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<b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">t</font> be    <a href="ami_1.html#M1">FinPartState</a> of  <a href="scmfsa_2.html#K1">SCM+FSA</a> ;<br/><b>let </b><font color="Maroon">p</font> be   <a href="scmfsa6a.html#NM1">Macro-Instruction</a>;<br/><b>let </b><font color="Maroon">s1</font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> , <font color="Maroon">s2</font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> ;<br/>









<b>set </b><font color="Maroon">Dloc</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span>;<br/>
<b>assume </b><a NAME="E1:22"/><i><font color="Green">E41</font></i>: 
( <font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> &amp; <font color="Maroon">p</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">s1</font> &amp; <font color="Maroon">p</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">s2</font> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font> <a href="tarski.html#R1">c=</a> <a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="finsub_1.html#K1">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a>  &amp; ( for <font color="Olive">j</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds <br/> (  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">j</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font> &amp;  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">j</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font> ) ) &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span></span>)</span> )
 ;<br/>

<b>then consider </b><font color="Maroon">m</font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E3:22"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">m</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T28">NAT_1:28</a></i>;<br/>
<b>reconsider </b><font color="Maroon">m</font> = <font color="Maroon">m</font> as    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  <b>by </b><i><a class="ref" href="ordinal1.html#D13">ORDINAL1:def 13</a></i>;<br/>
<a NAME="E5:22"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font>
 
<b>by </b><i/>;<br/>
<a NAME="E6:22"/><i><font color="Green">E48</font></i>: 
 <a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E7:22"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T4">XBOOLE_1:4</a></i>;<br/>
<a NAME="E8:22"/><b>then </b><i><font color="Green">E55</font></i>: 
 <a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ] <b>means </b>( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">a<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">a<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">a<sub>1</sub></font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">a<sub>1</sub></font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span></span>)</span> );<br/>
<a NAME="E9:22"/><i><font color="Green">E60</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[0]
 
<b>by </b><i/>;<br/>
<div><i><font color="Green">E62</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">m</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:22_1"/><i><font color="Green">E63</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">m</font>]
 ;<br/><b>set </b><font color="Maroon">sk1</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span>;<br/><b>set </b><font color="Maroon">sk11</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>;<br/><b>set </b><font color="Maroon">i1</font> =  <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span>;<br/><b>set </b><font color="Maroon">sk2</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span>;<br/><b>set </b><font color="Maroon">sk12</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>;<br/><b>set </b><font color="Maroon">i2</font> =  <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span>;<br/><a NAME="E2:22_1"/><i><font color="Green">E64</font></i>: 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span>
 <b>by </b><i/>;<br/><a NAME="E3:22_1"/><i><font color="Green">E65</font></i>: 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font>
 <b>by </b><i/>;<br/><a NAME="E4:22_1"/><i><font color="Green">E66</font></i>: 
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>;<br/> <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> = 
<font color="Maroon">s1</font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T54">AMI_1:54</a></i>
<br/>.= 
<font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, , <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>
;<br/><a NAME="E6:22_1"/><b>then </b><i><font color="Green">E67</font></i>: 
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">p</font>
 <b>by </b><i>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/><a NAME="E7:22_1"/><i><font color="Green">E68</font></i>: 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font>
 <b>by </b><i/>;<br/><i><font color="Green">E69</font></i>:  <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span>
<b>by </b><i>, , , </i>
;<br/><i><font color="Green">E70</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>

<br/>.= 
 <a href="ami_1.html#K9">Following</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span>

;<br/><i><font color="Green">E71</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>

<br/>.= 
 <a href="ami_1.html#K9">Following</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span>

;<br/><i><font color="Green">E72</font></i>:  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> = 
the <a href="struct_0.html#U1">carrier</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> 
<b>by </b><i><a class="ref" href="ami_3.html#T36">AMI_3:36</a></i>
<br/>.= 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_3.html#T36">AMI_3:36</a></i>
;<br/><a NAME="E12:22_1"/><i><font color="Green">E73</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 12
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T35">SCMFSA_2:35</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:22_1_6"/>
(  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 0 or  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 1 or  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 2 or  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 3 or  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 4 or  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 5 or  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 6 or  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 7 or  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 8 or  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 9 or  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 10 or  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 11 or  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 12 )
 </span><b>by </b><i>, </i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_1"><b>suppose </b></a><a NAME="E1:22_1_6_1"/>
 <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><a NAME="E2:22_1_6_1"/><b>then </b><i><font color="Green">E74</font></i>: 
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> 
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T122">SCMFSA_2:122</a></i>;<br/><a NAME="E3:22_1_6_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="ami_1.html#D8">AMI_1:def 8</a></i>;<br/><b>hence </b><a NAME="E4:22_1_6_1"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1]
 <b>by </b><i>, , , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, <a class="ref" href="ami_1.html#D8">AMI_1:def 8</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_2"><b>suppose </b></a><a NAME="E1:22_1_6_2"/>
 <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">da</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">db</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:22_1_6_2"/><i><font color="Green">E75</font></i>: 
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">da</font> <a href="scmfsa_2.html#K8">:=</a> <font color="Maroon">db</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T54">SCMFSA_2:54</a></i>;<br/><i><font color="Green">E76</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> = 
 <a href="scmfsa_2.html#K7">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, <a class="ref" href="scmfsa_2.html#T89">SCMFSA_2:89</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i>, , , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, <a class="ref" href="scmfsa_2.html#T89">SCMFSA_2:89</a></i>
;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_6_2_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:22_1_6_2_2"/><i><font color="Green">E77</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span>
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_2_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:22_1_6_2_2_1"/>
( <font color="Maroon">x</font> is    <a href="scmfsa_2.html#M1">Int-Location</a>  or <font color="Maroon">x</font> is    <a href="scmfsa_2.html#M2">FinSeq-Location</a>  )
 </span><b>by </b><i>, , </i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_2_2_1_1"><b>suppose </b></a><a NAME="E1:22_1_6_2_2_1_1"/><i><font color="Green">E78</font></i>: 
<font color="Maroon">x</font> is    <a href="scmfsa_2.html#M1">Int-Location</a> 
