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<span class="kw">let </span><font color="Maroon" title="c1">s</font> be   <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</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="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">a</font> being   <a href="sf_mastr.html#NV2" title="SF_MASTR:NV.2">read-write</a>   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <br/>  for <font color="Olive" title="b2">bb</font>, <font color="Olive" title="b3">cc</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <br/>  for <font color="Olive" title="b4">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> <br/>  for <font color="Olive" title="b5">I</font> being   <a href="compos_1.html#NM5" title="COMPOS_1:NM.5">Program</a> of <br/>  for <font color="Olive" title="b6">p</font> being   <a href="compos_1.html#NM2" title="COMPOS_1:NM.2">Instruction-Sequence</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sfmastr3.html#K1" title="SFMASTR3:func.1">StepForUp</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">bb</font>,<font color="Olive" title="b3">cc</font>,<font color="Olive" title="b5">I</font>,<font color="Olive" title="b6">p</font>,<font color="Maroon" title="c1">s</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive" title="b4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">s</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive" title="b4">f</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font> be   <a href="sf_mastr.html#NV2" title="SF_MASTR:NV.2">read-write</a>   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">bb</font>, <font color="Olive" title="b2">cc</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <br/>  for <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> <br/>  for <font color="Olive" title="b4">I</font> being   <a href="compos_1.html#NM5" title="COMPOS_1:NM.5">Program</a> of <br/>  for <font color="Olive" title="b5">p</font> being   <a href="compos_1.html#NM2" title="COMPOS_1:NM.2">Instruction-Sequence</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sfmastr3.html#K1" title="SFMASTR3:func.1">StepForUp</a> (<font color="Maroon" title="c2">a</font>,<font color="Olive" title="b1">bb</font>,<font color="Olive" title="b2">cc</font>,<font color="Olive" title="b4">I</font>,<font color="Olive" title="b5">p</font>,<font color="Maroon" title="c1">s</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive" title="b3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">s</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive" title="b3">f</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">bb</font>, <font color="Maroon" title="c4">cc</font> be    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> <br/>  for <font color="Olive" title="b2">I</font> being   <a href="compos_1.html#NM5" title="COMPOS_1:NM.5">Program</a> of <br/>  for <font color="Olive" title="b3">p</font> being   <a href="compos_1.html#NM2" title="COMPOS_1:NM.2">Instruction-Sequence</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sfmastr3.html#K1" title="SFMASTR3:func.1">StepForUp</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c4">cc</font>,<font color="Olive" title="b2">I</font>,<font color="Olive" title="b3">p</font>,<font color="Maroon" title="c1">s</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">s</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive" title="b1">f</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">f</font> be    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> ; <a class="txt" 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">Program</a> of <br/>  for <font color="Olive" title="b2">p</font> being   <a href="compos_1.html#NM2" title="COMPOS_1:NM.2">Instruction-Sequence</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sfmastr3.html#K1" title="SFMASTR3:func.1">StepForUp</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c4">cc</font>,<font color="Olive" title="b1">I</font>,<font color="Olive" title="b2">p</font>,<font color="Maroon" title="c1">s</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c5">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">s</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c5">f</font></span><br/><span class="kw">let </span><font color="Maroon" title="c6">I</font> be   <a href="compos_1.html#NM5" title="COMPOS_1:NM.5">Program</a> of ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">p</font> being   <a href="compos_1.html#NM2" title="COMPOS_1:NM.2">Instruction-Sequence</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sfmastr3.html#K1" title="SFMASTR3:func.1">StepForUp</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c4">cc</font>,<font color="Maroon" title="c6">I</font>,<font color="Olive" title="b1">p</font>,<font color="Maroon" title="c1">s</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c5">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">s</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c5">f</font></span><br/><span class="kw">let </span><font color="Maroon" title="c7">p</font> be   <a href="compos_1.html#NM2" title="COMPOS_1:NM.2">Instruction-Sequence</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="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sfmastr3.html#K1" title="SFMASTR3:func.1">StepForUp</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c4">cc</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c1">s</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c5">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">s</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c5">f</font></span><br/>













<span class="kw">set </span><font color="Maroon" title="c8">aux</font> = 1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p1">(<span class="default"><span class="p2"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c4">cc</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c6">I</font></span>)</span></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">S</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="scmfsa6b.html#K1" title="SCMFSA6B:func.1">+*</a> (<span class="p2">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p3">(<span class="default"><span class="p4"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c4">cc</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c6">I</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c4">cc</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c3">bb</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="scmfsa6b.html#K1" title="SCMFSA6B:func.1">+*</a> (<font color="Maroon" title="c2">a</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c3">bb</font></span>)</span>);<br/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="scmfsa6b.html#K1" title="SCMFSA6B:func.1">+*</a> (<span class="p3">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p4">(<span class="default"><span class="p5"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c4">cc</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p5">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c6">I</font></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c4">cc</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c3">bb</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="scmfsa6b.html#K1" title="SCMFSA6B:func.1">+*</a> (<font color="Maroon" title="c2">a</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c3">bb</font></span>)</span>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c5">f</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="scmfsa6b.html#K1" title="SCMFSA6B:func.1">+*</a> (<span class="p2">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p3">(<span class="default"><span class="p4"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c4">cc</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c6">I</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c4">cc</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c3">bb</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c5">f</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_7.html#T32" title="FUNCT_7:th.32">FUNCT_7:32</a>, <a class="ref" href="scmfsa_2.html#T58" title="SCMFSA_2:th.58">SCMFSA_2:58</a></span>
<br/>.= 
<font color="Maroon" title="c1">s</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c5">f</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_7.html#T32" title="FUNCT_7:th.32">FUNCT_7:32</a>, <a class="ref" href="scmfsa_2.html#T58" title="SCMFSA_2:th.58">SCMFSA_2:58</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E2:17"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sfmastr3.html#K1" title="SFMASTR3:func.1">StepForUp</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c4">cc</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c1">s</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c5">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">s</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c5">f</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_9.html#D5" title="SCMFSA_9:def.5">SCMFSA_9:def 5</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
