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<span class="kw">let </span><font color="Maroon" title="c1">S</font> be   <a href="amistd_4.html#V1" title="AMISTD_4:attr.1">with_non_trivial_Instructions</a>   <a href="compos_1.html#L1" title="COMPOS_1:struct.1">COM-Struct</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">I</font> being   <a href="compos_1.html#V4" title="COMPOS_1:attr.4">unique-halt</a>  <a href="compos_1.html#NM4" title="COMPOS_1:NM.4">Program</a> of <font color="Maroon" title="c1">S</font><br/>  for <font color="Olive" title="b2">J</font> being   <a href="compos_1.html#V3" title="COMPOS_1:attr.3">halt-ending</a>  <a href="compos_1.html#NM4" title="COMPOS_1:NM.4">Program</a> of <font color="Maroon" title="c1">S</font>  st  <a href="valued_1.html#K63" title="VALUED_1:func.63">CutLastLoc</a> <font color="Olive" title="b1">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">J</font> holds <br/> <a href="valued_1.html#K63" title="VALUED_1:func.63">CutLastLoc</a> <font color="Olive" title="b1">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="valued_1.html#K63" title="VALUED_1:func.63">CutLastLoc</a> <font color="Olive" title="b2">J</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">I</font> be   <a href="compos_1.html#V4" title="COMPOS_1:attr.4">unique-halt</a>  <a href="compos_1.html#NM4" title="COMPOS_1:NM.4">Program</a> of <font color="Maroon" title="c1">S</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">J</font> being   <a href="compos_1.html#V3" title="COMPOS_1:attr.3">halt-ending</a>  <a href="compos_1.html#NM4" title="COMPOS_1:NM.4">Program</a> of <font color="Maroon" title="c1">S</font>  st  <a href="valued_1.html#K63" title="VALUED_1:func.63">CutLastLoc</a> <font color="Maroon" title="c2">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">J</font> holds <br/> <a href="valued_1.html#K63" title="VALUED_1:func.63">CutLastLoc</a> <font color="Maroon" title="c2">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="valued_1.html#K63" title="VALUED_1:func.63">CutLastLoc</a> <font color="Olive" title="b1">J</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">J</font> be   <a href="compos_1.html#V3" title="COMPOS_1:attr.3">halt-ending</a>  <a href="compos_1.html#NM4" title="COMPOS_1:NM.4">Program</a> of <font color="Maroon" title="c1">S</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="valued_1.html#K63" title="VALUED_1:func.63">CutLastLoc</a> <font color="Maroon" title="c2">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">J</font> implies  <a href="valued_1.html#K63" title="VALUED_1:func.63">CutLastLoc</a> <font color="Maroon" title="c2">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="valued_1.html#K63" title="VALUED_1:func.63">CutLastLoc</a> <font color="Maroon" title="c3">J</font> )</span><br/>





<span class="kw">assume </span><a NAME="E1:19"/><span class="lab"><font color="Green" title="E10">A1</font></span>: 
 <a href="valued_1.html#K63" title="VALUED_1:func.63">CutLastLoc</a> <font color="Maroon" title="c2">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">J</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="valued_1.html#K63" title="VALUED_1:func.63">CutLastLoc</a> <font color="Maroon" title="c2">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="valued_1.html#K63" title="VALUED_1:func.63">CutLastLoc</a> <font color="Maroon" title="c3">J</font></span><br/>

<a NAME="E2:19"/><span class="lab"><font color="Green" title="E11">A2</font></span>: 
 not  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <font color="Maroon" title="c1">S</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><a href="valued_1.html#K63" title="VALUED_1:func.63">CutLastLoc</a> <font color="Maroon" title="c2">I</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="compos_1.html#D11" onmouseover="rs('compos_1/D11')" onmouseout="rh()">COMPOS_1:def 11</a></span>;<br/>
<a NAME="E3:19"/>
<font color="Maroon" title="c3">J</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="valued_1.html#K62" title="VALUED_1:func.62">LastLoc</a> <font color="Maroon" title="c3">J</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <font color="Maroon" title="c1">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="compos_1.html#D14" onmouseover="rs('compos_1/D14')" onmouseout="rh()">COMPOS_1:def 14</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:19"/>
 <a href="valued_1.html#K63" title="VALUED_1:func.63">CutLastLoc</a> <font color="Maroon" title="c2">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="valued_1.html#K63" title="VALUED_1:func.63">CutLastLoc</a> <font color="Maroon" title="c3">J</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:19"><span class="lab"><font color="Green" title="E11">A2</font></span></a>, <a class="txt" href="#E1:19"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="txt" href="compos_2.html#E22"><span class="lab"><font color="Green" title="E8">Lm1</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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