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<span class="kw">let </span><font color="Maroon" title="c1">I</font> be   <a href="scmnorm.html#NM2" title="SCMNORM:NM.2">Program</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">l</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds   <a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K1" title="SCMFSA6A:func.1">Directed</a> <font color="Maroon" title="c1">I</font>,<font color="Olive" title="b1">l</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c1">I</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">l</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K1" title="SCMFSA6A:func.1">Directed</a> <font color="Maroon" title="c1">I</font>,<font color="Maroon" title="c2">l</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c1">I</font></span><br/>



<span class="kw">consider </span><font color="Maroon" title="c3">UIL</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ,<span class="p1">(<span class="default"><a href="finsub_1.html#K5" title="FINSUB_1:func.5">Fin</a> <a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a> </span>)</span><span class="kw"> such that </span><br/><a NAME="E2:30"/><span class="lab"><font color="Green" title="E18">A1</font></span>: 
for <font color="Olive" title="b1">i</font> being  <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  holds  <font color="Maroon" title="c3">UIL</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="sf_mastr.html#K1" title="SF_MASTR:func.1">UsedIntLoc</a> <font color="Olive" title="b1">i</font>
 <span class="kw">and </span><br/><a NAME="E3:30"/><span class="lab"><font color="Green" title="E19">A2</font></span>: 
 <a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_3.html#K3" title="CARD_3:func.3">Union</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">UIL</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c1">I</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="sf_mastr.html#D2" title="SF_MASTR:def.2">SF_MASTR:def 2</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c4">UIL2</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ,<span class="p1">(<span class="default"><a href="finsub_1.html#K5" title="FINSUB_1:func.5">Fin</a> <a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a> </span>)</span><span class="kw"> such that </span><br/><a NAME="E5:30"/><span class="lab"><font color="Green" title="E20">A3</font></span>: 
for <font color="Olive" title="b1">i</font> being  <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  holds  <font color="Maroon" title="c4">UIL2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="sf_mastr.html#K1" title="SF_MASTR:func.1">UsedIntLoc</a> <font color="Olive" title="b1">i</font>
 <span class="kw">and </span><br/><a NAME="E6:30"/><span class="lab"><font color="Green" title="E21">A4</font></span>: 
 <a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K1" title="SCMFSA6A:func.1">Directed</a> <font color="Maroon" title="c1">I</font>,<font color="Maroon" title="c2">l</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_3.html#K3" title="CARD_3:func.3">Union</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">UIL2</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K1" title="SCMFSA6A:func.1">Directed</a> <font color="Maroon" title="c1">I</font>,<font color="Maroon" title="c2">l</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="sf_mastr.html#D2" title="SF_MASTR:def.2">SF_MASTR:def 2</a></span>;<br/>
<a NAME="E7:30"/><span class="lab"><font color="Green" title="E22">A5</font></span>: 
for <font color="Olive" title="b1">c</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  holds  <font color="Maroon" title="c3">UIL</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">UIL2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">c</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="30_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c5">c</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">UIL</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">UIL2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">c</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c6">d</font> = <font color="Maroon" title="c5">c</font> as   <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  ;<br/>
<span class="kw">thus </span><font color="Maroon" title="c3">UIL</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">c</font> = 
 <a href="sf_mastr.html#K1" title="SF_MASTR:func.1">UsedIntLoc</a> <font color="Maroon" title="c6">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:30"><span class="lab"><font color="Green" title="E18">A1</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c4">UIL2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">c</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:30"><span class="lab"><font color="Green" title="E20">A3</font></span></a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E8:30"/><span class="lab"><font color="Green" title="E23">A6</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">UIL</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E9:30"/><span class="lab"><font color="Green" title="E24">A7</font></span>: 
<font color="Maroon" title="c3">UIL</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </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="#E2:30"><span class="lab"><font color="Green" title="E18">A1</font></span></a>, <a class="ref" href="sf_mastr.html#T17" title="SF_MASTR:th.17">SF_MASTR:17</a></span>;<br/>
<span class="lab"><font color="Green" title="E25">A8</font></span>: <font color="Maroon" title="c3">UIL</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <font color="Maroon" title="c2">l</font></span>)</span> = 
 <a href="sf_mastr.html#K1" title="SF_MASTR:func.1">UsedIntLoc</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <font color="Maroon" title="c2">l</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:30"><span class="lab"><font color="Green" title="E18">A1</font></span></a></span>
<br/>.= 
 <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="sf_mastr.html#T19" title="SF_MASTR:th.19">SF_MASTR:19</a></span>
;<br/>
<a NAME="E11:30"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c1">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D19" title="RELAT_1:def.19">RELAT_1:def 19</a></span>;<br/>
<span class="kw">then </span><font color="Maroon" title="c3">UIL</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K1" title="SCMFSA6A:func.1">Directed</a> <font color="Maroon" title="c1">I</font>,<font color="Maroon" title="c2">l</font></span>)</span> = 
<font color="Maroon" title="c3">UIL</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="funct_7.html#K15" title="FUNCT_7:func.15">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <font color="Maroon" title="c2">l</font></span>)</span></span>)</span> <a href="ami_1.html#K25" title="AMI_1:func.25">*</a> <font color="Maroon" title="c1">I</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_7.html#T118" title="FUNCT_7:th.118">FUNCT_7:118</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">UIL</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="funct_7.html#K15" title="FUNCT_7:func.15">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <font color="Maroon" title="c2">l</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c1">I</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T55" title="RELAT_1:th.55">RELAT_1:55</a></span>
<br/>.= 
<font color="Maroon" title="c3">UIL</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c1">I</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:30"><span class="lab"><font color="Green" title="E23">A6</font></span></a>, <a class="txt" href="#E9:30"><span class="lab"><font color="Green" title="E24">A7</font></span></a>, <a class="txt" href="#E10:30"><span class="lab"><font color="Green" title="E25">A8</font></span></a>, <a class="ref" href="funct_7.html#T110" title="FUNCT_7:th.110">FUNCT_7:110</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E13:30"/>
 <a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K1" title="SCMFSA6A:func.1">Directed</a> <font color="Maroon" title="c1">I</font>,<font color="Maroon" title="c2">l</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c1">I</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:30"><span class="lab"><font color="Green" title="E19">A2</font></span></a>, <a class="txt" href="#E6:30"><span class="lab"><font color="Green" title="E21">A4</font></span></a>, <a class="txt" href="#E7:30"><span class="lab"><font color="Green" title="E22">A5</font></span></a>, <a class="ref" href="funct_2.html#T113" title="FUNCT_2:th.113">FUNCT_2:113</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
