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<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="nat_1.html#NM1">Nat</a>] means for <font color="Olive">b<sub>1</sub></font> being  <a href="ami_1.html#NM4">State</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  st <font color="Olive">b<sub>1</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">a<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="scmfsa_2.html#K21">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span></span>)</span> holds <br/>( <span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p4">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="scmfsa_2.html#K21">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p4">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p4">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> &amp; ( <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R1">=</a> 0 or ex <font color="Olive">b<sub>2</sub></font> being  <a href="nat_1.html#NM1">Nat</a>ex <font color="Olive">b<sub>3</sub></font> being  <a href="int_1.html#NM1">Integer</a> st <br/>( <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p3">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p5">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p5">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> &amp; <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">a<sub>1</sub></font> &amp; ( <font color="Maroon">a<sub>1</sub></font> <a href="xcmplx_0.html#K6">-</a> <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 implies ( <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="scmfsa_2.html#K21">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">a<sub>1</sub></font> <a href="xcmplx_0.html#K6">-</a> <font color="Olive">b<sub>2</sub></font></span>)</span> &amp; <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Olive">b<sub>1</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> ) ) &amp; ( for <font color="Olive">b<sub>4</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>4</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">a<sub>1</sub></font> <a href="xcmplx_0.html#K6">-</a> <font color="Olive">b<sub>2</sub></font> &amp; <font color="Olive">b<sub>4</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">a<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 holds <br/>ex <font color="Olive">b<sub>5</sub></font> being  <a href="int_1.html#NM1">Integer</a> st <br/>( <font color="Olive">b<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="scmfsa_2.html#K21">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Olive">b<sub>4</sub></font> &amp; <font color="Olive">b<sub>5</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> ) ) ) ) );<br/>
<a NAME="E1:63"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[0]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>49</sub></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">c<sub>50</sub></font> =  <a href="scmfsa6c.html#K1">Initialize</a> <font color="Maroon">c<sub>49</sub></font>;<br/>
<b>assume </b><a NAME="E1:63_1"/><i><font color="Green">E51</font></i>: 
( <font color="Maroon">c<sub>49</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">c<sub>49</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>49</sub></font> <a href="scmfsa_2.html#K21">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span></span>)</span> )
 ;<br/>

<b>hence </b><a NAME="E2:63_1"/>
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p4">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>49</sub></font> <a href="scmfsa_2.html#K21">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>
 <b>by </b><i><a class="ref" href="scmisort.html#T34" target="_self">Th34</a></i>;<br/>

<b>thus </b><span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p4">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmfsa6c.html#K1">Initialize</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmisort.html#E1:63_1"><i><font color="Green">E51</font></i></a>, <a class="ref" href="scmisort.html#T35" target="_self">Th35</a></i>
<br/>.= 
<font color="Maroon">c<sub>49</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa6c.html#T3">SCMFSA6C:3</a></i>
;<br/>

<b>thus </b><span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p4">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmfsa6c.html#K1">Initialize</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmisort.html#E1:63_1"><i><font color="Green">E51</font></i></a>, <a class="ref" href="scmisort.html#T35" target="_self">Th35</a></i>
<br/>.= 
<font color="Maroon">c<sub>49</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa6c.html#T3">SCMFSA6C:3</a></i>
;<br/>

<b>thus </b><a NAME="E5:63_1"/>
( 0 <a href="hidden.html#R1">=</a> 0 or ex <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a>ex <font color="Olive">b<sub>2</sub></font> being  <a href="int_1.html#NM1">Integer</a> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p3">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p5">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p5">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>49</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 0 &amp; ( 0 <a href="xcmplx_0.html#K6">-</a> <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 implies ( <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>49</sub></font> <a href="scmfsa_2.html#K21">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default">0 <a href="xcmplx_0.html#K6">-</a> <font color="Olive">b<sub>1</sub></font></span>)</span> &amp; <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>49</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> ) ) &amp; ( for <font color="Olive">b<sub>3</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 <a href="xcmplx_0.html#K6">-</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 <a href="nat_1.html#K1">+</a> 1 holds <br/>ex <font color="Olive">b<sub>4</sub></font> being  <a href="int_1.html#NM1">Integer</a> st <br/>( <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>49</sub></font> <a href="scmfsa_2.html#K21">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Olive">b<sub>3</sub></font> &amp; <font color="Olive">b<sub>4</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>49</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> ) ) ) )
