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<span class="kw">let </span><font color="Maroon" title="c17">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> holds   <a href="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> (<font color="Maroon" title="c17">I</font>,2) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="scpinvar.html#K4" title="SCPINVAR:func.4">while&lt;&gt;0</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">i</font>,<font color="Maroon" title="c17">I</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c18">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> holds   <a href="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> (<font color="Maroon" title="c17">I</font>,2) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="scpinvar.html#K4" title="SCPINVAR:func.4">while&lt;&gt;0</a> (<font color="Maroon" title="c18">a</font>,<font color="Olive" title="b1">i</font>,<font color="Maroon" title="c17">I</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c19">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">  <a href="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> (<font color="Maroon" title="c17">I</font>,2) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="scpinvar.html#K4" title="SCPINVAR:func.4">while&lt;&gt;0</a> (<font color="Maroon" title="c18">a</font>,<font color="Maroon" title="c19">i</font>,<font color="Maroon" title="c17">I</font>)</span><br/>





<span class="kw">set </span><font color="Maroon" title="c20">i1</font> = (<font color="Maroon" title="c18">a</font>,<font color="Maroon" title="c19">i</font>) <a href="scmpds_2.html#K8" title="SCMPDS_2:func.8">&lt;&gt;0_goto</a> 2;<br/>
<span class="kw">set </span><font color="Maroon" title="c21">i2</font> =  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">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="c17">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c22">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="c17">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span>;<br/>
<a NAME="E1:30"/>
(  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">(<font color="Maroon" title="c18">a</font>,<font color="Maroon" title="c19">i</font>) <a href="scmpds_2.html#K8" title="SCMPDS_2:func.8">&lt;&gt;0_goto</a> 2</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"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp;  <a href="scpinvar.html#K4" title="SCPINVAR:func.4">while&lt;&gt;0</a> (<font color="Maroon" title="c18">a</font>,<font color="Maroon" title="c19">i</font>,<font color="Maroon" title="c17">I</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">(<font color="Maroon" title="c18">a</font>,<font color="Maroon" title="c19">i</font>) <a href="scmpds_2.html#K8" title="SCMPDS_2:func.8">&lt;&gt;0_goto</a> 2</span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">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="c17">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</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"><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="c17">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#D3" title="SCMPDS_4:def.3">SCMPDS_4:def 3</a>, <a class="ref" href="scmp_gcd.html#T5" title="SCMP_GCD:th.5">SCMP_GCD:5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:30"/>
 <a href="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> (<font color="Maroon" title="c17">I</font>,2) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="scpinvar.html#K4" title="SCPINVAR:func.4">while&lt;&gt;0</a> (<font color="Maroon" title="c18">a</font>,<font color="Maroon" title="c19">i</font>,<font color="Maroon" title="c17">I</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_7.html#T3" title="SCMPDS_7:th.3">SCMPDS_7:3</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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