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<span class="kw">let </span><font color="Maroon" title="c1">I</font> be   <a href="compos_1.html#NM5" title="COMPOS_1:NM.5">Program</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>; <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">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>   st  not <font color="Maroon" title="c1">I</font> <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">destroys</a> <font color="Olive" title="b2">b</font> holds <br/> not  <a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> (<font color="Olive" title="b1">a</font>,<font color="Maroon" title="c1">I</font>) <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">destroys</a> <font color="Olive" title="b2">b</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> be    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c1">I</font> <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">destroys</a> <font color="Maroon" title="c3">b</font> implies  not  <a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">I</font>) <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">destroys</a> <font color="Maroon" title="c3">b</font> )</span><br/>



<span class="kw">set </span><font color="Maroon" title="c4">J</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 4</span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">Gi</font> =  <a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">SS</font> =  <a href="compos_1.html#K6" title="COMPOS_1:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">F</font> =  <a href="scmfsa8b.html#K2" title="SCMFSA8B:func.2">if&gt;0</a> (<font color="Maroon" title="c2">a</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <span class="p2">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="compos_1.html#K6" title="COMPOS_1:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span>);<br/>
<a NAME="E1:4"/><span class="lab"><font color="Green" title="E3">A1</font></span>: 
 not  <a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">destroys</a> <font color="Maroon" title="c3">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa8c.html#T57" title="SCMFSA8C:th.57">SCMFSA8C:57</a></span>;<br/>
<a NAME="E2:4"/><span class="lab"><font color="Green" title="E4">A2</font></span>: 
 not  <a href="compos_1.html#K6" title="COMPOS_1:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">destroys</a> <font color="Maroon" title="c3">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa8c.html#T56" title="SCMFSA8C:th.56">SCMFSA8C:56</a></span>;<br/>
<span class="kw">assume </span><a NAME="E3:4"/>
 not <font color="Maroon" title="c1">I</font> <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">destroys</a> <font color="Maroon" title="c3">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not  <a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">I</font>) <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">destroys</a> <font color="Maroon" title="c3">b</font></span><br/>

<a NAME="E4:4"/><span class="kw">then </span>
 not <font color="Maroon" title="c1">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <span class="p1">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">destroys</a> <font color="Maroon" title="c3">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:4"><span class="lab"><font color="Green" title="E3">A1</font></span></a>, <a class="ref" href="scmfsa8c.html#T52" title="SCMFSA8C:th.52">SCMFSA8C:52</a></span>;<br/>
<a NAME="E5:4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E5">A3</font></span>: 
 not  <a href="scmfsa8b.html#K2" title="SCMFSA8B:func.2">if&gt;0</a> (<font color="Maroon" title="c2">a</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <span class="p2">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="compos_1.html#K6" title="COMPOS_1:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span>) <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">destroys</a> <font color="Maroon" title="c3">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:4"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="ref" href="scmfsa8c.html#T88" title="SCMFSA8C:th.88">SCMFSA8C:88</a></span>;<br/>
<a NAME="E6:4"/><span class="lab"><font color="Green" title="E6">A4</font></span>: 
 <a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">I</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K2" title="SCMFSA8B:func.2">if&gt;0</a> (<font color="Maroon" title="c2">a</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="compos_1.html#K6" title="COMPOS_1:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 4</span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_9.html#D2" title="SCMFSA_9:def.2">SCMFSA_9:def 2</a></span>;<br/>
<a NAME="E7:4"/>
 not <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 4</span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">destroys</a> <font color="Maroon" title="c3">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_9.html#T30" title="SCMFSA_9:th.30">SCMFSA_9:30</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:4"/>
 not  <a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">I</font>) <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">destroys</a> <font color="Maroon" title="c3">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:4"><span class="lab"><font color="Green" title="E5">A3</font></span></a>, <a class="txt" href="#E6:4"><span class="lab"><font color="Green" title="E6">A4</font></span></a>, <a class="ref" href="scmfsa8a.html#T11" title="SCMFSA8A:th.11">SCMFSA8A:11</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/>


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