 ;<br/>


</div><b>end;</b></div>
<div><i><font color="Green">E51</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="63_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>49</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:63_2"/><i><font color="Green">E52</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">c<sub>49</sub></font>]
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>50</sub></font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> ;<br/><b>assume </b><a NAME="E1:63_2_1"/><i><font color="Green">E53</font></i>: 
( <font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>49</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K21">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span></span>)</span> )
 ;<br/><a NAME="E2:63_2_1"/><b>then </b><i><font color="Green">E54</font></i>: 
<font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/><a NAME="E3:63_2_1"/><b>then </b><i><font color="Green">E55</font></i>: 
<font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 <a href="nat_1.html#K1">+</a> 0
 <b>by </b><i><a class="ref" href="int_1.html#T20">INT_1:20</a></i>;<br/><b>set </b><font color="Maroon">c<sub>51</sub></font> =  <a href="scmfsa6b.html#K3">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p5">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p5">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p5">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p5">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p4">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>50</sub></font>;<br/><b>set </b><font color="Maroon">c<sub>52</sub></font> =  <a href="scmfsa6c.html#K1">Initialize</a> <span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p3">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p5">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>50</sub></font></span>)</span>;<br/><b>consider </b><font color="Maroon">c<sub>53</sub></font> being   <a href="int_1.html#NM1">Integer</a><b> such that </b><br/><a NAME="E5:63_2_1"/><i><font color="Green">E56</font></i>: 
( <font color="Maroon">c<sub>53</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K21">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> &amp; ( <font color="Maroon">c<sub>53</sub></font> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 implies ( <span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p3">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p5">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 0 &amp; <span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p3">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p5">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> ) ) &amp; ( <font color="Maroon">c<sub>53</sub></font> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 0 implies ( <span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p3">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p5">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 &amp; <span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p3">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p5">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1 ) ) )
 <b>by </b><i><a class="txt" href="scmisort.html#E1:63_2_1"><i><font color="Green">E53</font></i></a>, <a class="txt" href="scmisort.html#E3:63_2_1"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scmisort.html#E63"><i><font color="Green">Lemma48</font></i></a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="63_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:63_2_1_1"/>
( <font color="Maroon">c<sub>53</sub></font> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 or <font color="Maroon">c<sub>53</sub></font> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="63_2_1_1_1"><b>suppose </b></a><a NAME="E1:63_2_1_1_1"/><i><font color="Green">E57</font></i>: 
<font color="Maroon">c<sub>53</sub></font> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/><div class="add"><b>thus </b><span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p4">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span> = 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p4">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>50</sub></font></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmisort.html#E2:63_2_1"><i><font color="Green">E54</font></i></a>, <a class="txt" href="scmisort.html#E51"><i><font color="Green">Lemma36</font></i></a>, <a class="ref" href="scmisort.html#T36" target="_self">Th36</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p3">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p5">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmisort.html#E5:63_2_1"><i><font color="Green">E56</font></i></a>, <a class="txt" href="scmisort.html#E1:63_2_1_1_1"><i><font color="Green">E57</font></i></a>, <a class="ref" href="scmisort.html#T34" target="_self">Th34</a></i>
<br/>.= 
<font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K21">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmisort.html#E1:63_2_1"><i><font color="Green">E53</font></i></a>, <a class="txt" href="scmisort.html#E3:63_2_1"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scmisort.html#E63"><i><font color="Green">Lemma48</font></i></a></i>
;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p4">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p4">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>50</sub></font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmisort.html#E2:63_2_1"><i><font color="Green">E54</font></i></a>, <a class="txt" href="scmisort.html#E51"><i><font color="Green">Lemma36</font></i></a>, <a class="ref" href="scmisort.html#T37" target="_self">Th37</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa6c.html#K1">Initialize</a> <span class="p2">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>50</sub></font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmisort.html#E5:63_2_1"><i><font color="Green">E56</font></i></a>, <a class="txt" href="scmisort.html#E1:63_2_1_1_1"><i><font color="Green">E57</font></i></a>, <a class="ref" href="scmisort.html#T35" target="_self">Th35</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p3">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p5">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa6c.html#T3">SCMFSA6C:3</a></i>
