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<b>let </b><font color="Maroon" title="c3">n</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">I</font> being  <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>   st  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Olive" title="b1">I</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  holds <br/><span class="p1">(<span class="default"><a href="scmnorm.html#K4" title="SCMNORM:func.4">Shift</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Olive" title="b1">I</font></span>)</span>,<font color="Maroon" title="c3">n</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="scmnorm.html#K4" title="SCMNORM:func.4">Shift</a> <font color="Olive" title="b1">I</font>,<font color="Maroon" title="c3">n</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <font color="Maroon" title="c3">n</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c4">I</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies <span class="p1">(<span class="default"><a href="scmnorm.html#K4" title="SCMNORM:func.4">Shift</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c3">n</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="scmnorm.html#K4" title="SCMNORM:func.4">Shift</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c3">n</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <font color="Maroon" title="c3">n</font></span>)</span> )</span><br/>



<b>assume </b><a NAME="E1:15"/>
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="scmnorm.html#K4" title="SCMNORM:func.4">Shift</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c3">n</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="scmnorm.html#K4" title="SCMNORM:func.4">Shift</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c3">n</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <font color="Maroon" title="c3">n</font></span>)</span></span><br/>

<a NAME="E2:15"/><b>then </b><i><font color="Green" title="E14">A1</font></i>: 
 <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">I</font>
 
<b>by </b><i><a class="ref" href="scmpds_4.html#T1" title="SCMPDS_4:th.1">SCMPDS_4:1</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="scmnorm.html#K4" title="SCMNORM:func.4">Shift</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c3">n</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <font color="Maroon" title="c3">n</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmnorm.html#K4" title="SCMNORM:func.4">Shift</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c3">n</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <span class="p2">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c3">n</font></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="scmnorm.html#K4" title="SCMNORM:func.4">Shift</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c3">n</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c3">n</font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="scmnorm.html#K4" title="SCMNORM:func.4">Shift</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c3">n</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c3">n</font></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_7.html#E2:15"><i><font color="Green" title="E14">A1</font></i></a>, <a class="ref" href="scmpds_7.html#T18" target="_self" title="SCMPDS_7:th.18">Th18</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmnorm.html#K4" title="SCMNORM:func.4">Shift</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c3">n</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <span class="p2">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c3">n</font></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="scmnorm.html#K4" title="SCMNORM:func.4">Shift</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c3">n</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <font color="Maroon" title="c3">n</font></span>)</span>

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


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