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<b>let </b><font color="Maroon">c<sub>1</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>2</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="amistd_1.html#V4">standard</a> <a href="amistd_2.html#V8" target="_self">regular</a>  <a href="ami_1.html#L1">AMI-Struct</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be  non <a href="xboole_0.html#V1">empty</a> <a href="ami_3.html#V1">programmed</a> <a href="amistd_1.html#V9">lower</a>  <a href="ami_1.html#M1">FinPartState</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>





<b>set </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="amistd_2.html#K12" target="_self">';'</a> <font color="Maroon">c<sub>4</sub></font>;<br/>
<a NAME="E1:125"/><i><font color="Green">E70</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="amistd_2.html#K12" target="_self">';'</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K11" target="_self">CutLastLoc</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K10" target="_self">Shift</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="amistd_2.html#E80"><i><font color="Green">Lemma67</font></i></a></i>;<br/>
<a NAME="E2:125"/><i><font color="Green">E71</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K11" target="_self">CutLastLoc</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="realset1.html#K5">{</a><span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K10">LastLoc</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="realset1.html#K5">}</a></span>
 
<b>by </b><i><a class="ref" href="amistd_2.html#T48" target="_self">Th48</a></i>;<br/>
<b>let </b><font color="Maroon">c<sub>6</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E3:125"/><i><font color="Green">E72</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="125_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:125_1"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K11" target="_self">CutLastLoc</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> or <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="realset1.html#K5">{</a><span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K10">LastLoc</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="realset1.html#K5">}</a></span> )
 </span><b>by </b><i><a class="txt" href="amistd_2.html#E2:125"><i><font color="Green">E71</font></i></a>, <a class="txt" href="amistd_2.html#E3:125"><i><font color="Green">E72</font></i></a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="125_1_1"><b>suppose </b></a><a NAME="E1:125_1_1"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K11" target="_self">CutLastLoc</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:125_1_1"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="amistd_2.html#K12" target="_self">';'</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E1:125"><i><font color="Green">E70</font></i></a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="125_1_2"><b>suppose </b></a><a NAME="E1:125_1_2"/><i><font color="Green">E73</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="realset1.html#K5">{</a><span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K10">LastLoc</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="realset1.html#K5">}</a></span>
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>6</sub></font> as   <a href="ami_1.html#NM2">Instruction-Location</a> of <font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E3:125_1_2"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="amistd_1.html#K10">LastLoc</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="amistd_2.html#E1:125_1_2"><i><font color="Green">E73</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>then </b><i><font color="Green">E74</font></i>:  <a href="amistd_1.html#K7">locnum</a> <font color="Maroon">c<sub>7</sub></font> = 
 <a href="amistd_1.html#K7">locnum</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="amistd_1.html#T55">AMISTD_1:55</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1
<b>by </b><i><a class="ref" href="amistd_1.html#D13">AMISTD_1:def 13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2">+</a> 0
<b>by </b><i><a class="ref" href="amistd_2.html#T4" target="_self">Th4</a></i>
;<br/><i><font color="Green">E75</font></i>:  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="amistd_2.html#K12" target="_self">';'</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
<b>by </b><i><a class="ref" href="amistd_2.html#T52" target="_self">Th52</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>

;<br/><a NAME="E6:125_1_2"/>
0 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="card_2.html#T59">CARD_2:59</a></i>;<br/><a NAME="E7:125_1_2"/><b>then </b>
0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/><a NAME="E8:125_1_2"/><b>then </b>
 <a href="amistd_1.html#K7">locnum</a> <font color="Maroon">c<sub>7</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="amistd_2.html#K12" target="_self">';'</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E4:125_1_2"><i><font color="Green">E74</font></i></a>, <a class="txt" href="amistd_2.html#E5:125_1_2"><i><font color="Green">E75</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E9:125_1_2"/><b>then </b>
 <a href="amistd_1.html#K5">il.</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="amistd_1.html#K7">locnum</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="amistd_2.html#K12" target="_self">';'</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_1.html#T50">AMISTD_1:50</a></i>;<br/><b>hence </b><a NAME="E10:125_1_2"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="amistd_2.html#K12" target="_self">';'</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_1.html#D13">AMISTD_1:def 13</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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