<br/>.= 
<font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmisort.html#E1:63_2_1"><i><font color="Green">E53</font></i></a>, <a class="txt" href="scmisort.html#E3:63_2_1"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scmisort.html#E63"><i><font color="Green">Lemma48</font></i></a></i>
;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p4">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p4">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>50</sub></font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmisort.html#E2:63_2_1"><i><font color="Green">E54</font></i></a>, <a class="txt" href="scmisort.html#E51"><i><font color="Green">Lemma36</font></i></a>, <a class="ref" href="scmisort.html#T37" target="_self">Th37</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa6c.html#K1">Initialize</a> <span class="p2">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>50</sub></font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmisort.html#E5:63_2_1"><i><font color="Green">E56</font></i></a>, <a class="txt" href="scmisort.html#E1:63_2_1_1_1"><i><font color="Green">E57</font></i></a>, <a class="ref" href="scmisort.html#T35" target="_self">Th35</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p3">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p5">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa6c.html#T3">SCMFSA6C:3</a></i>
<br/>.= 
<font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmisort.html#E1:63_2_1"><i><font color="Green">E53</font></i></a>, <a class="txt" href="scmisort.html#E3:63_2_1"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scmisort.html#E63"><i><font color="Green">Lemma48</font></i></a></i>
;<br/><i><font color="Green">E58</font></i>: <span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p4">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p4">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>50</sub></font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmisort.html#E2:63_2_1"><i><font color="Green">E54</font></i></a>, <a class="txt" href="scmisort.html#E51"><i><font color="Green">Lemma36</font></i></a>, <a class="ref" href="scmisort.html#T37" target="_self">Th37</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa6c.html#K1">Initialize</a> <span class="p2">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>50</sub></font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmisort.html#E5:63_2_1"><i><font color="Green">E56</font></i></a>, <a class="txt" href="scmisort.html#E1:63_2_1_1_1"><i><font color="Green">E57</font></i></a>, <a class="ref" href="scmisort.html#T35" target="_self">Th35</a></i>
<br/>.= 
<font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmisort.html#E5:63_2_1"><i><font color="Green">E56</font></i></a>, <a class="txt" href="scmisort.html#E1:63_2_1_1_1"><i><font color="Green">E57</font></i></a>, <a class="ref" href="scmfsa6c.html#T3">SCMFSA6C:3</a></i>
;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_2_1_1_1_5"><b>now </b></a><div class="add"><b>take </b><font color="Maroon">c<sub>54</sub></font> = 0;<br/><b>take </b><font color="Maroon">c<sub>55</sub></font> = <font color="Maroon">c<sub>53</sub></font>;<br/><b>thus </b><a NAME="E1:63_2_1_1_1_5"/>
<font color="Maroon">c<sub>54</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p3">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p5">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p5">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmisort.html#E5:63_2_1_1_1"><i><font color="Green">E58</font></i></a></i>;<br/><b>thus </b><a NAME="E2:63_2_1_1_1_5"/>
<font color="Maroon">c<sub>54</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>49</sub></font> <a href="nat_1.html#K1">+</a> 1
 ;<br/><b>thus </b><a NAME="E3:63_2_1_1_1_5"/>
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>49</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>54</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 implies ( <font color="Maroon">c<sub>55</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K21">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>49</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>54</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>55</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> ) )
 <b>by </b><i><a class="txt" href="scmisort.html#E1:63_2_1"><i><font color="Green">E53</font></i></a>, <a class="txt" href="scmisort.html#E5:63_2_1"><i><font color="Green">E56</font></i></a>, <a class="txt" href="scmisort.html#E1:63_2_1_1_1"><i><font color="Green">E57</font></i></a>, <a class="ref" href="xreal_1.html#T21">XREAL_1:21</a></i>;<br/><b>thus </b><a NAME="E4:63_2_1_1_1_5"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>49</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>54</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>49</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 holds <br/>ex <font color="Olive">b<sub>2</sub></font> being  <a href="int_1.html#NM1">Integer</a> st <br/>( <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K21">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> )
 <b>by </b><i><a class="ref" href="int_1.html#T20">INT_1:20</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E7:63_2_1_1_1"/>
