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<span class="kw">let </span><font color="Maroon" title="c1">I</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_1.html#K7" title="CARD_1:func.7">Segm</a> 14; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">x</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="scmpds_1.html#K1" title="SCMPDS_1:func.1">SCMPDS-Instr</a> <br/> for <font color="Olive" title="b2">d1</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> <br/> for <font color="Olive" title="b3">k1</font>, <font color="Olive" title="b4">k2</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>  st <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c1">I</font>,<span class="p2"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Olive" title="b2">d1</font>,<font color="Olive" title="b3">k1</font>,<font color="Olive" title="b4">k2</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> holds <br/>( <font color="Olive" title="b1">x</font> <a href="scmpds_1.html#K14" title="SCMPDS_1:func.14">P31address</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">d1</font> &amp; <font color="Olive" title="b1">x</font> <a href="scmpds_1.html#K15" title="SCMPDS_1:func.15">P32const</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">k1</font> &amp; <font color="Olive" title="b1">x</font> <a href="scmpds_1.html#K16" title="SCMPDS_1:func.16">P33const</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">k2</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">x</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="scmpds_1.html#K1" title="SCMPDS_1:func.1">SCMPDS-Instr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">d1</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> <br/> for <font color="Olive" title="b2">k1</font>, <font color="Olive" title="b3">k2</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>  st <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c1">I</font>,<span class="p2"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Olive" title="b1">d1</font>,<font color="Olive" title="b2">k1</font>,<font color="Olive" title="b3">k2</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> holds <br/>( <font color="Maroon" title="c2">x</font> <a href="scmpds_1.html#K14" title="SCMPDS_1:func.14">P31address</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">d1</font> &amp; <font color="Maroon" title="c2">x</font> <a href="scmpds_1.html#K15" title="SCMPDS_1:func.15">P32const</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">k1</font> &amp; <font color="Maroon" title="c2">x</font> <a href="scmpds_1.html#K16" title="SCMPDS_1:func.16">P33const</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">k2</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">d1</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">k1</font>, <font color="Olive" title="b2">k2</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>  st <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c1">I</font>,<span class="p2"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Maroon" title="c3">d1</font>,<font color="Olive" title="b1">k1</font>,<font color="Olive" title="b2">k2</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> holds <br/>( <font color="Maroon" title="c2">x</font> <a href="scmpds_1.html#K14" title="SCMPDS_1:func.14">P31address</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">d1</font> &amp; <font color="Maroon" title="c2">x</font> <a href="scmpds_1.html#K15" title="SCMPDS_1:func.15">P32const</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">k1</font> &amp; <font color="Maroon" title="c2">x</font> <a href="scmpds_1.html#K16" title="SCMPDS_1:func.16">P33const</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">k2</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">k1</font>, <font color="Maroon" title="c5">k2</font> be   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c1">I</font>,<span class="p2"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Maroon" title="c3">d1</font>,<font color="Maroon" title="c4">k1</font>,<font color="Maroon" title="c5">k2</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> implies ( <font color="Maroon" title="c2">x</font> <a href="scmpds_1.html#K14" title="SCMPDS_1:func.14">P31address</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">d1</font> &amp; <font color="Maroon" title="c2">x</font> <a href="scmpds_1.html#K15" title="SCMPDS_1:func.15">P32const</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">k1</font> &amp; <font color="Maroon" title="c2">x</font> <a href="scmpds_1.html#K16" title="SCMPDS_1:func.16">P33const</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">k2</font> ) )</span><br/>







