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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><br/>  for <font color="Olive" title="b3">j</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b3">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="valued_1.html#K62" title="VALUED_1:func.62">LastLoc</a> <font color="Olive" title="b2">J</font> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b1">I</font> <a href="compos_1.html#K8" title="COMPOS_1:func.8">';'</a> <font color="Olive" title="b2">J</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1: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="Olive" title="b1">I</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b3">j</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_0.html#K8" title="COMPOS_0:func.8">IncAddr</a> (<span class="p1">(<span class="default"><font color="Olive" title="b2">J</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b3">j</font></span>)</span>,<span class="p1">(<span class="default"><a href="valued_1.html#K62" title="VALUED_1:func.62">LastLoc</a> <font color="Olive" title="b1">I</font></span>)</span>)</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">  for <font color="Olive" title="b1">j</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b1">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="valued_1.html#K62" title="VALUED_1:func.62">LastLoc</a> <font color="Maroon" title="c3">J</font> holds <br/><span class="p1">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="compos_1.html#K8" title="COMPOS_1:func.8">';'</a> <font color="Maroon" title="c3">J</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1: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">I</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b1">j</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_0.html#K8" title="COMPOS_0:func.8">IncAddr</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c3">J</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b1">j</font></span>)</span>,<span class="p1">(<span class="default"><a href="valued_1.html#K62" title="VALUED_1:func.62">LastLoc</a> <font color="Maroon" title="c2">I</font></span>)</span>)</span><br/><span class="kw">let </span><font color="Maroon" title="c4">j</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="c4">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="valued_1.html#K62" title="VALUED_1:func.62">LastLoc</a> <font color="Maroon" title="c3">J</font> implies <span class="p1">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="compos_1.html#K8" title="COMPOS_1:func.8">';'</a> <font color="Maroon" title="c3">J</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1: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">I</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">j</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_0.html#K8" title="COMPOS_0:func.8">IncAddr</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c3">J</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c4">j</font></span>)</span>,<span class="p1">(<span class="default"><a href="valued_1.html#K62" title="VALUED_1:func.62">LastLoc</a> <font color="Maroon" title="c2">I</font></span>)</span>) )</span><br/>







<span class="kw">assume </span><a NAME="E1:45"/><span class="lab"><font color="Green" title="E28">A1</font></span>: 
<font color="Maroon" title="c4">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="valued_1.html#K62" title="VALUED_1:func.62">LastLoc</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"> <span class="p1">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="compos_1.html#K8" title="COMPOS_1:func.8">';'</a> <font color="Maroon" title="c3">J</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1: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">I</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">j</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_0.html#K8" title="COMPOS_0:func.8">IncAddr</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c3">J</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c4">j</font></span>)</span>,<span class="p1">(<span class="default"><a href="valued_1.html#K62" title="VALUED_1:func.62">LastLoc</a> <font color="Maroon" title="c2">I</font></span>)</span>)</span><br/>

<span class="kw">set </span><font color="Maroon" title="c5">k</font> = <span class="p1">(<span class="default"><a href="valued_1.html#K62" title="VALUED_1:func.62">LastLoc</a> <font color="Maroon" title="c2">I</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">j</font>;<br/>
<a NAME="E2:45"/><span class="lab"><font color="Green" title="E29">A2</font></span>: 
 <a href="valued_1.html#K62" title="VALUED_1:func.62">LastLoc</a> <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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="ref" href="afinsq_1.html#T70" onmouseover="rs('afinsq_1/T70')" onmouseout="rh()">AFINSQ_1:70</a></span>;<br/>
<a NAME="E3:45"/><span class="lab"><font color="Green" title="E30">A3</font></span>: 
<font color="Maroon" title="c4">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">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="txt" href="#E1:45"><span class="lab"><font color="Green" title="E28">A1</font></span></a>, <a class="ref" href="afinsq_1.html#T91" onmouseover="rs('afinsq_1/T91')" onmouseout="rh()">AFINSQ_1:91</a></span>;<br/>
<a NAME="E4:45"/>
<span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">J</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">J</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T44" onmouseover="rs('xreal_1/T44')" onmouseout="rh()">XREAL_1:44</a></span>;<br/>
<a NAME="E5:45"/><span class="kw">then </span>
<font color="Maroon" title="c4">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">J</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:45"><span class="lab"><font color="Green" title="E30">A3</font></span></a>, <a class="ref" href="xxreal_0.html#T2" onmouseover="rs('xxreal_0/T2')" onmouseout="rh()">XXREAL_0:2</a></span>;<br/>
<a NAME="E6:45"/><span class="kw">then </span><span class="lab"><font color="Green" title="E31">A4</font></span>: 
<font color="Maroon" title="c4">j</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> <font color="Maroon" title="c3">J</font>
 