( <font color="Maroon">c<sub>49</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> 0 or ex <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a>ex <font color="Olive">b<sub>2</sub></font> being  <a href="int_1.html#NM1">Integer</a> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p3">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p5">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p5">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>49</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>49</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 implies ( <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K21">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>49</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Olive">b<sub>1</sub></font></span>)</span> &amp; <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> ) ) &amp; ( for <font color="Olive">b<sub>3</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>49</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>49</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 holds <br/>ex <font color="Olive">b<sub>4</sub></font> being  <a href="int_1.html#NM1">Integer</a> st <br/>( <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K21">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Olive">b<sub>3</sub></font> &amp; <font color="Olive">b<sub>4</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> ) ) ) )
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="63_2_1_1_2"><b>suppose </b></a><a NAME="E1:63_2_1_1_2"/><i><font color="Green">E57</font></i>: 
<font color="Maroon">c<sub>53</sub></font> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 0
 ;<br/><div class="add"><a NAME="E2:63_2_1_1_2"/><b>then </b><i><font color="Green">E58</font></i>: 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p3">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p5">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>49</sub></font>
 <b>by </b><i><a class="txt" href="scmisort.html#E1:63_2_1"><i><font color="Green">E53</font></i></a>, <a class="txt" href="scmisort.html#E5:63_2_1"><i><font color="Green">E56</font></i></a></i>;<br/><a NAME="E3:63_2_1_1_2"/><i><font color="Green">E59</font></i>: 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p3">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p5">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K21">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>
 <b>by </b><i><a class="txt" href="scmisort.html#E1:63_2_1"><i><font color="Green">E53</font></i></a>, <a class="txt" href="scmisort.html#E3:63_2_1"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scmisort.html#E63"><i><font color="Green">Lemma48</font></i></a></i>;<br/><a NAME="E4:63_2_1_1_2"/>
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p3">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p5">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>49</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="txt" href="scmisort.html#E2:63_2_1_1_2"><i><font color="Green">E58</font></i></a>, <a class="ref" href="xreal_1.html#T31">XREAL_1:31</a></i>;<br/><a NAME="E5:63_2_1_1_2"/><b>then </b><i><font color="Green">E60</font></i>: 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p3">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p5">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K21">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmisort.html#E1:63_2_1"><i><font color="Green">E53</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E6:63_2_1_1_2"/><i><font color="Green">E61</font></i>: 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p3">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p5">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmisort.html#E1:63_2_1"><i><font color="Green">E53</font></i></a>, <a class="txt" href="scmisort.html#E3:63_2_1"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scmisort.html#E63"><i><font color="Green">Lemma48</font></i></a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p4">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span> = 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p4">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>50</sub></font></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmisort.html#E2:63_2_1"><i><font color="Green">E54</font></i></a>, <a class="txt" href="scmisort.html#E51"><i><font color="Green">Lemma36</font></i></a>, <a class="ref" href="scmisort.html#T36" target="_self">Th36</a></i>
<br/>.= 
<font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K21">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmisort.html#E1:63_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="scmisort.html#E2:63_2_1_1_2"><i><font color="Green">E58</font></i></a>, <a class="txt" href="scmisort.html#E3:63_2_1_1_2"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scmisort.html#E5:63_2_1_1_2"><i><font color="Green">E60</font></i></a></i>
;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p4">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p4">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>50</sub></font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmisort.html#E2:63_2_1"><i><font color="Green">E54</font></i></a>, <a class="txt" href="scmisort.html#E51"><i><font color="Green">Lemma36</font></i></a>, <a class="ref" href="scmisort.html#T37" target="_self">Th37</a></i>
<br/>.= 
<font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmisort.html#E1:63_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="scmisort.html#E2:63_2_1_1_2"><i><font color="Green">E58</font></i></a>, <a class="txt" href="scmisort.html#E3:63_2_1_1_2"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scmisort.html#E5:63_2_1_1_2"><i><font color="Green">E60</font></i></a>, <a class="txt" href="scmisort.html#E6:63_2_1_1_2"><i><font color="Green">E61</font></i></a></i>
;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p4">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p4">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>50</sub></font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmisort.html#E2:63_2_1"><i><font color="Green">E54</font></i></a>, <a class="txt" href="scmisort.html#E51"><i><font color="Green">Lemma36</font></i></a>, <a class="ref" href="scmisort.html#T37" target="_self">Th37</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p3">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p5">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmisort.html#E1:63_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="scmisort.html#E2:63_2_1_1_2"><i><font color="Green">E58</font></i></a>, <a class="txt" href="scmisort.html#E3:63_2_1_1_2"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scmisort.html#E5:63_2_1_1_2"><i><font color="Green">E60</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmisort.html#E1:63_2_1"><i><font color="Green">E53</font></i></a>, <a class="txt" href="scmisort.html#E3:63_2_1"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scmisort.html#E63"><i><font color="Green">Lemma48</font></i></a></i>
