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<span class="kw">let </span><font color="Maroon" title="c1">I</font>, <font color="Maroon" title="c2">J</font>, <font color="Maroon" title="c3">K</font> be   <a href="scmnorm.html#NM2" title="SCMNORM:NM.2">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="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <font color="Maroon" title="c2">J</font></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <font color="Maroon" title="c3">K</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">I</font> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">J</font> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <font color="Maroon" title="c3">K</font></span>)</span></span><br/>





 <a href="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">J</font> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <font color="Maroon" title="c3">K</font></span>)</span>,<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c1">I</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> <font color="Maroon" title="c2">J</font>,<span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> <span class="p2">(<span class="default"><a href="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> <font color="Maroon" title="c3">K</font>,<span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c2">J</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="valued_1.html#T24" title="VALUED_1:th.24">VALUED_1:24</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> <font color="Maroon" title="c2">J</font>,<span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> <font color="Maroon" title="c3">K</font>,<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="c2">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="valued_1.html#T22" title="VALUED_1:th.22">VALUED_1:22</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> <font color="Maroon" title="c2">J</font>,<span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> <font color="Maroon" title="c3">K</font>,<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="c1">I</font> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <font color="Maroon" title="c2">J</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_4.html#T45" target="_self" title="SCMPDS_4:th.45">Th45</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E2:49"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <font color="Maroon" title="c2">J</font></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <font color="Maroon" title="c3">K</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">I</font> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">J</font> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <font color="Maroon" title="c3">K</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T15" title="FUNCT_4:th.15">FUNCT_4:15</a></span>; <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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