 ;<br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_6_2_2_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_2_2_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:22_1_6_2_2_1_1_1_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">da</font> or <font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">da</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_2_2_1_1_1_1_1"><b>case </b></a><a NAME="E1:22_1_6_2_2_1_1_1_1_1"/><i><font color="Green">E79</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">da</font>
 ;<br/><div class="add"><a NAME="E2:22_1_6_2_2_1_1_1_1_1"/><b>then </b><i><font color="Green">E80</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">db</font>
 <b>by </b><i>, , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, <a class="ref" href="scmfsa_2.html#T89">SCMFSA_2:89</a></i>;<br/><a NAME="E3:22_1_6_2_2_1_1_1_1_1"/><i><font color="Green">E81</font></i>: 
<font color="Maroon">db</font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font>
 <b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, </i>;<br/><b>then </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">db</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">db</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">db</font>
<b>by </b><i>, <a class="txt" href="scmbsort.html#E5:22"><i><font color="Green">E47</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><b>hence </b><a NAME="E5:22_1_6_2_2_1_1_1_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, , , <a class="ref" href="scmfsa_2.html#T89">SCMFSA_2:89</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_2_2_1_1_1_1_2"><b>case </b></a><a NAME="E1:22_1_6_2_2_1_1_1_1_2"/><i><font color="Green">E82</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">da</font>
 ;<br/><div class="add"><a NAME="E2:22_1_6_2_2_1_1_1_1_2"/><b>then </b><i><font color="Green">E83</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, , <a class="ref" href="scmfsa_2.html#T89">SCMFSA_2:89</a></i>;<br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><b>hence </b><a NAME="E4:22_1_6_2_2_1_1_1_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, , , , <a class="ref" href="scmfsa_2.html#T89">SCMFSA_2:89</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:22_1_6_2_2_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_2_2_1_2"><b>suppose </b></a><a NAME="E1:22_1_6_2_2_1_2"/><i><font color="Green">E85</font></i>: 
<font color="Maroon">x</font> is    <a href="scmfsa_2.html#M2">FinSeq-Location</a> 
 ;<br/><div class="add"><a NAME="E2:22_1_6_2_2_1_2"/><b>then </b><i><font color="Green">E86</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, <a class="ref" href="scmfsa_2.html#T89">SCMFSA_2:89</a></i>;<br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><b>hence </b><a NAME="E4:22_1_6_2_2_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, , , <a class="ref" href="scmfsa_2.html#T89">SCMFSA_2:89</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E6:22_1_6_2"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1]
 <b>by </b><i><a class="ref" href="scmbsort.html#T3" target="_self">Th3</a>, <a class="txt" href="scmbsort.html#E3:22"><i><font color="Green">E42</font></i></a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_3"><b>suppose </b></a><a NAME="E1:22_1_6_3"/>
 <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 2
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">da</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">db</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:22_1_6_3"/><i><font color="Green">E87</font></i>: 
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">AddTo</a> <font color="Maroon">da</font>,<font color="Maroon">db</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T55">SCMFSA_2:55</a></i>;<br/><i><font color="Green">E88</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> = 
 <a href="scmfsa_2.html#K7">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, <a class="ref" href="scmfsa_2.html#T90">SCMFSA_2:90</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i>, , , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, <a class="ref" href="scmfsa_2.html#T90">SCMFSA_2:90</a></i>
;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_6_3_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:22_1_6_3_2"/><i><font color="Green">E89</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span>
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_3_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:22_1_6_3_2_1"/>
( <font color="Maroon">x</font> is    <a href="scmfsa_2.html#M1">Int-Location</a>  or <font color="Maroon">x</font> is    <a href="scmfsa_2.html#M2">FinSeq-Location</a>  )
 </span><b>by </b><i>, , </i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_3_2_1_1"><b>suppose </b></a><a NAME="E1:22_1_6_3_2_1_1"/><i><font color="Green">E90</font></i>: 
<font color="Maroon">x</font> is    <a href="scmfsa_2.html#M1">Int-Location</a> 
 ;<br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_6_3_2_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_3_2_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:22_1_6_3_2_1_1_1_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">da</font> or <font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">da</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_3_2_1_1_1_1_1"><b>case </b></a><a NAME="E1:22_1_6_3_2_1_1_1_1_1"/><i><font color="Green">E127</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">da</font>
 ;<br/><div class="add"><a NAME="E2:22_1_6_3_2_1_1_1_1_1"/><b>then </b><i><font color="Green">E128</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">db</font></span>)</span>
 <b>by </b><i>, , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, <a class="ref" href="scmfsa_2.html#T90">SCMFSA_2:90</a></i>;<br/><a NAME="E3:22_1_6_3_2_1_1_1_1_1"/><i><font color="Green">E129</font></i>: 
<font color="Maroon">da</font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font>
 <b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, </i>;<br/><b>then </b><i><font color="Green">E130</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">da</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font>
<b>by </b><i>, <a class="txt" href="scmbsort.html#E5:22"><i><font color="Green">E47</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><a NAME="E5:22_1_6_3_2_1_1_1_1_1"/><i><font color="Green">E131</font></i>: 
<font color="Maroon">db</font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font>
 <b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, </i>;<br/><b>then </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">db</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">db</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">db</font>
<b>by </b><i>, <a class="ref" href="scmbsort.html#T4" target="_self">Th4</a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><b>hence </b><a NAME="E7:22_1_6_3_2_1_1_1_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, , , <a class="txt" href="scmbsort.html#E6:22"><i><font color="Green">E48</font></i></a>, <a class="ref" href="scmfsa_2.html#T90">SCMFSA_2:90</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_3_2_1_1_1_1_2"><b>case </b></a><a NAME="E1:22_1_6_3_2_1_1_1_1_2"/><i><font color="Green">E132</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">da</font>
 ;<br/><div class="add"><a NAME="E2:22_1_6_3_2_1_1_1_1_2"/><b>then </b><i><font color="Green">E133</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, , <a class="ref" href="scmfsa_2.html#T90">SCMFSA_2:90</a></i>;<br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><b>hence </b><a NAME="E4:22_1_6_3_2_1_1_1_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, , , , <a class="ref" href="scmfsa_2.html#T90">SCMFSA_2:90</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:22_1_6_3_2_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_3_2_1_2"><b>suppose </b></a><a NAME="E1:22_1_6_3_2_1_2"/><i><font color="Green">E134</font></i>: 
<font color="Maroon">x</font> is    <a href="scmfsa_2.html#M2">FinSeq-Location</a> 
 ;<br/><div class="add"><a NAME="E2:22_1_6_3_2_1_2"/><b>then </b><i><font color="Green">E135</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, <a class="ref" href="scmfsa_2.html#T90">SCMFSA_2:90</a></i>;<br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><b>hence </b><a NAME="E4:22_1_6_3_2_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, , , <a class="ref" href="scmfsa_2.html#T90">SCMFSA_2:90</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E6:22_1_6_3"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1]
 <b>by </b><i><a class="ref" href="scmbsort.html#T3" target="_self">Th3</a>, <a class="txt" href="scmbsort.html#E3:22"><i><font color="Green">E42</font></i></a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_4"><b>suppose </b></a><a NAME="E1:22_1_6_4"/>
 <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 3
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">da</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">db</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:22_1_6_4"/><i><font color="Green">E136</font></i>: 
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">SubFrom</a> <font color="Maroon">da</font>,<font color="Maroon">db</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T56">SCMFSA_2:56</a></i>;<br/><i><font color="Green">E137</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> = 