;<br/><div><b>hereby </b>
<div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="63_2_1_1_2_4_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:63_2_1_1_2_4_1"/>
( <font color="Maroon">c<sub>49</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 or <font color="Maroon">c<sub>49</sub></font> <a href="hidden.html#R1">=</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="63_2_1_1_2_4_1_1"><b>suppose </b></a><a NAME="E1:63_2_1_1_2_4_1_1"/>
<font color="Maroon">c<sub>49</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>54</sub></font> being   <a href="nat_1.html#NM1">Nat</a>, <font color="Maroon">c<sub>55</sub></font> being   <a href="int_1.html#NM1">Integer</a><b> such that </b><br/><a NAME="E3:63_2_1_1_2_4_1_1"/><i><font color="Green">E62</font></i>: 
( <font color="Maroon">c<sub>54</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p3">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p5">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p5">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p5">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>50</sub></font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> &amp; <font color="Maroon">c<sub>54</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>49</sub></font> &amp; ( <font color="Maroon">c<sub>49</sub></font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>54</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 implies ( <font color="Maroon">c<sub>55</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>49</sub></font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>54</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>55</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p3">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p5">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> ) ) &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">c<sub>49</sub></font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>54</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>49</sub></font> <a href="nat_1.html#K1">+</a> 1 holds <br/>ex <font color="Olive">b<sub>2</sub></font> being  <a href="int_1.html#NM1">Integer</a> st <br/>( <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p3">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p5">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> ) ) )
 <b>by </b><i><a class="txt" href="scmisort.html#E1:63_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="scmisort.html#E2:63_2_1_1_2"><i><font color="Green">E58</font></i></a>, <a class="txt" href="scmisort.html#E3:63_2_1_1_2"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scmisort.html#E5:63_2_1_1_2"><i><font color="Green">E60</font></i></a></i>;<br/><a NAME="E4:63_2_1_1_2_4_1_1"/><i><font color="Green">E63</font></i>: 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p4">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>54</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scmisort.html#E2:63_2_1"><i><font color="Green">E54</font></i></a>, <a class="txt" href="scmisort.html#E5:63_2_1"><i><font color="Green">E56</font></i></a>, <a class="txt" href="scmisort.html#E1:63_2_1_1_2"><i><font color="Green">E57</font></i></a>, <a class="txt" href="scmisort.html#E3:63_2_1_1_2_4_1_1"><i><font color="Green">E62</font></i></a>, <a class="txt" href="scmisort.html#E51"><i><font color="Green">Lemma36</font></i></a>, <a class="ref" href="scmisort.html#T37" target="_self">Th37</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_2_1_1_2_4_1_1_1"><b>now </b></a><div class="add"><b>take </b><font color="Maroon">c<sub>56</sub></font> = 1 <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>54</sub></font>;<br/><b>take </b><font color="Maroon">c<sub>57</sub></font> = <font color="Maroon">c<sub>55</sub></font>;<br/><b>thus </b><a NAME="E1:63_2_1_1_2_4_1_1_1"/>
<font color="Maroon">c<sub>56</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p3">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p5">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p5">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmisort.html#E4:63_2_1_1_2_4_1_1"><i><font color="Green">E63</font></i></a></i>;<br/><b>thus </b><a NAME="E2:63_2_1_1_2_4_1_1_1"/>
<font color="Maroon">c<sub>56</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>49</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="txt" href="scmisort.html#E3:63_2_1_1_2_4_1_1"><i><font color="Green">E62</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><b>thus </b><a NAME="E3:63_2_1_1_2_4_1_1_1"/>
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>49</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>56</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 implies ( <font color="Maroon">c<sub>57</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K21">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>49</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>56</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>57</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> ) )
 <b>by </b><i><a class="txt" href="scmisort.html#E1:63_2_1"><i><font color="Green">E53</font></i></a>, <a class="txt" href="scmisort.html#E3:63_2_1"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scmisort.html#E3:63_2_1_1_2_4_1_1"><i><font color="Green">E62</font></i></a>, <a class="txt" href="scmisort.html#E63"><i><font color="Green">Lemma48</font></i></a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_2_1_1_2_4_1_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>58</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:63_2_1_1_2_4_1_1_1_1"/><i><font color="Green">E64</font></i>: 
