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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_0.html#V6" title="COMPOS_0:attr.6">No-StopCode</a>  <a href="compos_1.html#NM1" title="COMPOS_1:NM.1">Instruction</a> of <font color="Maroon" title="c1">S</font>  st <font color="Olive" title="b1">i</font> is  <a href="compos_0.html#V4" title="COMPOS_0:attr.4">ins-loc-free</a>  holds <br/> <a href="compos_1.html#K11" title="COMPOS_1:func.11">Macro</a> <font color="Olive" title="b1">i</font> is  <a href="compos_2.html#V1" title="COMPOS_2:attr.1">closed</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">i</font> be   <a href="compos_0.html#V6" title="COMPOS_0:attr.6">No-StopCode</a>  <a href="compos_1.html#NM1" title="COMPOS_1:NM.1">Instruction</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"> ( <font color="Maroon" title="c2">i</font> is  <a href="compos_0.html#V4" title="COMPOS_0:attr.4">ins-loc-free</a>  implies  <a href="compos_1.html#K11" title="COMPOS_1:func.11">Macro</a> <font color="Maroon" title="c2">i</font> is  <a href="compos_2.html#V1" title="COMPOS_2:attr.1">closed</a>  )</span><br/>



<span class="kw">assume </span><a NAME="E1:65"/><span class="lab"><font color="Green" title="E40">A1</font></span>: 
<font color="Maroon" title="c2">i</font> is  <a href="compos_0.html#V4" title="COMPOS_0:attr.4">ins-loc-free</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">  <a href="compos_1.html#K11" title="COMPOS_1:func.11">Macro</a> <font color="Maroon" title="c2">i</font> is  <a href="compos_2.html#V1" title="COMPOS_2:attr.1">closed</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c3">i1</font> be   <a href="compos_1.html#NM1" title="COMPOS_1:NM.1">Instruction</a> of <font color="Maroon" title="c1">S</font>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="compos_2.html#D5" target="_self" onmouseover="rs('compos_2/D5')" onmouseout="rh()">COMPOS_2:def 5</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"> ( <font color="Maroon" title="c3">i1</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="compos_1.html#K11" title="COMPOS_1:func.11">Macro</a> <font color="Maroon" title="c2">i</font></span>)</span> implies  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c3">i1</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#K11" title="COMPOS_1:func.11">Macro</a> <font color="Maroon" title="c2">i</font></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E2:65"/>
<font color="Maroon" title="c3">i1</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="compos_1.html#K11" title="COMPOS_1:func.11">Macro</a> <font color="Maroon" title="c2">i</font></span>)</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">  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c3">i1</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#K11" title="COMPOS_1:func.11">Macro</a> <font color="Maroon" title="c2">i</font></span>)</span></span><br/>

<a NAME="E3:65"/><span class="kw">then </span>
<font color="Maroon" title="c3">i1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c2">i</font>,<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><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="compos_1.html#T67" onmouseover="rs('compos_1/T67')" onmouseout="rh()">COMPOS_1:67</a></span>;<br/>
<a NAME="E4:65"/><span class="kw">then </span>
( <font color="Maroon" title="c3">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">i</font> or <font color="Maroon" title="c3">i1</font> <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="tarski.html#D2" onmouseover="rs('tarski/D2')" onmouseout="rh()">TARSKI:def 2</a></span>;<br/>
<a NAME="E5:65"/><span class="kw">then </span>
 <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c3">i1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:65"><span class="lab"><font color="Green" title="E40">A1</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:65"/>
 <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c3">i1</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#K11" title="COMPOS_1:func.11">Macro</a> <font color="Maroon" title="c2">i</font></span>)</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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