 <a href="scmfsa_2.html#K7">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, <a class="ref" href="scmfsa_2.html#T91">SCMFSA_2:91</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i>, , , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, <a class="ref" href="scmfsa_2.html#T91">SCMFSA_2:91</a></i>
;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_6_4_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:22_1_6_4_2"/><i><font color="Green">E138</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span>
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_4_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:22_1_6_4_2_1"/>
( <font color="Maroon">x</font> is    <a href="scmfsa_2.html#M1">Int-Location</a>  or <font color="Maroon">x</font> is    <a href="scmfsa_2.html#M2">FinSeq-Location</a>  )
 </span><b>by </b><i>, , </i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_4_2_1_1"><b>suppose </b></a><a NAME="E1:22_1_6_4_2_1_1"/><i><font color="Green">E139</font></i>: 
<font color="Maroon">x</font> is    <a href="scmfsa_2.html#M1">Int-Location</a> 
 ;<br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_6_4_2_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_4_2_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:22_1_6_4_2_1_1_1_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">da</font> or <font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">da</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_4_2_1_1_1_1_1"><b>case </b></a><a NAME="E1:22_1_6_4_2_1_1_1_1_1"/><i><font color="Green">E140</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">da</font>
 ;<br/><div class="add"><a NAME="E2:22_1_6_4_2_1_1_1_1_1"/><b>then </b><i><font color="Green">E141</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">db</font></span>)</span>
 <b>by </b><i>, , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, <a class="ref" href="scmfsa_2.html#T91">SCMFSA_2:91</a></i>;<br/><a NAME="E3:22_1_6_4_2_1_1_1_1_1"/><i><font color="Green">E142</font></i>: 
<font color="Maroon">da</font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font>
 <b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, </i>;<br/><b>then </b><i><font color="Green">E143</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">da</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font>
<b>by </b><i>, <a class="txt" href="scmbsort.html#E5:22"><i><font color="Green">E47</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><a NAME="E5:22_1_6_4_2_1_1_1_1_1"/><i><font color="Green">E144</font></i>: 
<font color="Maroon">db</font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font>
 <b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, </i>;<br/><b>then </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">db</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">db</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">db</font>
<b>by </b><i>, <a class="ref" href="scmbsort.html#T4" target="_self">Th4</a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><b>hence </b><a NAME="E7:22_1_6_4_2_1_1_1_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, , , <a class="txt" href="scmbsort.html#E6:22"><i><font color="Green">E48</font></i></a>, <a class="ref" href="scmfsa_2.html#T91">SCMFSA_2:91</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_4_2_1_1_1_1_2"><b>case </b></a><a NAME="E1:22_1_6_4_2_1_1_1_1_2"/><i><font color="Green">E145</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">da</font>
 ;<br/><div class="add"><a NAME="E2:22_1_6_4_2_1_1_1_1_2"/><b>then </b><i><font color="Green">E146</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, , <a class="ref" href="scmfsa_2.html#T91">SCMFSA_2:91</a></i>;<br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><b>hence </b><a NAME="E4:22_1_6_4_2_1_1_1_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, , , , <a class="ref" href="scmfsa_2.html#T91">SCMFSA_2:91</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:22_1_6_4_2_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_4_2_1_2"><b>suppose </b></a><a NAME="E1:22_1_6_4_2_1_2"/><i><font color="Green">E147</font></i>: 
<font color="Maroon">x</font> is    <a href="scmfsa_2.html#M2">FinSeq-Location</a> 
 ;<br/><div class="add"><a NAME="E2:22_1_6_4_2_1_2"/><b>then </b><i><font color="Green">E148</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, <a class="ref" href="scmfsa_2.html#T91">SCMFSA_2:91</a></i>;<br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><b>hence </b><a NAME="E4:22_1_6_4_2_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, , , <a class="ref" href="scmfsa_2.html#T91">SCMFSA_2:91</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E6:22_1_6_4"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1]
 <b>by </b><i><a class="ref" href="scmbsort.html#T3" target="_self">Th3</a>, <a class="txt" href="scmbsort.html#E3:22"><i><font color="Green">E42</font></i></a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_5"><b>suppose </b></a><a NAME="E1:22_1_6_5"/>
 <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 4
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">da</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">db</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:22_1_6_5"/><i><font color="Green">E149</font></i>: 
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11">MultBy</a> <font color="Maroon">da</font>,<font color="Maroon">db</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T57">SCMFSA_2:57</a></i>;<br/><i><font color="Green">E150</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> = 
 <a href="scmfsa_2.html#K7">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, <a class="ref" href="scmfsa_2.html#T92">SCMFSA_2:92</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i>, , , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, <a class="ref" href="scmfsa_2.html#T92">SCMFSA_2:92</a></i>
;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_6_5_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:22_1_6_5_2"/><i><font color="Green">E151</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span>
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_5_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:22_1_6_5_2_1"/>
( <font color="Maroon">x</font> is    <a href="scmfsa_2.html#M1">Int-Location</a>  or <font color="Maroon">x</font> is    <a href="scmfsa_2.html#M2">FinSeq-Location</a>  )
 </span><b>by </b><i>, , </i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_5_2_1_1"><b>suppose </b></a><a NAME="E1:22_1_6_5_2_1_1"/><i><font color="Green">E152</font></i>: 
<font color="Maroon">x</font> is    <a href="scmfsa_2.html#M1">Int-Location</a> 
 ;<br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_6_5_2_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_5_2_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:22_1_6_5_2_1_1_1_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">da</font> or <font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">da</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_5_2_1_1_1_1_1"><b>case </b></a><a NAME="E1:22_1_6_5_2_1_1_1_1_1"/><i><font color="Green">E153</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">da</font>
 ;<br/><div class="add"><a NAME="E2:22_1_6_5_2_1_1_1_1_1"/><b>then </b><i><font color="Green">E154</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">db</font></span>)</span>
 <b>by </b><i>, , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, <a class="ref" href="scmfsa_2.html#T92">SCMFSA_2:92</a></i>;<br/><a NAME="E3:22_1_6_5_2_1_1_1_1_1"/><i><font color="Green">E155</font></i>: 
<font color="Maroon">da</font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font>
 <b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, </i>;<br/><b>then </b><i><font color="Green">E156</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">da</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font>
<b>by </b><i>, <a class="txt" href="scmbsort.html#E5:22"><i><font color="Green">E47</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><a NAME="E5:22_1_6_5_2_1_1_1_1_1"/><i><font color="Green">E157</font></i>: 
<font color="Maroon">db</font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font>
 <b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, </i>;<br/><b>then </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">db</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">db</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">db</font>
<b>by </b><i>, <a class="ref" href="scmbsort.html#T4" target="_self">Th4</a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><b>hence </b><a NAME="E7:22_1_6_5_2_1_1_1_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, , , <a class="txt" href="scmbsort.html#E6:22"><i><font color="Green">E48</font></i></a>, <a class="ref" href="scmfsa_2.html#T92">SCMFSA_2:92</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_5_2_1_1_1_1_2"><b>case </b></a><a NAME="E1:22_1_6_5_2_1_1_1_1_2"/><i><font color="Green">E158</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">da</font>
 ;<br/><div class="add"><a NAME="E2:22_1_6_5_2_1_1_1_1_2"/><b>then </b><i><font color="Green">E159</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, , <a class="ref" href="scmfsa_2.html#T92">SCMFSA_2:92</a></i>;<br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><b>hence </b><a NAME="E4:22_1_6_5_2_1_1_1_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, , , , <a class="ref" href="scmfsa_2.html#T92">SCMFSA_2:92</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:22_1_6_5_2_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_5_2_1_2"><b>suppose </b></a><a NAME="E1:22_1_6_5_2_1_2"/><i><font color="Green">E160</font></i>: 
