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<span class="kw">let </span><font color="Maroon" title="c1">s</font> be   <a href="ami_1.html#NM5" title="AMI_1:NM.5">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="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">aa</font>, <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">I</font> being  <a href="scmfsa6b.html#V2" title="SCMFSA6B:attr.2">parahalting</a>  <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>  holds   <a href="sfmastr3.html#R1" title="SFMASTR3:pred.1">ProperForUpBody</a> <font color="Olive" title="b1">aa</font>,<font color="Olive" title="b2">bb</font>,<font color="Olive" title="b3">cc</font>,<font color="Olive" title="b4">I</font>,<font color="Maroon" title="c1">s</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">aa</font>, <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="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">I</font> being  <a href="scmfsa6b.html#V2" title="SCMFSA6B:attr.2">parahalting</a>  <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>  holds   <a href="sfmastr3.html#R1" title="SFMASTR3:pred.1">ProperForUpBody</a> <font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c4">cc</font>,<font color="Olive" title="b1">I</font>,<font color="Maroon" title="c1">s</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">I</font> be   <a href="scmfsa6b.html#V2" title="SCMFSA6B:attr.2">parahalting</a>  <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">  <a href="sfmastr3.html#R1" title="SFMASTR3:pred.1">ProperForUpBody</a> <font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c4">cc</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c1">s</font></span><br/><span class="kw">let </span><font color="Maroon" title="c6">i</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> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="sfmastr3.html#D7" target="_self" title="SFMASTR3:def.7">SFMASTR3:def 7</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="c6">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><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="c4">cc</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <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="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 implies ( <font color="Maroon" title="c5">I</font> <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <span class="p1">(<span class="default"><a href="sfmastr3.html#K1" title="SFMASTR3:func.1">StepForUp</a> <font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c4">cc</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c1">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c6">i</font> &amp; <font color="Maroon" title="c5">I</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <span class="p1">(<span class="default"><a href="sfmastr3.html#K1" title="SFMASTR3:func.1">StepForUp</a> <font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c4">cc</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c1">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c6">i</font> ) )</span><br/>











<span class="kw">assume </span><a NAME="E1:26"/>
<font color="Maroon" title="c6">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><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="c4">cc</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <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="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1
 ; <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="c5">I</font> <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <span class="p1">(<span class="default"><a href="sfmastr3.html#K1" title="SFMASTR3:func.1">StepForUp</a> <font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c4">cc</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c1">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c6">i</font> &amp; <font color="Maroon" title="c5">I</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <span class="p1">(<span class="default"><a href="sfmastr3.html#K1" title="SFMASTR3:func.1">StepForUp</a> <font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c4">cc</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c1">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c6">i</font> )</span><br/>

<span class="kw">thus </span><a NAME="E2:26"/>
<font color="Maroon" title="c5">I</font> <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <span class="p1">(<span class="default"><a href="sfmastr3.html#K1" title="SFMASTR3:func.1">StepForUp</a> <font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c4">cc</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c1">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c6">i</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa7b.html#T24" title="SCMFSA7B:th.24">SCMFSA7B:24</a></span>; <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="c5">I</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <span class="p1">(<span class="default"><a href="sfmastr3.html#K1" title="SFMASTR3:func.1">StepForUp</a> <font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c4">cc</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c1">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c6">i</font></span><br/>

<span class="kw">thus </span><a NAME="E3:26"/>
<font color="Maroon" title="c5">I</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <span class="p1">(<span class="default"><a href="sfmastr3.html#K1" title="SFMASTR3:func.1">StepForUp</a> <font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c4">cc</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c1">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c6">i</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa7b.html#T25" title="SCMFSA7B:th.25">SCMFSA7B:25</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/>


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