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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">J</font> being   <a href="compos_1.html#NM5" title="COMPOS_1:NM.5">MacroInstruction</a> of <font color="Maroon" title="c1">S</font><br/>  for <font color="Olive" title="b2">I</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="b2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="valued_1.html#K63" title="VALUED_1:func.63">CutLastLoc</a> <font color="Olive" title="b1">J</font> holds <br/><font color="Olive" title="b2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">J</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">J</font> be   <a href="compos_1.html#NM5" title="COMPOS_1:NM.5">MacroInstruction</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">I</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="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="valued_1.html#K63" title="VALUED_1:func.63">CutLastLoc</a> <font color="Maroon" title="c2">J</font> holds <br/><font color="Olive" title="b1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">J</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">I</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="c3">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="valued_1.html#K63" title="VALUED_1:func.63">CutLastLoc</a> <font color="Maroon" title="c2">J</font> implies <font color="Maroon" title="c3">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">J</font> )</span><br/>





<span class="kw">assume </span><a NAME="E1:22"/><span class="lab"><font color="Green" title="E12">A1</font></span>: 
 <a href="valued_1.html#K63" title="VALUED_1:func.63">CutLastLoc</a> <font color="Maroon" title="c3">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="valued_1.html#K63" title="VALUED_1:func.63">CutLastLoc</a> <font color="Maroon" title="c2">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"> <font color="Maroon" title="c3">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">J</font></span><br/>

<span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">I</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 = 
 <a href="card_1.html#K4" title="CARD_1:func.4">card</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">J</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="ref" href="valued_1.html#T38" onmouseover="rs('valued_1/T38')" onmouseout="rh()">VALUED_1:38</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c2">J</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
<span class="kw">by</span> <span class="lab"><a class="ref" href="valued_1.html#T38" onmouseover="rs('valued_1/T38')" onmouseout="rh()">VALUED_1:38</a></span>
;<br/>
<span class="kw">then </span> <a href="valued_1.html#K62" title="VALUED_1:func.62">LastLoc</a> <font color="Maroon" title="c3">I</font> = 
<span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c2">J</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T70" onmouseover="rs('afinsq_1/T70')" onmouseout="rh()">AFINSQ_1:70</a></span>
<br/>.= 
 <a href="valued_1.html#K62" title="VALUED_1:func.62">LastLoc</a> <font color="Maroon" title="c2">J</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T70" onmouseover="rs('afinsq_1/T70')" onmouseout="rh()">AFINSQ_1:70</a></span>
;<br/>
<span class="kw">hence </span><font color="Maroon" title="c3">I</font> = 
<span class="p1">(<span class="default"><a href="valued_1.html#K63" title="VALUED_1:func.63">CutLastLoc</a> <font color="Maroon" title="c3">I</font></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"><a href="valued_1.html#K62" title="VALUED_1:func.62">LastLoc</a> <font color="Maroon" title="c2">J</font></span>)</span> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <span class="p2">(<span class="default"><a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <font color="Maroon" title="c1">S</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="compos_2.html#T20" target="_self" onmouseover="rs('compos_2/T20')" onmouseout="rh()">Th20</a></span>
<br/>.= 
<font color="Maroon" title="c2">J</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="ref" href="compos_2.html#T20" target="_self" onmouseover="rs('compos_2/T20')" onmouseout="rh()">Th20</a></span>
;<br/> <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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