<font color="Maroon">x</font> is    <a href="scmfsa_2.html#M2">FinSeq-Location</a> 
 ;<br/><div class="add"><a NAME="E2:22_1_6_5_2_1_2"/><b>then </b><i><font color="Green">E161</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, <a class="ref" href="scmfsa_2.html#T92">SCMFSA_2:92</a></i>;<br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><b>hence </b><a NAME="E4:22_1_6_5_2_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, , , <a class="ref" href="scmfsa_2.html#T92">SCMFSA_2:92</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E6:22_1_6_5"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1]
 <b>by </b><i><a class="ref" href="scmbsort.html#T3" target="_self">Th3</a>, <a class="txt" href="scmbsort.html#E3:22"><i><font color="Green">E42</font></i></a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_6"><b>suppose </b></a><a NAME="E1:22_1_6_6"/>
 <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 5
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">da</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">db</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:22_1_6_6"/><i><font color="Green">E162</font></i>: 
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12">Divide</a> <font color="Maroon">da</font>,<font color="Maroon">db</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T58">SCMFSA_2:58</a></i>;<br/><i><font color="Green">E163</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> = 
 <a href="scmfsa_2.html#K7">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, <a class="ref" href="scmfsa_2.html#T93">SCMFSA_2:93</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i>, , , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, <a class="ref" href="scmfsa_2.html#T93">SCMFSA_2:93</a></i>
;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_6_6_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:22_1_6_6_2"/><i><font color="Green">E164</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span>
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_6_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:22_1_6_6_2_1"/>
( <font color="Maroon">x</font> is    <a href="scmfsa_2.html#M1">Int-Location</a>  or <font color="Maroon">x</font> is    <a href="scmfsa_2.html#M2">FinSeq-Location</a>  )
 </span><b>by </b><i>, , </i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_6_2_1_1"><b>suppose </b></a><a NAME="E1:22_1_6_6_2_1_1"/><i><font color="Green">E165</font></i>: 
<font color="Maroon">x</font> is    <a href="scmfsa_2.html#M1">Int-Location</a> 
 ;<br/><div class="add"><a NAME="E2:22_1_6_6_2_1_1"/><i><font color="Green">E166</font></i>: 
<font color="Maroon">da</font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font>
 <b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, </i>;<br/><b>then </b><i><font color="Green">E167</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">da</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><a NAME="E4:22_1_6_6_2_1_1"/><i><font color="Green">E168</font></i>: 
<font color="Maroon">db</font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font>
 <b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, </i>;<br/><b>then </b><i><font color="Green">E169</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">db</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">db</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">db</font>
<b>by </b><i>, <a class="txt" href="scmbsort.html#E5:22"><i><font color="Green">E47</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><i><font color="Green">E170</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_6_6_2_1_1_4"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_6_2_1_1_4_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:22_1_6_6_2_1_1_4_1"/>
( <font color="Maroon">da</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">db</font> or <font color="Maroon">da</font> <a href="hidden.html#R1">=</a> <font color="Maroon">db</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_6_2_1_1_4_1_1"><b>suppose </b></a><a NAME="E1:22_1_6_6_2_1_1_4_1_1"/><i><font color="Green">E171</font></i>: 
<font color="Maroon">da</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">db</font>
 ;<br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_6_6_2_1_1_4_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_6_2_1_1_4_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:22_1_6_6_2_1_1_4_1_1_1_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">da</font> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">db</font> or ( <font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">da</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">db</font> ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_6_2_1_1_4_1_1_1_1_1"><b>suppose </b></a><a NAME="E1:22_1_6_6_2_1_1_4_1_1_1_1_1"/><i><font color="Green">E172</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">da</font>
 ;<br/><div class="add"><a NAME="E2:22_1_6_6_2_1_1_4_1_1_1_1_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font></span>)</span> <a href="int_1.html#K5">div</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">db</font></span>)</span>
 <b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, , <a class="ref" href="scmfsa_2.html#T93">SCMFSA_2:93</a></i>;<br/><b>hence </b><a NAME="E3:22_1_6_6_2_1_1_4_1_1_1_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, , <a class="txt" href="scmbsort.html#E6:22"><i><font color="Green">E48</font></i></a>, , , <a class="ref" href="scmfsa_2.html#T93">SCMFSA_2:93</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_6_2_1_1_4_1_1_1_1_2"><b>suppose </b></a><a NAME="E1:22_1_6_6_2_1_1_4_1_1_1_1_2"/><i><font color="Green">E173</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">db</font>
 ;<br/><div class="add"><a NAME="E2:22_1_6_6_2_1_1_4_1_1_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font></span>)</span> <a href="int_1.html#K6">mod</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">db</font></span>)</span>
 <b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, <a class="ref" href="scmfsa_2.html#T93">SCMFSA_2:93</a></i>;<br/><b>hence </b><a NAME="E3:22_1_6_6_2_1_1_4_1_1_1_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, , <a class="txt" href="scmbsort.html#E6:22"><i><font color="Green">E48</font></i></a>, , <a class="ref" href="scmfsa_2.html#T93">SCMFSA_2:93</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_6_2_1_1_4_1_1_1_1_3"><b>suppose </b></a><a NAME="E1:22_1_6_6_2_1_1_4_1_1_1_1_3"/><i><font color="Green">E174</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">da</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">db</font> )
 ;<br/><div class="add"><a NAME="E2:22_1_6_6_2_1_1_4_1_1_1_1_3"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, , <a class="ref" href="scmfsa_2.html#T93">SCMFSA_2:93</a></i>;<br/><b>hence </b><a NAME="E3:22_1_6_6_2_1_1_4_1_1_1_1_3"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, , <a class="ref" href="scmbsort.html#T4" target="_self">Th4</a>, , <a class="ref" href="scmfsa_2.html#T93">SCMFSA_2:93</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:22_1_6_6_2_1_1_4_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_6_2_1_1_4_1_2"><b>suppose </b></a><a NAME="E1:22_1_6_6_2_1_1_4_1_2"/><i><font color="Green">E175</font></i>: 
<font color="Maroon">da</font> <a href="hidden.html#R1">=</a> <font color="Maroon">db</font>
 ;<br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_6_6_2_1_1_4_1_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_6_2_1_1_4_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:22_1_6_6_2_1_1_4_1_2_1_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">da</font> or <font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">da</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_6_2_1_1_4_1_2_1_1_1"><b>case </b></a><a NAME="E1:22_1_6_6_2_1_1_4_1_2_1_1_1"/><i><font color="Green">E176</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">da</font>
 ;<br/><div class="add"><a NAME="E2:22_1_6_6_2_1_1_4_1_2_1_1_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font></span>)</span> <a href="int_1.html#K6">mod</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font></span>)</span>
 <b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, , <a class="ref" href="scmfsa_2.html#T94">SCMFSA_2:94</a></i>;<br/><b>hence </b><a NAME="E3:22_1_6_6_2_1_1_4_1_2_1_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, , , , <a class="ref" href="scmfsa_2.html#T94">SCMFSA_2:94</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_6_2_1_1_4_1_2_1_1_2"><b>case </b></a><a NAME="E1:22_1_6_6_2_1_1_4_1_2_1_1_2"/><i><font color="Green">E177</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">da</font>
 ;<br/><div class="add"><a NAME="E2:22_1_6_6_2_1_1_4_1_2_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, , , <a class="ref" href="scmfsa_2.html#T94">SCMFSA_2:94</a></i>;<br/><b>hence </b><a NAME="E3:22_1_6_6_2_1_1_4_1_2_1_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, , <a class="ref" href="scmbsort.html#T4" target="_self">Th4</a>, , , <a class="ref" href="scmfsa_2.html#T94">SCMFSA_2:94</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:22_1_6_6_2_1_1_4_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E8:22_1_6_6_2_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_6_2_1_2"><b>suppose </b></a><a NAME="E1:22_1_6_6_2_1_2"/><i><font color="Green">E178</font></i>: 