( <font color="Maroon">c<sub>58</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>49</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>56</sub></font> &amp; <font color="Maroon">c<sub>58</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>49</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 )
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="63_2_1_1_2_4_1_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="E1:63_2_1_1_2_4_1_1_1_1_1"/>
( <font color="Maroon">c<sub>58</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>49</sub></font> <a href="nat_1.html#K1">+</a> 1 or <font color="Maroon">c<sub>58</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>49</sub></font> <a href="nat_1.html#K1">+</a> 1 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="63_2_1_1_2_4_1_1_1_1_1_1"><b>suppose </b></a><a NAME="E1:63_2_1_1_2_4_1_1_1_1_1_1"/><i><font color="Green">E65</font></i>: 
<font color="Maroon">c<sub>58</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>49</sub></font> <a href="nat_1.html#K1">+</a> 1
 ;<br/><div class="add"><b>take </b><font color="Maroon">c<sub>59</sub></font> = <font color="Maroon">c<sub>53</sub></font>;<br/><b>thus </b><a NAME="E2:63_2_1_1_2_4_1_1_1_1_1_1"/>
<font color="Maroon">c<sub>59</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K21">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>58</sub></font>
 <b>by </b><i><a class="txt" href="scmisort.html#E1:63_2_1"><i><font color="Green">E53</font></i></a>, <a class="txt" href="scmisort.html#E5:63_2_1"><i><font color="Green">E56</font></i></a>, <a class="txt" href="scmisort.html#E1:63_2_1_1_2_4_1_1_1_1_1_1"><i><font color="Green">E65</font></i></a></i>;<br/><a NAME="E3:63_2_1_1_2_4_1_1_1_1_1_1"/>
<font color="Maroon">c<sub>59</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 0 <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmisort.html#E1:63_2_1_1_2"><i><font color="Green">E57</font></i></a>, <a class="ref" href="xreal_1.html#T22">XREAL_1:22</a></i>;<br/><b>hence </b><a NAME="E4:63_2_1_1_2_4_1_1_1_1_1_1"/>
<font color="Maroon">c<sub>59</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="63_2_1_1_2_4_1_1_1_1_1_2"><b>suppose </b></a><a NAME="E1:63_2_1_1_2_4_1_1_1_1_1_2"/><i><font color="Green">E65</font></i>: 
<font color="Maroon">c<sub>58</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>49</sub></font> <a href="nat_1.html#K1">+</a> 1
 ;<br/><div class="add"><a NAME="E2:63_2_1_1_2_4_1_1_1_1_1_2"/>
<font color="Maroon">c<sub>58</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>49</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="txt" href="scmisort.html#E1:63_2_1_1_2_4_1_1_1_1"><i><font color="Green">E64</font></i></a>, <a class="ref" href="int_1.html#T20">INT_1:20</a></i>;<br/><a NAME="E3:63_2_1_1_2_4_1_1_1_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>58</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>49</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="txt" href="scmisort.html#E1:63_2_1_1_2_4_1_1_1_1_1_2"><i><font color="Green">E65</font></i></a>, <a class="ref" href="real_1.html#D5">REAL_1:def 5</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>59</sub></font> being   <a href="int_1.html#NM1">Integer</a><b> such that </b><br/><a NAME="E5:63_2_1_1_2_4_1_1_1_1_1_2"/><i><font color="Green">E66</font></i>: 
( <font color="Maroon">c<sub>59</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>58</sub></font> &amp; <font color="Maroon">c<sub>59</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p3">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p5">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> )
 <b>by </b><i><a class="txt" href="scmisort.html#E3:63_2_1_1_2_4_1_1"><i><font color="Green">E62</font></i></a>, <a class="txt" href="scmisort.html#E1:63_2_1_1_2_4_1_1_1_1"><i><font color="Green">E64</font></i></a></i>;<br/><b>take </b><font color="Maroon">c<sub>60</sub></font> = <font color="Maroon">c<sub>59</sub></font>;<br/><b>thus </b><a NAME="E6:63_2_1_1_2_4_1_1_1_1_1_2"/>
<font color="Maroon">c<sub>60</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K21">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>58</sub></font>
 <b>by </b><i><a class="txt" href="scmisort.html#E1:63_2_1"><i><font color="Green">E53</font></i></a>, <a class="txt" href="scmisort.html#E3:63_2_1"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scmisort.html#E5:63_2_1_1_2_4_1_1_1_1_1_2"><i><font color="Green">E66</font></i></a>, <a class="txt" href="scmisort.html#E63"><i><font color="Green">Lemma48</font></i></a></i>;<br/><b>thus </b><a NAME="E7:63_2_1_1_2_4_1_1_1_1_1_2"/>
<font color="Maroon">c<sub>60</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmisort.html#E1:63_2_1"><i><font color="Green">E53</font></i></a>, <a class="txt" href="scmisort.html#E3:63_2_1"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scmisort.html#E5:63_2_1_1_2_4_1_1_1_1_1_2"><i><font color="Green">E66</font></i></a>, <a class="txt" href="scmisort.html#E63"><i><font color="Green">Lemma48</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E5:63_2_1_1_2_4_1_1_1"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>49</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>56</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>49</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 holds <br/>ex <font color="Olive">b<sub>2</sub></font> being  <a href="int_1.html#NM1">Integer</a> st <br/>( <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K21">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> )
 ;<br/></div><b>end;</b></div><b>hence </b><a NAME="E6:63_2_1_1_2_4_1_1"/>
