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<span class="kw">thus </span> <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <a href="scpinvar.html#K5" title="SCPINVAR:func.5">GCD-Algorithm</a>  = 
<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>  <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,3 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,2</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p2">(<span class="default"><a href="scpinvar.html#K4" title="SCPINVAR:func.4">while&lt;&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,3,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmpds_6.html#K3" title="SCMPDS_6:func.3">if&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,3,<span class="p0">(<span class="default"><a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,2</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,3 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</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#T45" title="SCMPDS_4:th.45">SCMPDS_4:45</a></span>
<br/>.= 
<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> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>  <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,3 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,1</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p2">(<span class="default"><a href="scpinvar.html#K4" title="SCPINVAR:func.4">while&lt;&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,3,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmpds_6.html#K3" title="SCMPDS_6:func.3">if&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,3,<span class="p0">(<span class="default"><a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,2</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,3 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,2</span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmp_gcd.html#T8" title="SCMP_GCD:th.8">SCMP_GCD:8</a></span>
<br/>.= 
<span class="p1">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 9
<span class="kw">by</span> <span class="lab"><a class="txt" href="scpinvar.html#E38"><span class="lab"><font color="Green" title="E27">Lm13</font></span></a>, <a class="ref" href="scmp_gcd.html#T9" title="SCMP_GCD:th.9">SCMP_GCD:9</a></span>
<br/>.= 
12

; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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