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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  <a href="setfam_1.html#V1">with_non-empty_elements</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be  non <a href="struct_0.html#V3">empty</a> non <a href="ami_1.html#V2">void</a> <a href="ami_1.html#V5">IC-Ins-separated</a> <a href="ami_1.html#V8">definite</a>  <a href="ami_1.html#L1">AMI-Struct</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be  <a href="ami_3.html#V1">programmed</a>  <a href="ami_1.html#M1">FinPartState</a> of <font color="Maroon">c<sub>3</sub></font>;<br/>







<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>4</sub></font> <a href="subset_1.html#K6">\</a> <font color="Maroon">c<sub>1</sub></font> as    <a href="ami_1.html#M1">FinPartState</a> of <font color="Maroon">c<sub>3</sub></font> <b>by </b><i><a class="ref" href="amistd_2.html#T11" target="_self">Th11</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:20_1"/>
( <font color="Maroon">c<sub>5</sub></font> is <a href="xboole_0.html#V1">empty</a> or  not <font color="Maroon">c<sub>5</sub></font> is <a href="xboole_0.html#V1">empty</a> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_1_1"><b>suppose </b></a><a NAME="E1:20_1_1"/>
<font color="Maroon">c<sub>5</sub></font> is <a href="xboole_0.html#V1">empty</a>
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>5</sub></font> as  <a href="xboole_0.html#V1">empty</a>  <a href="ami_1.html#M1">FinPartState</a> of <font color="Maroon">c<sub>3</sub></font> ;<br/><a NAME="E3:20_1_1"/>
<font color="Maroon">c<sub>6</sub></font> is <a href="ami_3.html#V1">programmed</a>
 ;<br/><b>hence </b><a NAME="E4:20_1_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="subset_1.html#K6">\</a> <font color="Maroon">c<sub>1</sub></font> is  <a href="ami_3.html#V1">programmed</a>  <a href="ami_1.html#M1">FinPartState</a> of <font color="Maroon">c<sub>3</sub></font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_1_2"><b>suppose </b></a><a NAME="E1:20_1_2"/>
not <font color="Maroon">c<sub>5</sub></font> is <a href="xboole_0.html#V1">empty</a>
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>5</sub></font> as  non <a href="xboole_0.html#V1">empty</a>  <a href="ami_1.html#M1">FinPartState</a> of <font color="Maroon">c<sub>3</sub></font> ;<br/><a NAME="E3:20_1_2"/>
<font color="Maroon">c<sub>6</sub></font> is <a href="ami_3.html#V1">programmed</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_2_1"><b>proof </b></a><div class="add">

<a NAME="E1:20_1_2_1"/><i><font color="Green">E15</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/>
<a NAME="E2:20_1_2_1"/>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>4</sub></font> <a href="tarski.html#R1">c=</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="ami_3.html#D13">AMI_3:def 13</a></i>;<br/>
<b>hence </b><a NAME="E3:20_1_2_1"/>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="amistd_2.html#E1:20_1_2_1"><i><font color="Green">E15</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_3.html#D13">AMI_3:def 13</a><br/>


</div><b>end;</b></div><b>hence </b><a NAME="E4:20_1_2"/>
<font color="Maroon">c<sub>4</sub></font> <a href="subset_1.html#K6">\</a> <font color="Maroon">c<sub>1</sub></font> is  <a href="ami_3.html#V1">programmed</a>  <a href="ami_1.html#M1">FinPartState</a> of <font color="Maroon">c<sub>3</sub></font>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