<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>;<br/>
<a NAME="E7:45"/><span class="kw">then </span><span class="lab"><font color="Green" title="E32">A5</font></span>: 
<font color="Maroon" title="c4">j</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="compos_1.html#K5" title="COMPOS_1:func.5">IncAddr</a> (<font color="Maroon" title="c3">J</font>,<span class="p2">(<span class="default"><a href="valued_1.html#K62" title="VALUED_1:func.62">LastLoc</a> <font color="Maroon" title="c2">I</font></span>)</span>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="compos_1.html#D21" onmouseover="rs('compos_1/D21')" onmouseout="rh()">COMPOS_1:def 21</a></span>;<br/>
<a NAME="E8:45"/><span class="lab"><font color="Green" title="E33">A6</font></span>: 
<span class="p1">(<span class="default"><a href="valued_1.html#K62" title="VALUED_1:func.62">LastLoc</a> <font color="Maroon" title="c2">I</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">j</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</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#K6" title="COMPOS_1:func.6">Reloc</a> (<font color="Maroon" title="c3">J</font>,<span class="p2">(<span class="default"><a href="valued_1.html#K62" title="VALUED_1:func.62">LastLoc</a> <font color="Maroon" title="c2">I</font></span>)</span>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:45"><span class="lab"><font color="Green" title="E31">A4</font></span></a>, <a class="ref" href="compos_1.html#T46" onmouseover="rs('compos_1/T46')" onmouseout="rh()">COMPOS_1:46</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c6">j</font> = <font color="Maroon" title="c4">j</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal1.html#D12" onmouseover="rs('ordinal1/D12')" onmouseout="rh()">ORDINAL1:def 12</a></span>;<br/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="compos_1.html#K8" title="COMPOS_1:func.8">';'</a> <font color="Maroon" title="c3">J</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1: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">I</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c6">j</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="compos_1.html#K6" title="COMPOS_1:func.6">Reloc</a> (<font color="Maroon" title="c3">J</font>,<span class="p2">(<span class="default"><a href="valued_1.html#K62" title="VALUED_1:func.62">LastLoc</a> <font color="Maroon" title="c2">I</font></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1: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">I</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c6">j</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:45"><span class="lab"><font color="Green" title="E33">A6</font></span></a>, <a class="txt" href="#E2:45"><span class="lab"><font color="Green" title="E29">A2</font></span></a>, <a class="ref" href="funct_4.html#T13" onmouseover="rs('funct_4/T13')" onmouseout="rh()">FUNCT_4:13</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">IncAddr</a> (<font color="Maroon" title="c3">J</font>,<span class="p2">(<span class="default"><a href="valued_1.html#K62" title="VALUED_1:func.62">LastLoc</a> <font color="Maroon" title="c2">I</font></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">j</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:45"><span class="lab"><font color="Green" title="E32">A5</font></span></a>, <a class="ref" href="valued_1.html#D12" onmouseover="rs('valued_1/D12')" onmouseout="rh()">VALUED_1:def 12</a></span>
<br/>.= 
 <a href="compos_0.html#K8" title="COMPOS_0:func.8">IncAddr</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c3">J</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">j</font></span>)</span>,<span class="p1">(<span class="default"><a href="valued_1.html#K62" title="VALUED_1:func.62">LastLoc</a> <font color="Maroon" title="c2">I</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:45"><span class="lab"><font color="Green" title="E31">A4</font></span></a>, <a class="ref" href="compos_1.html#D21" onmouseover="rs('compos_1/D21')" onmouseout="rh()">COMPOS_1:def 21</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E11:45"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="compos_1.html#K8" title="COMPOS_1:func.8">';'</a> <font color="Maroon" title="c3">J</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1: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">I</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">j</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_0.html#K8" title="COMPOS_0:func.8">IncAddr</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c3">J</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c4">j</font></span>)</span>,<span class="p1">(<span class="default"><a href="valued_1.html#K62" title="VALUED_1:func.62">LastLoc</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/>


</div>
