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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>, <font color="Olive" title="b2">J</font> being   <a href="compos_1.html#NM5" title="COMPOS_1:NM.5">MacroInstruction</a> of <font color="Maroon" title="c1">S</font>  st <font color="Olive" title="b1">I</font> <a href="compos_2.html#R2" title="COMPOS_2:pred.2">&lt;=</a> <font color="Olive" title="b2">J</font> &amp; <font color="Olive" title="b2">J</font> <a href="compos_2.html#R2" title="COMPOS_2:pred.2">&lt;=</a> <font color="Olive" title="b1">I</font> holds <br/><font color="Olive" title="b1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">J</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">I</font>, <font color="Maroon" title="c3">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"> ( <font color="Maroon" title="c2">I</font> <a href="compos_2.html#R2" title="COMPOS_2:pred.2">&lt;=</a> <font color="Maroon" title="c3">J</font> &amp; <font color="Maroon" title="c3">J</font> <a href="compos_2.html#R2" title="COMPOS_2:pred.2">&lt;=</a> <font color="Maroon" title="c2">I</font> implies <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">J</font> )</span><br/>





<span class="kw">assume </span><a NAME="E1:23"/>
 <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>
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="compos_2.html#D4" target="_self" onmouseover="rs('compos_2/D4')" onmouseout="rh()">COMPOS_2:def 4</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"> (  not <font color="Maroon" title="c3">J</font> <a href="compos_2.html#R2" title="COMPOS_2:pred.2">&lt;=</a> <font color="Maroon" title="c2">I</font> or <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">J</font> )</span><br/>

<a NAME="E2:23"/><span class="kw">then </span><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="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="ref" href="compos_2.html#T18" target="_self" onmouseover="rs('compos_2/T18')" onmouseout="rh()">Th18</a></span>;<br/>
<span class="kw">assume </span><a NAME="E3:23"/>
 <a href="valued_1.html#K63" title="VALUED_1:func.63">CutLastLoc</a> <font color="Maroon" title="c3">J</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">I</font>
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="compos_2.html#D4" target="_self" onmouseover="rs('compos_2/D4')" onmouseout="rh()">COMPOS_2:def 4</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="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">J</font></span><br/>

<a NAME="E4:23"/><span class="kw">then </span>
 <a href="valued_1.html#K63" title="VALUED_1:func.63">CutLastLoc</a> <font color="Maroon" title="c3">J</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="c2">I</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="compos_2.html#T18" target="_self" onmouseover="rs('compos_2/T18')" onmouseout="rh()">Th18</a></span>;<br/>
<a NAME="E5:23"/><span class="kw">then </span>
 <a href="valued_1.html#K63" title="VALUED_1:func.63">CutLastLoc</a> <font color="Maroon" title="c2">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="c3">J</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:23"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="ref" href="xboole_0.html#D10" onmouseover="rs('xboole_0/D10')" onmouseout="rh()">XBOOLE_0:def 10</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:23"/>
<font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">J</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="compos_2.html#T21" target="_self" onmouseover="rs('compos_2/T21')" onmouseout="rh()">Th21</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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