<font color="Maroon">x</font> is    <a href="scmfsa_2.html#M2">FinSeq-Location</a> 
 ;<br/><div class="add"><a NAME="E2:22_1_6_6_2_1_2"/><b>then </b><i><font color="Green">E179</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, <a class="ref" href="scmfsa_2.html#T93">SCMFSA_2:93</a></i>;<br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><b>hence </b><a NAME="E4:22_1_6_6_2_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, , , <a class="ref" href="scmfsa_2.html#T93">SCMFSA_2:93</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E6:22_1_6_6"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1]
 <b>by </b><i><a class="ref" href="scmbsort.html#T3" target="_self">Th3</a>, <a class="txt" href="scmbsort.html#E3:22"><i><font color="Green">E42</font></i></a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_7"><b>suppose </b></a><a NAME="E1:22_1_6_7"/>
 <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 6
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">lb</font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E3:22_1_6_7"/><i><font color="Green">E180</font></i>: 
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K13">goto</a> <font color="Maroon">lb</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T59">SCMFSA_2:59</a></i>;<br/><i><font color="Green">E181</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> = 
<font color="Maroon">lb</font>
<b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, <a class="ref" href="scmfsa_2.html#T95">SCMFSA_2:95</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i>, , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, <a class="ref" href="scmfsa_2.html#T95">SCMFSA_2:95</a></i>
;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_6_7_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:22_1_6_7_2"/><i><font color="Green">E182</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span>
 ;<br/><b>then </b><i><font color="Green">E183</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_7_2_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:22_1_6_7_2_2"/>
( <font color="Maroon">x</font> is    <a href="scmfsa_2.html#M1">Int-Location</a>  or <font color="Maroon">x</font> is    <a href="scmfsa_2.html#M2">FinSeq-Location</a>  )
 </span><b>by </b><i>, , </i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_7_2_2_1"><b>suppose </b></a><a NAME="E1:22_1_6_7_2_2_1"/><i><font color="Green">E184</font></i>: 
<font color="Maroon">x</font> is    <a href="scmfsa_2.html#M1">Int-Location</a> 
 ;<br/><div class="add"><a NAME="E2:22_1_6_7_2_2_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, <a class="ref" href="scmfsa_2.html#T95">SCMFSA_2:95</a></i>;<br/><b>hence </b><a NAME="E3:22_1_6_7_2_2_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, , , <a class="ref" href="scmfsa_2.html#T95">SCMFSA_2:95</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_7_2_2_2"><b>suppose </b></a><a NAME="E1:22_1_6_7_2_2_2"/><i><font color="Green">E185</font></i>: 
<font color="Maroon">x</font> is    <a href="scmfsa_2.html#M2">FinSeq-Location</a> 
 ;<br/><div class="add"><a NAME="E2:22_1_6_7_2_2_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, <a class="ref" href="scmfsa_2.html#T95">SCMFSA_2:95</a></i>;<br/><b>hence </b><a NAME="E3:22_1_6_7_2_2_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, , , <a class="ref" href="scmfsa_2.html#T95">SCMFSA_2:95</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E6:22_1_6_7"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1]
 <b>by </b><i><a class="ref" href="scmbsort.html#T3" target="_self">Th3</a>, <a class="txt" href="scmbsort.html#E3:22"><i><font color="Green">E42</font></i></a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_8"><b>suppose </b></a><a NAME="E1:22_1_6_8"/>
 <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 7
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">lb</font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> , <font color="Maroon">da</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:22_1_6_8"/><i><font color="Green">E186</font></i>: 
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">da</font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Maroon">lb</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T60">SCMFSA_2:60</a></i>;<br/><a NAME="E4:22_1_6_8"/><i><font color="Green">E187</font></i>: 
<font color="Maroon">da</font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font>
 <b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, </i>;<br/><b>then </b><i><font color="Green">E188</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">da</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font>
<b>by </b><i>, <a class="txt" href="scmbsort.html#E3:22"><i><font color="Green">E42</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><div><i><font color="Green">E189</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_6_8_2"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_8_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:22_1_6_8_2_1"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font> <a href="hidden.html#R1">=</a> 0 or <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_8_2_1_1"><b>suppose </b></a><a NAME="E1:22_1_6_8_2_1_1"/><i><font color="Green">E190</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> = 
<font color="Maroon">lb</font>
<b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, <a class="ref" href="scmfsa_2.html#T96">SCMFSA_2:96</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i>, , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, , , <a class="ref" href="scmfsa_2.html#T96">SCMFSA_2:96</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_8_2_1_2"><b>suppose </b></a><a NAME="E1:22_1_6_8_2_1_2"/><i><font color="Green">E191</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> = 
 <a href="scmfsa_2.html#K7">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, <a class="ref" href="scmfsa_2.html#T96">SCMFSA_2:96</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i>, , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, , , <a class="ref" href="scmfsa_2.html#T96">SCMFSA_2:96</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_6_8_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:22_1_6_8_3"/><i><font color="Green">E192</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span>
 ;<br/><b>then </b><i><font color="Green">E193</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_8_3_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:22_1_6_8_3_2"/>
( <font color="Maroon">x</font> is    <a href="scmfsa_2.html#M1">Int-Location</a>  or <font color="Maroon">x</font> is    <a href="scmfsa_2.html#M2">FinSeq-Location</a>  )
 </span><b>by </b><i>, , </i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_8_3_2_1"><b>suppose </b></a><a NAME="E1:22_1_6_8_3_2_1"/><i><font color="Green">E194</font></i>: 
<font color="Maroon">x</font> is    <a href="scmfsa_2.html#M1">Int-Location</a> 
 ;<br/><div class="add"><a NAME="E2:22_1_6_8_3_2_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, <a class="ref" href="scmfsa_2.html#T96">SCMFSA_2:96</a></i>;<br/><b>hence </b><a NAME="E3:22_1_6_8_3_2_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, , <a class="txt" href="scmbsort.html#E5:22"><i><font color="Green">E47</font></i></a>, <a class="ref" href="scmfsa_2.html#T96">SCMFSA_2:96</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_8_3_2_2"><b>suppose </b></a><a NAME="E1:22_1_6_8_3_2_2"/><i><font color="Green">E195</font></i>: 
<font color="Maroon">x</font> is    <a href="scmfsa_2.html#M2">FinSeq-Location</a> 
 ;<br/><div class="add"><a NAME="E2:22_1_6_8_3_2_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, <a class="ref" href="scmfsa_2.html#T96">SCMFSA_2:96</a></i>;<br/><b>hence </b><a NAME="E3:22_1_6_8_3_2_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, , <a class="txt" href="scmbsort.html#E5:22"><i><font color="Green">E47</font></i></a>, <a class="ref" href="scmfsa_2.html#T96">SCMFSA_2:96</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E8:22_1_6_8"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1]
 <b>by </b><i><a class="ref" href="scmbsort.html#T3" target="_self">Th3</a>, , </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_9"><b>suppose </b></a><a NAME="E1:22_1_6_9"/>
 <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 8
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">lb</font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> , <font color="Maroon">da</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:22_1_6_9"/><i><font color="Green">E196</font></i>: 
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">da</font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Maroon">lb</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T61">SCMFSA_2:61</a></i>;<br/><a NAME="E4:22_1_6_9"/><i><font color="Green">E197</font></i>: 
<font color="Maroon">da</font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font>
 <b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, </i>;<br/><b>then </b><i><font color="Green">E198</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">da</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font>
