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<b>let </b><font color="Maroon" title="c1">W</font> be   <a href="ami_1.html#NM4" title="AMI_1:NM.4">Instruction</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">W</font> is <a href="ami_1.html#V3" title="AMI_1:attr.3">halting</a> implies <font color="Maroon" title="c1">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> ,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> )</span><br/>

<b>assume </b><a NAME="E1:29"/><i><font color="Green" title="E23">A1</font></i>: 
<font color="Maroon" title="c1">W</font> is <a href="ami_1.html#V3" title="AMI_1:attr.3">halting</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> ,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><br/>

<b>set </b><font color="Maroon" title="c2">I</font> = <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> ,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>;<br/>
<b>assume </b><a NAME="E2:29"/><i><font color="Green" title="E24">A2</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> ,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c1">W</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:29_1"/>
( <font color="Maroon" title="c1">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> ,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a>  st <font color="Maroon" title="c1">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a>  st <font color="Maroon" title="c1">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K4" title="AMI_3:func.4">AddTo</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a>  st <font color="Maroon" title="c1">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K5" title="AMI_3:func.5">SubFrom</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a>  st <font color="Maroon" title="c1">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K6" title="AMI_3:func.6">MultBy</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a>  st <font color="Maroon" title="c1">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">loc</font> being   <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of  <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  st <font color="Maroon" title="c1">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K8" title="AMI_3:func.8">goto</a> <font color="Olive" title="b1">loc</font> or  ex <font color="Olive" title="b1">a</font> being   <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a>  ex <font color="Olive" title="b2">loc</font> being   <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of  <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  st <font color="Maroon" title="c1">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="ami_3.html#K9" title="AMI_3:func.9">=0_goto</a> <font color="Olive" title="b2">loc</font> or  ex <font color="Olive" title="b1">a</font> being   <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a>  ex <font color="Olive" title="b2">loc</font> being   <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of  <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  st <font color="Maroon" title="c1">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="ami_3.html#K10" title="AMI_3:func.10">&gt;0_goto</a> <font color="Olive" title="b2">loc</font> )
 </span><b>by </b><i><a class="txt" href="ami_3.html#E36"><i><font color="Green" title="E21">Lm11</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_1"><b>suppose </b></a><a NAME="E1:29_1_1"/>
<font color="Maroon" title="c1">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> ,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><div class="add"><b>hence </b><a NAME="E2:29_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E2:29"><i><font color="Green" title="E24">A2</font></i></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><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_2"><b>suppose </b></a><a NAME="E1:29_1_2"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a>  st <font color="Maroon" title="c1">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Olive" title="b2">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><div class="add"><b>hence </b><a NAME="E2:29_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="#E1:29"><i><font color="Green" title="E23">A1</font></i></a>, <a class="txt" href="ami_3.html#E28"><i><font color="Green" title="E13">Lm3</font></i></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><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_3"><b>suppose </b></a><a NAME="E1:29_1_3"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a>  st <font color="Maroon" title="c1">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K4" title="AMI_3:func.4">AddTo</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><div class="add"><b>hence </b><a NAME="E2:29_1_3"/>
contradiction
 <b>by </b><i><a class="txt" href="#E1:29"><i><font color="Green" title="E23">A1</font></i></a>, <a class="txt" href="ami_3.html#E29"><i><font color="Green" title="E14">Lm4</font></i></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><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_4"><b>suppose </b></a><a NAME="E1:29_1_4"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a>  st <font color="Maroon" title="c1">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K5" title="AMI_3:func.5">SubFrom</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><div class="add"><b>hence </b><a NAME="E2:29_1_4"/>
contradiction
 <b>by </b><i><a class="txt" href="#E1:29"><i><font color="Green" title="E23">A1</font></i></a>, <a class="txt" href="ami_3.html#E30"><i><font color="Green" title="E15">Lm5</font></i></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><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_5"><b>suppose </b></a><a NAME="E1:29_1_5"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a>  st <font color="Maroon" title="c1">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K6" title="AMI_3:func.6">MultBy</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><div class="add"><b>hence </b><a NAME="E2:29_1_5"/>
contradiction
 <b>by </b><i><a class="txt" href="#E1:29"><i><font color="Green" title="E23">A1</font></i></a>, <a class="txt" href="ami_3.html#E31"><i><font color="Green" title="E16">Lm6</font></i></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><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_6"><b>suppose </b></a><a NAME="E1:29_1_6"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a>  st <font color="Maroon" title="c1">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><div class="add"><b>hence </b><a NAME="E2:29_1_6"/>
contradiction
 <b>by </b><i><a class="txt" href="#E1:29"><i><font color="Green" title="E23">A1</font></i></a>, <a class="txt" href="ami_3.html#E32"><i><font color="Green" title="E17">Lm7</font></i></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><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_7"><b>suppose </b></a><a NAME="E1:29_1_7"/>
 ex <font color="Olive" title="b1">loc</font> being   <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of  <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  st <font color="Maroon" title="c1">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K8" title="AMI_3:func.8">goto</a> <font color="Olive" title="b1">loc</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><div class="add"><b>hence </b><a NAME="E2:29_1_7"/>
contradiction
 <b>by </b><i><a class="txt" href="#E1:29"><i><font color="Green" title="E23">A1</font></i></a>, <a class="txt" href="ami_3.html#E33"><i><font color="Green" title="E18">Lm8</font></i></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><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_8"><b>suppose </b></a><a NAME="E1:29_1_8"/>
 ex <font color="Olive" title="b1">a</font> being   <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a>  ex <font color="Olive" title="b2">loc</font> being   <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of  <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  st <font color="Maroon" title="c1">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="ami_3.html#K9" title="AMI_3:func.9">=0_goto</a> <font color="Olive" title="b2">loc</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><div class="add"><b>hence </b><a NAME="E2:29_1_8"/>
contradiction
 <b>by </b><i><a class="txt" href="#E1:29"><i><font color="Green" title="E23">A1</font></i></a>, <a class="txt" href="ami_3.html#E34"><i><font color="Green" title="E19">Lm9</font></i></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><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_9"><b>suppose </b></a><a NAME="E1:29_1_9"/>
 ex <font color="Olive" title="b1">a</font> being   <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a>  ex <font color="Olive" title="b2">loc</font> being   <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of  <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  st <font color="Maroon" title="c1">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="ami_3.html#K10" title="AMI_3:func.10">&gt;0_goto</a> <font color="Olive" title="b2">loc</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><div class="add"><b>hence </b><a NAME="E2:29_1_9"/>
contradiction
 <b>by </b><i><a class="txt" href="#E1:29"><i><font color="Green" title="E23">A1</font></i></a>, <a class="txt" href="ami_3.html#E35"><i><font color="Green" title="E20">Lm10</font></i></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><b>end;</b></div></div><b>end;</b></div>

</div>
