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<span class="kw">let </span><font color="Maroon" title="c3">a</font> be   <a href="scmpds_2.html#NM1" title="SCMPDS_2:NM.1">Int_position</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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">I</font> being   <a href="compos_1.html#NM4" title="COMPOS_1:NM.4">Program</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> holds   <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon" title="c3">a</font>,<font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">I</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Olive" title="b2">I</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span><br/><span class="kw">let </span><font color="Maroon" title="c4">i</font> be   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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="compos_1.html#NM4" title="COMPOS_1:NM.4">Program</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> holds   <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">i</font>,<font color="Olive" title="b1">I</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Olive" title="b1">I</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span><br/><span class="kw">let </span><font color="Maroon" title="c5">I</font> be   <a href="compos_1.html#NM4" title="COMPOS_1:NM.4">Program</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c5">I</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c5">I</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span><br/>





<span class="kw">set </span><font color="Maroon" title="c6">i1</font> = (<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">i</font>) <a href="scmpds_2.html#K9" title="SCMPDS_2:func.9">&gt;=0_goto</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c5">I</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">I4</font> = <span class="p1">(<span class="default">(<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">i</font>) <a href="scmpds_2.html#K9" title="SCMPDS_2:func.9">&gt;=0_goto</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c5">I</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span></span>)</span> <a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">';'</a> <font color="Maroon" title="c5">I</font>;<br/>
<span class="kw">thus </span> <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c5">I</font>)</span>)</span> = 
<span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">(<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">i</font>) <a href="scmpds_2.html#K9" title="SCMPDS_2:func.9">&gt;=0_goto</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c5">I</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span></span>)</span> <a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">';'</a> <font color="Maroon" title="c5">I</font></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmp_gcd.html#T4" onmouseover="rs('scmp_gcd/T4')" onmouseout="rh()">SCMP_GCD:4</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c5">I</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_6.html#T6" onmouseover="rs('scmpds_6/T6')" onmouseout="rh()">SCMPDS_6:6</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c5">I</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2

; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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