( <font color="Maroon">c<sub>49</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> 0 or ex <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a>ex <font color="Olive">b<sub>2</sub></font> being  <a href="int_1.html#NM1">Integer</a> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p3">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p5">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p5">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>49</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>49</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 implies ( <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K21">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>49</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Olive">b<sub>1</sub></font></span>)</span> &amp; <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> ) ) &amp; ( for <font color="Olive">b<sub>3</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>49</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>49</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 holds <br/>ex <font color="Olive">b<sub>4</sub></font> being  <a href="int_1.html#NM1">Integer</a> st <br/>( <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K21">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Olive">b<sub>3</sub></font> &amp; <font color="Olive">b<sub>4</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> ) ) ) )
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="63_2_1_1_2_4_1_2"><b>suppose </b></a><a NAME="E1:63_2_1_1_2_4_1_2"/><i><font color="Green">E62</font></i>: 
<font color="Maroon">c<sub>49</sub></font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><i><font color="Green">E63</font></i>: <span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p4">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p4">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>50</sub></font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmisort.html#E2:63_2_1"><i><font color="Green">E54</font></i></a>, <a class="txt" href="scmisort.html#E51"><i><font color="Green">Lemma36</font></i></a>, <a class="ref" href="scmisort.html#T37" target="_self">Th37</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa6c.html#K1">Initialize</a> <span class="p2">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>50</sub></font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmisort.html#E1:63_2_1"><i><font color="Green">E53</font></i></a>, <a class="txt" href="scmisort.html#E5:63_2_1"><i><font color="Green">E56</font></i></a>, <a class="txt" href="scmisort.html#E1:63_2_1_1_2_4_1_2"><i><font color="Green">E62</font></i></a>, <a class="ref" href="scmisort.html#T35" target="_self">Th35</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1
<b>by </b><i><a class="txt" href="scmisort.html#E5:63_2_1"><i><font color="Green">E56</font></i></a>, <a class="txt" href="scmisort.html#E1:63_2_1_1_2"><i><font color="Green">E57</font></i></a>, <a class="ref" href="scmfsa6c.html#T3">SCMFSA6C:3</a></i>
;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_2_1_1_2_4_1_2_2"><b>now </b></a><div class="add"><b>take </b><font color="Maroon">c<sub>54</sub></font> = 1;<br/><b>take </b><font color="Maroon">c<sub>55</sub></font> = 0;<br/><b>thus </b><a NAME="E1:63_2_1_1_2_4_1_2_2"/>
<font color="Maroon">c<sub>54</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p3">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p5">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p5">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmisort.html#E2:63_2_1_1_2_4_1_2"><i><font color="Green">E63</font></i></a></i>;<br/><b>thus </b><a NAME="E2:63_2_1_1_2_4_1_2_2"/>
<font color="Maroon">c<sub>54</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>49</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="txt" href="scmisort.html#E1:63_2_1_1_2_4_1_2"><i><font color="Green">E62</font></i></a></i>;<br/><b>thus </b><a NAME="E3:63_2_1_1_2_4_1_2_2"/>
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>49</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>54</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 implies ( <font color="Maroon">c<sub>55</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K21">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>49</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>54</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>55</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> ) )
 <b>by </b><i><a class="txt" href="scmisort.html#E1:63_2_1_1_2_4_1_2"><i><font color="Green">E62</font></i></a></i>;<br/><div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">c<sub>56</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:63_2_1_1_2_4_1_2_2_1"/><i><font color="Green">E64</font></i>: 
( <font color="Maroon">c<sub>56</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>49</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>54</sub></font> &amp; <font color="Maroon">c<sub>56</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>49</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 )
 ;<br/><a NAME="E2:63_2_1_1_2_4_1_2_2_1"/><b>then </b><i><font color="Green">E65</font></i>: 
<font color="Maroon">c<sub>56</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="int_1.html#T20">INT_1:20</a></i>;<br/><a NAME="E3:63_2_1_1_2_4_1_2_2_1"/><i><font color="Green">E66</font></i>: 
<font color="Maroon">c<sub>56</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 1
 <b>by </b><i><a class="txt" href="scmisort.html#E1:63_2_1_1_2_4_1_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="scmisort.html#E1:63_2_1_1_2_4_1_2_2_1"><i><font color="Green">E64</font></i></a>, <a class="ref" href="int_1.html#T20">INT_1:20</a></i>;<br/><b>take </b><font color="Maroon">c<sub>57</sub></font> = <font color="Maroon">c<sub>53</sub></font>;<br/><b>thus </b><a NAME="E4:63_2_1_1_2_4_1_2_2_1"/>
<font color="Maroon">c<sub>57</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K21">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>56</sub></font>
 <b>by </b><i><a class="txt" href="scmisort.html#E1:63_2_1"><i><font color="Green">E53</font></i></a>, <a class="txt" href="scmisort.html#E5:63_2_1"><i><font color="Green">E56</font></i></a>, <a class="txt" href="scmisort.html#E1:63_2_1_1_2_4_1_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="scmisort.html#E2:63_2_1_1_2_4_1_2_2_1"><i><font color="Green">E65</font></i></a>, <a class="txt" href="scmisort.html#E3:63_2_1_1_2_4_1_2_2_1"><i><font color="Green">E66</font></i></a>, <a class="ref" href="xreal_1.html#T1">XREAL_1:1</a></i>;<br/><a NAME="E5:63_2_1_1_2_4_1_2_2_1"/>
