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<div class="add">

<b>let </b><font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font> be    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a> ;<br/>



<b>set </b><font color="Maroon" title="c5">I</font> =  <a href="ami_3.html#K6" title="AMI_3:func.6">MultBy</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>;<br/>
<div><b>hereby </b> <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a>,<a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a>
<div class="add"><b>let </b><font color="Maroon" title="c6">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:60_1"/><i><font color="Green" title="E44">A1</font></i>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_7.html#K2" title="AMI_7:func.2">Output</a> <span class="p1">(<span class="default"><a href="ami_3.html#K6" title="AMI_3:func.6">MultBy</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>
 ;<br/><a NAME="E2:60_1"/><b>then </b><i><font color="Green" title="E45">A2</font></i>: 
 ex <font color="Olive" title="b1">s</font> being  <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  st <font color="Olive" title="b1">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_3.html#K6" title="AMI_3:func.6">MultBy</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>,<font color="Olive" title="b1">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font>
 <b>by </b><i><a class="ref" href="ami_7.html#D3" target="_self" title="AMI_7:def.3">Def3</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:60_1_1"/>
( <font color="Maroon" title="c6">x</font> is    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a>  or <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  or <font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  )
 </span><b>by </b><i><a class="txt" href="ami_7.html#E1:60_1"><i><font color="Green" title="E44">A1</font></i></a>, <a class="ref" href="ami_6.html#T3" title="AMI_6:th.3">AMI_6:3</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_1_1_1"><b>suppose </b></a><a NAME="E1:60_1_1_1"/>
<font color="Maroon" title="c6">x</font> is    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a> 
 ;<br/><div class="add"><a NAME="E2:60_1_1_1"/><b>then </b>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 <b>by </b><i><a class="txt" href="ami_7.html#E2:60_1"><i><font color="Green" title="E45">A2</font></i></a>, <a class="ref" href="ami_3.html#T11" title="AMI_3:th.11">AMI_3:11</a></i>;<br/><b>hence </b><a NAME="E3:60_1_1_1"/>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c3">a</font>,<span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_1_1_2"><b>suppose </b></a><a NAME="E1:60_1_1_2"/>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> 
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon" title="c7">l</font> = <font color="Maroon" title="c6">x</font> as    <a href="ami_1.html#M1" title="AMI_1:mode.1">Instruction-Location</a> of  <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  <b>by </b><i><a class="ref" href="ami_1.html#D4" title="AMI_1:def.4">AMI_1:def 4</a></i>;<br/><a NAME="E3:60_1_1_2"/>
<font color="Maroon" title="c7">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">x</font>
 ;<br/><b>hence </b><a NAME="E4:60_1_1_2"/>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c3">a</font>,<span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>by </b><i><a class="txt" href="ami_7.html#E2:60_1"><i><font color="Green" title="E45">A2</font></i></a>, <a class="ref" href="ami_1.html#D13" title="AMI_1:def.13">AMI_1:def 13</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_1_1_3"><b>suppose </b></a><a NAME="E1:60_1_1_3"/>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> 
 ;<br/><div class="add"><b>hence </b><a NAME="E2:60_1_1_3"/>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c3">a</font>,<span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div>

<b>let </b><font color="Maroon" title="c6">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="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E2:60"/>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c3">a</font>,<span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 ;<br/>

<a NAME="E3:60"/><b>then </b><i><font color="Green" title="E44">A3</font></i>: 
( <font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> or <font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  )
 
<b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c7">s</font> being   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> ;<br/>
<b>set </b><font color="Maroon" title="c8">t</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c7">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 2</span>)</span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="60_2"><b>now </b></a><div class="add"><a NAME="E1:60_2"/>
( <font color="Maroon" title="c3">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">b</font> or <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> )
 ;<br/><a NAME="E2:60_2"/><b>then </b><i><font color="Green" title="E45">A4</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 2</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c3">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0
 <b>by </b><i><a class="ref" href="bvfunc14.html#T15" title="BVFUNC14:th.15">BVFUNC14:15</a>, <a class="ref" href="funct_7.html#T96" title="FUNCT_7:th.96">FUNCT_7:96</a></i>;<br/><b>assume </b><a NAME="E3:60_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 2</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_3.html#K6" title="AMI_3:func.6">MultBy</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 2</span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c3">a</font>
 ;<br/><a NAME="E4:60_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 2</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 2</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 2</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c4">b</font></span>)</span>
 <b>by </b><i><a class="ref" href="ami_3.html#T11" title="AMI_3:th.11">AMI_3:11</a></i>;<br/><a NAME="E5:60_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> 2</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <b>by </b><i><a class="txt" href="ami_7.html#E2:60_2"><i><font color="Green" title="E45">A4</font></i></a>, <a class="ref" href="xcmplx_1.html#T7" title="XCMPLX_1:th.7">XCMPLX_1:7</a></i>;<br/><b>hence </b><a NAME="E6:60_2"/>
contradiction
 <b>by </b><i><a class="ref" href="funct_7.html#T96" title="FUNCT_7:th.96">FUNCT_7:96</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:60"/>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_7.html#K2" title="AMI_7:func.2">Output</a> <span class="p1">(<span class="default"><a href="ami_3.html#K6" title="AMI_3:func.6">MultBy</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>
 <b>by </b><i><a class="txt" href="ami_7.html#E3:60"><i><font color="Green" title="E44">A3</font></i></a>, <a class="ref" href="ami_7.html#D3" target="_self" title="AMI_7:def.3">Def3</a>, <a class="ref" href="ami_7.html#T25" target="_self" title="AMI_7:th.25">Th25</a></i>;<br/>


</div>
