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<span class="kw">let </span><font color="Maroon" title="c3">x1</font>, <font color="Maroon" title="c4">x2</font>, <font color="Maroon" title="c5">x3</font>, <font color="Maroon" title="c6">x4</font> be   <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction</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="Red">::  thesis: </font></span></a><span class="hide">  <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"><span class="p3">(<span class="default"><font color="Maroon" title="c3">x1</font> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <font color="Maroon" title="c4">x2</font></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <font color="Maroon" title="c5">x3</font></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <font color="Maroon" title="c6">x4</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4</span><br/>

<span class="kw">thus </span> <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"><span class="p3">(<span class="default"><font color="Maroon" title="c3">x1</font> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <font color="Maroon" title="c4">x2</font></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <font color="Maroon" title="c5">x3</font></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <font color="Maroon" title="c6">x4</font></span>)</span> = 
<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"><font color="Maroon" title="c3">x1</font> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <font color="Maroon" title="c4">x2</font></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <font color="Maroon" title="c5">x3</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
<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"><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"><font color="Maroon" title="c3">x1</font> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <font color="Maroon" title="c4">x2</font></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> 1
<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> 1
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmp_gcd.html#T9" title="SCMP_GCD:th.9">SCMP_GCD:9</a></span>
<br/>.= 
4

; <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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