<b>by </b><i>, <a class="txt" href="scmbsort.html#E3:22"><i><font color="Green">E42</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><div><i><font color="Green">E199</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_6_9_2"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_9_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:22_1_6_9_2_1"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 or <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font> <a href="xxreal_0.html#R1">&lt;=</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_9_2_1_1"><b>suppose </b></a><a NAME="E1:22_1_6_9_2_1_1"/><i><font color="Green">E200</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> = 
<font color="Maroon">lb</font>
<b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, <a class="ref" href="scmfsa_2.html#T97">SCMFSA_2:97</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i>, , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, , , <a class="ref" href="scmfsa_2.html#T97">SCMFSA_2:97</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_9_2_1_2"><b>suppose </b></a><a NAME="E1:22_1_6_9_2_1_2"/><i><font color="Green">E201</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font> <a href="xxreal_0.html#R1">&lt;=</a> 0
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> = 
 <a href="scmfsa_2.html#K7">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, <a class="ref" href="scmfsa_2.html#T97">SCMFSA_2:97</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i>, , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, , , <a class="ref" href="scmfsa_2.html#T97">SCMFSA_2:97</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_6_9_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:22_1_6_9_3"/><i><font color="Green">E202</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span>
 ;<br/><b>then </b><i><font color="Green">E203</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_9_3_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:22_1_6_9_3_2"/>
( <font color="Maroon">x</font> is    <a href="scmfsa_2.html#M1">Int-Location</a>  or <font color="Maroon">x</font> is    <a href="scmfsa_2.html#M2">FinSeq-Location</a>  )
 </span><b>by </b><i>, , </i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_9_3_2_1"><b>suppose </b></a><a NAME="E1:22_1_6_9_3_2_1"/><i><font color="Green">E204</font></i>: 
<font color="Maroon">x</font> is    <a href="scmfsa_2.html#M1">Int-Location</a> 
 ;<br/><div class="add"><a NAME="E2:22_1_6_9_3_2_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, <a class="ref" href="scmfsa_2.html#T97">SCMFSA_2:97</a></i>;<br/><b>hence </b><a NAME="E3:22_1_6_9_3_2_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, , <a class="txt" href="scmbsort.html#E5:22"><i><font color="Green">E47</font></i></a>, <a class="ref" href="scmfsa_2.html#T97">SCMFSA_2:97</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_9_3_2_2"><b>suppose </b></a><a NAME="E1:22_1_6_9_3_2_2"/><i><font color="Green">E205</font></i>: 
<font color="Maroon">x</font> is    <a href="scmfsa_2.html#M2">FinSeq-Location</a> 
 ;<br/><div class="add"><a NAME="E2:22_1_6_9_3_2_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, <a class="ref" href="scmfsa_2.html#T97">SCMFSA_2:97</a></i>;<br/><b>hence </b><a NAME="E3:22_1_6_9_3_2_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, , <a class="txt" href="scmbsort.html#E5:22"><i><font color="Green">E47</font></i></a>, <a class="ref" href="scmfsa_2.html#T97">SCMFSA_2:97</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E8:22_1_6_9"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1]
 <b>by </b><i><a class="ref" href="scmbsort.html#T3" target="_self">Th3</a>, , </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_10"><b>suppose </b></a><a NAME="E1:22_1_6_10"/>
 <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 9
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">b</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">fa</font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:22_1_6_10"/><i><font color="Green">E206</font></i>: 
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="scmfsa_2.html#K16">:=</a> <font color="Maroon">fa</font>,<font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T62">SCMFSA_2:62</a></i>;<br/><i><font color="Green">E207</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> = 
 <a href="scmfsa_2.html#K7">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, <a class="ref" href="scmfsa_2.html#T98">SCMFSA_2:98</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i>, , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, <a class="ref" href="scmfsa_2.html#T98">SCMFSA_2:98</a></i>
;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_6_10_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:22_1_6_10_2"/><i><font color="Green">E208</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span>
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_10_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:22_1_6_10_2_1"/>
( <font color="Maroon">x</font> is    <a href="scmfsa_2.html#M1">Int-Location</a>  or <font color="Maroon">x</font> is    <a href="scmfsa_2.html#M2">FinSeq-Location</a>  )
 </span><b>by </b><i>, , </i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_10_2_1_1"><b>suppose </b></a><a NAME="E1:22_1_6_10_2_1_1"/><i><font color="Green">E209</font></i>: 
<font color="Maroon">x</font> is    <a href="scmfsa_2.html#M1">Int-Location</a> 
 ;<br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_6_10_2_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_10_2_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:22_1_6_10_2_1_1_1_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> or <font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_10_2_1_1_1_1_1"><b>case </b></a><a NAME="E1:22_1_6_10_2_1_1_1_1_1"/><i><font color="Green">E210</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 ;<br/><div class="add"><b>consider </b><font color="Maroon">k1</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E3:22_1_6_10_2_1_1_1_1_1"/><i><font color="Green">E212</font></i>: 
( <font color="Maroon">k1</font> <a href="hidden.html#R1">=</a>  <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="scmfsa_2.html#K16">:=</a> <font color="Maroon">fa</font>,<font color="Maroon">a</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">fa</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">k1</font> )
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T98">SCMFSA_2:98</a></i>;<br/><b>consider </b><font color="Maroon">k2</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E5:22_1_6_10_2_1_1_1_1_1"/><i><font color="Green">E214</font></i>: 
( <font color="Maroon">k2</font> <a href="hidden.html#R1">=</a>  <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="scmfsa_2.html#K16">:=</a> <font color="Maroon">fa</font>,<font color="Maroon">a</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">fa</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">k2</font> )
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T98">SCMFSA_2:98</a></i>;<br/><a NAME="E6:22_1_6_10_2_1_1_1_1_1"/><i><font color="Green">E215</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font>
 <b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, </i>;<br/><b>then </b><i><font color="Green">E216</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="txt" href="scmbsort.html#E6:22"><i><font color="Green">E48</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><a NAME="E8:22_1_6_10_2_1_1_1_1_1"/><i><font color="Green">E217</font></i>: 
<font color="Maroon">fa</font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font>
 <b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, </i>;<br/><b>then </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">fa</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">fa</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">fa</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><b>hence </b><a NAME="E10:22_1_6_10_2_1_1_1_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, , , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, , , <a class="txt" href="scmbsort.html#E5:22"><i><font color="Green">E47</font></i></a>, <a class="ref" href="scmbsort.html#T4" target="_self">Th4</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_10_2_1_1_1_1_2"><b>case </b></a><a NAME="E1:22_1_6_10_2_1_1_1_1_2"/><i><font color="Green">E218</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font>
 ;<br/><div class="add"><a NAME="E2:22_1_6_10_2_1_1_1_1_2"/><b>then </b><i><font color="Green">E219</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, , <a class="ref" href="scmfsa_2.html#T98">SCMFSA_2:98</a></i>;<br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><b>hence </b><a NAME="E4:22_1_6_10_2_1_1_1_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, , , , <a class="ref" href="scmfsa_2.html#T98">SCMFSA_2:98</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:22_1_6_10_2_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_10_2_1_2"><b>suppose </b></a><a NAME="E1:22_1_6_10_2_1_2"/><i><font color="Green">E220</font></i>: 
<font color="Maroon">x</font> is    <a href="scmfsa_2.html#M2">FinSeq-Location</a> 
