<?xml version="1.0"?>
<div class="add">

<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#NM5" title="COMPOS_1:NM.5">MacroInstruction</a> of <font color="Maroon" title="c1">S</font><br/>  for <font color="Olive" title="b2">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds <br/> ( <font color="Olive" title="b2">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="valued_1.html#K62" title="VALUED_1:func.62">LastLoc</a> <font color="Olive" title="b1">I</font> iff <font color="Olive" title="b2">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <span class="p1">(<span class="default"><a href="valued_1.html#K63" title="VALUED_1:func.63">CutLastLoc</a> <font color="Olive" title="b1">I</font></span>)</span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">I</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">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds <br/> ( <font color="Olive" title="b1">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="valued_1.html#K62" title="VALUED_1:func.62">LastLoc</a> <font color="Maroon" title="c2">I</font> iff <font color="Olive" title="b1">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</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><br/><span class="kw">let </span><font color="Maroon" title="c3">k</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</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">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="valued_1.html#K62" title="VALUED_1:func.62">LastLoc</a> <font color="Maroon" title="c2">I</font> iff <font color="Maroon" title="c3">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</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><br/>





<a NAME="E1:27"/>
 <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c2">I</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 
;<br/>
<a NAME="E2:27"/><span class="kw">then </span><span class="lab"><font color="Green" title="E14">A1</font></span>: 
 <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c2">I</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T13" onmouseover="rs('nat_1/T13')" onmouseout="rh()">NAT_1:13</a></span>;<br/>
 <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">I</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c2">I</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="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c2">I</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="txt" href="#E2:27"><span class="lab"><font color="Green" title="E14">A1</font></span></a>, <a class="ref" href="xreal_1.html#T233" onmouseover="rs('xreal_1/T233')" onmouseout="rh()">XREAL_1:233</a></span>
<br/>.= 
 <a href="valued_1.html#K62" title="VALUED_1:func.62">LastLoc</a> <font color="Maroon" title="c2">I</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><a NAME="E4:27"/>
( <font color="Maroon" title="c3">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="valued_1.html#K62" title="VALUED_1:func.62">LastLoc</a> <font color="Maroon" title="c2">I</font> iff <font color="Maroon" title="c3">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</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="afinsq_1.html#T86" onmouseover="rs('afinsq_1/T86')" onmouseout="rh()">AFINSQ_1:86</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/>


</div>