<font color="Maroon">c<sub>57</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 0 <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmisort.html#E1:63_2_1_1_2"><i><font color="Green">E57</font></i></a>, <a class="ref" href="xreal_1.html#T22">XREAL_1:22</a></i>;<br/><b>hence </b><a NAME="E6:63_2_1_1_2_4_1_2_2_1"/>
<font color="Maroon">c<sub>57</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 ;<br/></div>
<b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E4:63_2_1_1_2_4_1_2"/>
( <font color="Maroon">c<sub>49</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> 0 or ex <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a>ex <font color="Olive">b<sub>2</sub></font> being  <a href="int_1.html#NM1">Integer</a> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p3">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p5">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p5">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>49</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>49</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 implies ( <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K21">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>49</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Olive">b<sub>1</sub></font></span>)</span> &amp; <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> ) ) &amp; ( for <font color="Olive">b<sub>3</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>49</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>49</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 holds <br/>ex <font color="Olive">b<sub>4</sub></font> being  <a href="int_1.html#NM1">Integer</a> st <br/>( <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K21">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Olive">b<sub>3</sub></font> &amp; <font color="Olive">b<sub>4</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>50</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> ) ) ) )
 ;<br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:63_2"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">c<sub>49</sub></font> <a href="nat_1.html#K1">+</a> 1]
 ;<br/></div><b>end;</b></div>
<a NAME="E3:63"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>]
 
<b>from </b><i><a class="ref" href="nat_1.html#S1">NAT_1:sch 1</a>(<a class="txt" href="scmisort.html#E1:63"><i><font color="Green">E50</font></i></a>, <a class="txt" href="scmisort.html#E2:63"><i><font color="Green">E51</font></i></a>);<br/></i>
<b>hence </b><a NAME="E4:63"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a><br/>for <font color="Olive">b<sub>2</sub></font> being  <a href="ami_1.html#NM4">State</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  st <font color="Olive">b<sub>2</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="scmfsa_2.html#K21">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span></span>)</span> holds <br/>( <font color="Olive">b<sub>2</sub></font> <a href="scmfsa_2.html#K21">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p4">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Olive">b<sub>2</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span> &amp; <font color="Olive">b<sub>2</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">5 <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="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p4">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Olive">b<sub>2</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> &amp; <font color="Olive">b<sub>2</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">2 <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="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p4">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p0">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Olive">b<sub>2</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> &amp; ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> 0 or ex <font color="Olive">b<sub>3</sub></font> being  <a href="nat_1.html#NM1">Nat</a>ex <font color="Olive">b<sub>4</sub></font> being  <a href="int_1.html#NM1">Integer</a> st <br/>( <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p3">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p5">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K16">:=</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p5">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa6a.html#K7">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Olive">b<sub>2</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p3">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> &amp; <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> &amp; ( <font color="Olive">b<sub>1</sub></font> <a href="xcmplx_0.html#K6">-</a> <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 implies ( <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="scmfsa_2.html#K21">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="xcmplx_0.html#K6">-</a> <font color="Olive">b<sub>3</sub></font></span>)</span> &amp; <font color="Olive">b<sub>4</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Olive">b<sub>2</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> ) ) &amp; ( for <font color="Olive">b<sub>5</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>5</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Olive">b<sub>1</sub></font> <a href="xcmplx_0.html#K6">-</a> <font color="Olive">b<sub>3</sub></font> &amp; <font color="Olive">b<sub>5</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">b<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 holds <br/>ex <font color="Olive">b<sub>6</sub></font> being  <a href="int_1.html#NM1">Integer</a> st <br/>( <font color="Olive">b<sub>6</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="scmfsa_2.html#K21">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Olive">b<sub>5</sub></font> &amp; <font color="Olive">b<sub>6</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>2</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <span class="p2">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> ) ) ) ) )
 ;<br/>


</div>