 ;<br/><div class="add"><a NAME="E2:22_1_6_10_2_1_2"/><b>then </b><i><font color="Green">E221</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, <a class="ref" href="scmfsa_2.html#T98">SCMFSA_2:98</a></i>;<br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><b>hence </b><a NAME="E4:22_1_6_10_2_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, , , <a class="ref" href="scmfsa_2.html#T98">SCMFSA_2:98</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E6:22_1_6_10"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1]
 <b>by </b><i><a class="ref" href="scmbsort.html#T3" target="_self">Th3</a>, <a class="txt" href="scmbsort.html#E3:22"><i><font color="Green">E42</font></i></a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_11"><b>suppose </b></a><a NAME="E1:22_1_6_11"/>
 <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 10
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">b</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">fa</font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:22_1_6_11"/><i><font color="Green">E222</font></i>: 
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">fa</font>,<font color="Maroon">a</font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">b</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T63">SCMFSA_2:63</a></i>;<br/><i><font color="Green">E223</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> = 
 <a href="scmfsa_2.html#K7">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, <a class="ref" href="scmfsa_2.html#T99">SCMFSA_2:99</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i>, , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, <a class="ref" href="scmfsa_2.html#T99">SCMFSA_2:99</a></i>
;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_6_11_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:22_1_6_11_2"/><i><font color="Green">E224</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span>
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_11_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:22_1_6_11_2_1"/>
( <font color="Maroon">x</font> is    <a href="scmfsa_2.html#M2">FinSeq-Location</a>  or <font color="Maroon">x</font> is    <a href="scmfsa_2.html#M1">Int-Location</a>  )
 </span><b>by </b><i>, , </i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_11_2_1_1"><b>suppose </b></a><a NAME="E1:22_1_6_11_2_1_1"/><i><font color="Green">E225</font></i>: 
<font color="Maroon">x</font> is    <a href="scmfsa_2.html#M2">FinSeq-Location</a> 
 ;<br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_6_11_2_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_11_2_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:22_1_6_11_2_1_1_1_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">fa</font> or <font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">fa</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_11_2_1_1_1_1_1"><b>case </b></a><a NAME="E1:22_1_6_11_2_1_1_1_1_1"/><i><font color="Green">E226</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">fa</font>
 ;<br/><div class="add"><b>consider </b><font color="Maroon">k1</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E3:22_1_6_11_2_1_1_1_1_1"/><i><font color="Green">E227</font></i>: 
( <font color="Maroon">k1</font> <a href="hidden.html#R1">=</a>  <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon">fa</font>,<font color="Maroon">a</font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">b</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">fa</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">fa</font></span>)</span> <a href="funct_7.html#K2">+*</a> <font color="Maroon">k1</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font></span>)</span> )
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T99">SCMFSA_2:99</a></i>;<br/><b>consider </b><font color="Maroon">k2</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E5:22_1_6_11_2_1_1_1_1_1"/><i><font color="Green">E228</font></i>: 
( <font color="Maroon">k2</font> <a href="hidden.html#R1">=</a>  <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon">fa</font>,<font color="Maroon">a</font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">b</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">fa</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">fa</font></span>)</span> <a href="funct_7.html#K2">+*</a> <font color="Maroon">k2</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font></span>)</span> )
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T99">SCMFSA_2:99</a></i>;<br/><a NAME="E6:22_1_6_11_2_1_1_1_1_1"/><i><font color="Green">E229</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font>
 <b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, </i>;<br/><b>then </b><i><font color="Green">E230</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="txt" href="scmbsort.html#E6:22"><i><font color="Green">E48</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><a NAME="E8:22_1_6_11_2_1_1_1_1_1"/><i><font color="Green">E231</font></i>: 
<font color="Maroon">b</font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font>
 <b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, </i>;<br/><b>then </b><i><font color="Green">E232</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">b</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><a NAME="E10:22_1_6_11_2_1_1_1_1_1"/><i><font color="Green">E233</font></i>: 
<font color="Maroon">fa</font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font>
 <b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, </i>;<br/><b>then </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">fa</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">fa</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">fa</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><b>hence </b><a NAME="E12:22_1_6_11_2_1_1_1_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, , , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, , , <a class="txt" href="scmbsort.html#E5:22"><i><font color="Green">E47</font></i></a>, <a class="ref" href="scmbsort.html#T4" target="_self">Th4</a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_11_2_1_1_1_1_2"><b>case </b></a><a NAME="E1:22_1_6_11_2_1_1_1_1_2"/><i><font color="Green">E234</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">fa</font>
 ;<br/><div class="add"><a NAME="E2:22_1_6_11_2_1_1_1_1_2"/><b>then </b><i><font color="Green">E235</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, , <a class="ref" href="scmfsa_2.html#T99">SCMFSA_2:99</a></i>;<br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><b>hence </b><a NAME="E4:22_1_6_11_2_1_1_1_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, , , , <a class="ref" href="scmfsa_2.html#T99">SCMFSA_2:99</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:22_1_6_11_2_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_11_2_1_2"><b>suppose </b></a><a NAME="E1:22_1_6_11_2_1_2"/><i><font color="Green">E236</font></i>: 
<font color="Maroon">x</font> is    <a href="scmfsa_2.html#M1">Int-Location</a> 
 ;<br/><div class="add"><a NAME="E2:22_1_6_11_2_1_2"/><b>then </b><i><font color="Green">E237</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, <a class="ref" href="scmfsa_2.html#T99">SCMFSA_2:99</a></i>;<br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><b>hence </b><a NAME="E4:22_1_6_11_2_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, , , <a class="ref" href="scmfsa_2.html#T99">SCMFSA_2:99</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E6:22_1_6_11"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1]
 <b>by </b><i><a class="ref" href="scmbsort.html#T3" target="_self">Th3</a>, <a class="txt" href="scmbsort.html#E3:22"><i><font color="Green">E42</font></i></a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_12"><b>suppose </b></a><a NAME="E1:22_1_6_12"/>
 <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 11
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">fa</font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:22_1_6_12"/><i><font color="Green">E238</font></i>: 
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Maroon">fa</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T64">SCMFSA_2:64</a></i>;<br/><i><font color="Green">E239</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> = 
 <a href="scmfsa_2.html#K7">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, <a class="ref" href="scmfsa_2.html#T100">SCMFSA_2:100</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i>, , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, <a class="ref" href="scmfsa_2.html#T100">SCMFSA_2:100</a></i>
;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_6_12_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:22_1_6_12_2"/><i><font color="Green">E240</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span>
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_12_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:22_1_6_12_2_1"/>
( <font color="Maroon">x</font> is    <a href="scmfsa_2.html#M1">Int-Location</a>  or <font color="Maroon">x</font> is    <a href="scmfsa_2.html#M2">FinSeq-Location</a>  )
 </span><b>by </b><i>, , </i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_12_2_1_1"><b>suppose </b></a><a NAME="E1:22_1_6_12_2_1_1"/><i><font color="Green">E241</font></i>: 
<font color="Maroon">x</font> is    <a href="scmfsa_2.html#M1">Int-Location</a> 
