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<span class="kw">let </span><font color="Maroon" title="c3">I</font> be   <a href="compos_1.html#NM5" title="COMPOS_1:NM.5">Program</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">a</font> being    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> <br/>  for <font color="Olive" title="b2">i</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><br/>  for <font color="Olive" title="b3">n</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds   <a href="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> (<font color="Maroon" title="c3">I</font>,1) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">i</font>,<font color="Olive" title="b3">n</font>,<font color="Maroon" title="c3">I</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c4">a</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">i</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><br/>  for <font color="Olive" title="b2">n</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds   <a href="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> (<font color="Maroon" title="c3">I</font>,1) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> (<font color="Maroon" title="c4">a</font>,<font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">n</font>,<font color="Maroon" title="c3">I</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c5">i</font> be   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">n</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds   <a href="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> (<font color="Maroon" title="c3">I</font>,1) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">i</font>,<font color="Olive" title="b1">n</font>,<font color="Maroon" title="c3">I</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c6">n</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> (<font color="Maroon" title="c3">I</font>,1) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c6">n</font>,<font color="Maroon" title="c3">I</font>)</span><br/>







<span class="kw">set </span><font color="Maroon" title="c7">i1</font> = (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">i</font>) <a href="scmpds_2.html#K10" title="SCMPDS_2:func.10">&gt;=0_goto</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">i2</font> =  <a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c6">n</font>);<br/>
<span class="kw">set </span><font color="Maroon" title="c9">i3</font> =  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span>;<br/>
<a NAME="E1:41"/><span class="lab"><font color="Green" title="E33">A1</font></span>: 
 <a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c6">n</font>,<font color="Maroon" title="c3">I</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <span class="p3">(<span class="default">(<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">i</font>) <a href="scmpds_2.html#K10" title="SCMPDS_2:func.10">&gt;=0_goto</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c3">I</font></span>)</span> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c6">n</font>)</span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_4.html#T13" title="SCMPDS_4:th.13">SCMPDS_4:13</a></span>;<br/>
<a NAME="E2:41"/>
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">i</font>) <a href="scmpds_2.html#K10" title="SCMPDS_2:func.10">&gt;=0_goto</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="compos_1.html#T54" title="COMPOS_1:th.54">COMPOS_1:54</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:41"/>
 <a href="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> (<font color="Maroon" title="c3">I</font>,1) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="scmpds_7.html#K1" title="SCMPDS_7:func.1">for-up</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c6">n</font>,<font color="Maroon" title="c3">I</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:41"><span class="lab"><font color="Green" title="E33">A1</font></span></a>, <a class="ref" href="scmpds_7.html#T3" target="_self" title="SCMPDS_7:th.3">Th16</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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