1.html#K14" title="AMI_1:func.14">FinPartSt</a> <font color="Maroon" title="c3">S</font>  st <font color="Olive" title="b1">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p1">(<span class="default"><a href="ami_1.html#K19" title="AMI_1:func.19">Result</a> <font color="Maroon" title="c4">p</font></span>)</span> holds <br/><font color="Maroon" title="c4">p</font> is    <a href="ami_1.html#M4" title="AMI_1:mode.4">Program</a> of <font color="Olive" title="b1">F</font></span><br/><b>let </b><font color="Maroon" title="c5">F</font> be   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of  <a href="ami_1.html#K14" title="AMI_1:func.14">FinPartSt</a> <font color="Maroon" title="c3">S</font>, <a href="ami_1.html#K14" title="AMI_1:func.14">FinPartSt</a> <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="c5">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p1">(<span class="default"><a href="ami_1.html#K19" title="AMI_1:func.19">Result</a> <font color="Maroon" title="c4">p</font></span>)</span> implies <font color="Maroon" title="c4">p</font> is    <a href="ami_1.html#M4" title="AMI_1:mode.4">Program</a> of <font color="Maroon" title="c5">F</font> )</span><br/>









<b>assume </b><a NAME="E1:96"/><i><font color="Green" title="E46">A1</font></i>: 
<font color="Maroon" title="c5">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p1">(<span class="default"><a href="ami_1.html#K19" title="AMI_1:func.19">Result</a> <font color="Maroon" title="c4">p</font></span>)</span>
 ; <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> is    <a href="ami_1.html#M4" title="AMI_1:mode.4">Program</a> of <font color="Maroon" title="c5">F</font></span><br/>

<b>hence </b><a NAME="E2:96"/>
<font color="Maroon" title="c5">F</font> is <a href="ami_1.html#V13" title="AMI_1:attr.13">computable</a>
 <b>by </b><i><a class="ref" href="ami_1.html#T73" target="_self" title="AMI_1:th.73">Th73</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D31" target="_self" title="AMI_1:def.31">AMI_1:def 31</a> <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> <font color="Maroon" title="c5">F</font></span><br/>

<b>thus </b><a NAME="E3:96"/>
<font color="Maroon" title="c4">p</font> <a href="ami_1.html#R1" title="AMI_1:pred.1">computes</a> <font color="Maroon" title="c5">F</font>
 <b>by </b><i><a class="txt" href="#E1:96"><i><font color="Green" title="E46">A1</font></i></a>, <a class="ref" href="ami_1.html#T69" target="_self" title="AMI_1:th.69">Th69</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>