 ;<br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_6_12_2_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_12_2_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:22_1_6_12_2_1_1_1_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> or <font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_12_2_1_1_1_1_1"><b>case </b></a><a NAME="E1:22_1_6_12_2_1_1_1_1_1"/><i><font color="Green">E242</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font>
 ;<br/><div class="add"><a NAME="E2:22_1_6_12_2_1_1_1_1_1"/><b>then </b><i><font color="Green">E243</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">fa</font></span>)</span>
 <b>by </b><i>, , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, <a class="ref" href="scmfsa_2.html#T100">SCMFSA_2:100</a></i>;<br/><a NAME="E3:22_1_6_12_2_1_1_1_1_1"/><i><font color="Green">E244</font></i>: 
<font color="Maroon">fa</font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font>
 <b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, </i>;<br/><b>then </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">fa</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">fa</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">fa</font>
<b>by </b><i>, <a class="txt" href="scmbsort.html#E5:22"><i><font color="Green">E47</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><b>hence </b><a NAME="E5:22_1_6_12_2_1_1_1_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, , , <a class="ref" href="scmfsa_2.html#T100">SCMFSA_2:100</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_12_2_1_1_1_1_2"><b>case </b></a><a NAME="E1:22_1_6_12_2_1_1_1_1_2"/><i><font color="Green">E245</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a</font>
 ;<br/><div class="add"><a NAME="E2:22_1_6_12_2_1_1_1_1_2"/><b>then </b><i><font color="Green">E246</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, , <a class="ref" href="scmfsa_2.html#T100">SCMFSA_2:100</a></i>;<br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><b>hence </b><a NAME="E4:22_1_6_12_2_1_1_1_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, , , , <a class="ref" href="scmfsa_2.html#T100">SCMFSA_2:100</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:22_1_6_12_2_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_12_2_1_2"><b>suppose </b></a><a NAME="E1:22_1_6_12_2_1_2"/><i><font color="Green">E247</font></i>: 
<font color="Maroon">x</font> is    <a href="scmfsa_2.html#M2">FinSeq-Location</a> 
 ;<br/><div class="add"><a NAME="E2:22_1_6_12_2_1_2"/><b>then </b><i><font color="Green">E248</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, <a class="ref" href="scmfsa_2.html#T100">SCMFSA_2:100</a></i>;<br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><b>hence </b><a NAME="E4:22_1_6_12_2_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, , , <a class="ref" href="scmfsa_2.html#T100">SCMFSA_2:100</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E6:22_1_6_12"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1]
 <b>by </b><i><a class="ref" href="scmbsort.html#T3" target="_self">Th3</a>, <a class="txt" href="scmbsort.html#E3:22"><i><font color="Green">E42</font></i></a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_13"><b>suppose </b></a><a NAME="E1:22_1_6_13"/>
 <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 12
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">fa</font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:22_1_6_13"/><i><font color="Green">E249</font></i>: 
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">fa</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T65">SCMFSA_2:65</a></i>;<br/><i><font color="Green">E250</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> = 
 <a href="scmfsa_2.html#K7">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, <a class="ref" href="scmfsa_2.html#T101">SCMFSA_2:101</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i>, , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, <a class="ref" href="scmfsa_2.html#T101">SCMFSA_2:101</a></i>
;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_6_13_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:22_1_6_13_2"/><i><font color="Green">E251</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span>
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_13_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:22_1_6_13_2_1"/>
( <font color="Maroon">x</font> is    <a href="scmfsa_2.html#M2">FinSeq-Location</a>  or <font color="Maroon">x</font> is    <a href="scmfsa_2.html#M1">Int-Location</a>  )
 </span><b>by </b><i>, , </i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_13_2_1_1"><b>suppose </b></a><a NAME="E1:22_1_6_13_2_1_1"/><i><font color="Green">E252</font></i>: 
<font color="Maroon">x</font> is    <a href="scmfsa_2.html#M2">FinSeq-Location</a> 
 ;<br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_6_13_2_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_13_2_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:22_1_6_13_2_1_1_1_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">fa</font> or <font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">fa</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_13_2_1_1_1_1_1"><b>case </b></a><a NAME="E1:22_1_6_13_2_1_1_1_1_1"/><i><font color="Green">E253</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">fa</font>
 ;<br/><div class="add"><b>consider </b><font color="Maroon">k1</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E3:22_1_6_13_2_1_1_1_1_1"/><i><font color="Green">E254</font></i>: 
( <font color="Maroon">k1</font> <a href="hidden.html#R1">=</a>  <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon">fa</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">a</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">fa</font> <a href="hidden.html#R1">=</a> <font color="Maroon">k1</font> <a href="finseq_2.html#K2">|-&gt;</a> 0 )
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T101">SCMFSA_2:101</a></i>;<br/><b>consider </b><font color="Maroon">k2</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E5:22_1_6_13_2_1_1_1_1_1"/><i><font color="Green">E255</font></i>: 
( <font color="Maroon">k2</font> <a href="hidden.html#R1">=</a>  <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon">fa</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">a</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">fa</font> <a href="hidden.html#R1">=</a> <font color="Maroon">k2</font> <a href="finseq_2.html#K2">|-&gt;</a> 0 )
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T101">SCMFSA_2:101</a></i>;<br/><a NAME="E6:22_1_6_13_2_1_1_1_1_1"/><i><font color="Green">E256</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font>
 <b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, </i>;<br/><b>then </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="txt" href="scmbsort.html#E6:22"><i><font color="Green">E48</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><b>hence </b><a NAME="E8:22_1_6_13_2_1_1_1_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, , , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, , , <a class="txt" href="scmbsort.html#E5:22"><i><font color="Green">E47</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_13_2_1_1_1_1_2"><b>case </b></a><a NAME="E1:22_1_6_13_2_1_1_1_1_2"/><i><font color="Green">E257</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">fa</font>
 ;<br/><div class="add"><a NAME="E2:22_1_6_13_2_1_1_1_1_2"/><b>then </b><i><font color="Green">E258</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, , <a class="ref" href="scmfsa_2.html#T101">SCMFSA_2:101</a></i>;<br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><b>hence </b><a NAME="E4:22_1_6_13_2_1_1_1_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, , , , <a class="ref" href="scmfsa_2.html#T101">SCMFSA_2:101</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:22_1_6_13_2_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_6_13_2_1_2"><b>suppose </b></a><a NAME="E1:22_1_6_13_2_1_2"/><i><font color="Green">E259</font></i>: 
<font color="Maroon">x</font> is    <a href="scmfsa_2.html#M1">Int-Location</a> 
 ;<br/><div class="add"><a NAME="E2:22_1_6_13_2_1_2"/><b>then </b><i><font color="Green">E260</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, , <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, <a class="ref" href="scmfsa_2.html#T101">SCMFSA_2:101</a></i>;<br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><b>hence </b><a NAME="E4:22_1_6_13_2_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, <a class="txt" href="scmbsort.html#E1:22"><i><font color="Green">E41</font></i></a>, , , <a class="ref" href="scmfsa_2.html#T101">SCMFSA_2:101</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E6:22_1_6_13"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1]
 <b>by </b><i><a class="ref" href="scmbsort.html#T3" target="_self">Th3</a>, <a class="txt" href="scmbsort.html#E3:22"><i><font color="Green">E42</font></i></a>, </i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<a NAME="E11:22"/>
for <font color="Olive">m</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">m</font>]
 
<b>from </b><i><a class="ref" href="nat_1.html#S1">NAT_1:sch 1</a>(, );<br/></i>
<b>hence </b><a NAME="E12:22"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span></span>)</span> )
 <b>by </b><i/>;<br/>


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