<a NAME="E1:51"/>
<font color="Maroon" title="c4">k1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="int_1.html#D2" title="INT_1:def.2">INT_1:def 2</a></span>;<br/>
<a NAME="E2:51"/><span class="kw">then </span><span class="lab"><font color="Green" title="E19">A1</font></span>: 
( <font color="Maroon" title="c3">d1</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  &amp; <font color="Maroon" title="c4">k1</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/>
<a NAME="E3:51"/>
<font color="Maroon" title="c5">k2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="int_1.html#D2" title="INT_1:def.2">INT_1:def 2</a></span>;<br/>
<a NAME="E4:51"/><span class="kw">then </span><span class="lab"><font color="Green" title="E20">A2</font></span>: 
<font color="Maroon" title="c5">k2</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/>
<span class="kw">assume </span><a NAME="E5:51"/><span class="lab"><font color="Green" title="E21">A3</font></span>: 
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c1">I</font>,<span class="p2"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Maroon" title="c3">d1</font>,<font color="Maroon" title="c4">k1</font>,<font color="Maroon" title="c5">k2</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">x</font> <a href="scmpds_1.html#K14" title="SCMPDS_1:func.14">P31address</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">d1</font> &amp; <font color="Maroon" title="c2">x</font> <a href="scmpds_1.html#K15" title="SCMPDS_1:func.15">P32const</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">k1</font> &amp; <font color="Maroon" title="c2">x</font> <a href="scmpds_1.html#K16" title="SCMPDS_1:func.16">P33const</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">k2</font> )</span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">f</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> <span class="kw"> such that </span><br/><a NAME="E7:51"/><span class="lab"><font color="Green" title="E22">A4</font></span>: 
<font color="Maroon" title="c6">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> 
 <span class="kw">and </span><br/><a NAME="E8:51"/><span class="lab"><font color="Green" title="E23">A5</font></span>: 
<font color="Maroon" title="c2">x</font> <a href="scmpds_1.html#K14" title="SCMPDS_1:func.14">P31address</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_1.html#D14" target="_self" title="SCMPDS_1:def.14">Def14</a></span>;<br/>
<a NAME="E9:51"/>
<font color="Maroon" title="c6">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Maroon" title="c3">d1</font>,<font color="Maroon" title="c4">k1</font>,<font color="Maroon" title="c5">k2</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:51"><span class="lab"><font color="Green" title="E21">A3</font></span></a>, <a class="txt" href="#E7:51"><span class="lab"><font color="Green" title="E22">A4</font></span></a>, <a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:51"/>
<font color="Maroon" title="c2">x</font> <a href="scmpds_1.html#K14" title="SCMPDS_1:func.14">P31address</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">d1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:51"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="txt" href="#E4:51"><span class="lab"><font color="Green" title="E20">A2</font></span></a>, <a class="txt" href="#E8:51"><span class="lab"><font color="Green" title="E23">A5</font></span></a>, <a class="ref" href="finseq_4.html#T27" title="FINSEQ_4:th.27">FINSEQ_4:27</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">x</font> <a href="scmpds_1.html#K15" title="SCMPDS_1:func.15">P32const</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">k1</font> &amp; <font color="Maroon" title="c2">x</font> <a href="scmpds_1.html#K16" title="SCMPDS_1:func.16">P33const</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">k2</font> )</span><br/>

<span class="kw">consider </span><font color="Maroon" title="c7">f</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> <span class="kw"> such that </span><br/><a NAME="E12:51"/><span class="lab"><font color="Green" title="E24">A6</font></span>: 
<font color="Maroon" title="c7">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> 
 <span class="kw">and </span><br/><a NAME="E13:51"/><span class="lab"><font color="Green" title="E25">A7</font></span>: 
<font color="Maroon" title="c2">x</font> <a href="scmpds_1.html#K15" title="SCMPDS_1:func.15">P32const</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:51"><span class="lab"><font color="Green" title="E21">A3</font></span></a>, <a class="ref" href="scmpds_1.html#D15" target="_self" title="SCMPDS_1:def.15">Def15</a></span>;<br/>
<a NAME="E14:51"/>
<font color="Maroon" title="c7">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Maroon" title="c3">d1</font>,<font color="Maroon" title="c4">k1</font>,<font color="Maroon" title="c5">k2</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:51"><span class="lab"><font color="Green" title="E21">A3</font></span></a>, <a class="txt" href="#E12:51"><span class="lab"><font color="Green" title="E24">A6</font></span></a>, <a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></span>;<br/>
<span class="kw">hence </span><a NAME="E15:51"/>
<font color="Maroon" title="c2">x</font> <a href="scmpds_1.html#K15" title="SCMPDS_1:func.15">P32const</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">k1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:51"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="txt" href="#E4:51"><span class="lab"><font color="Green" title="E20">A2</font></span></a>, <a class="txt" href="#E13:51"><span class="lab"><font color="Green" title="E25">A7</font></span></a>, <a class="ref" href="finseq_4.html#T27" title="FINSEQ_4:th.27">FINSEQ_4:27</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">x</font> <a href="scmpds_1.html#K16" title="SCMPDS_1:func.16">P33const</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">k2</font></span><br/>

<span class="kw">consider </span><font color="Maroon" title="c8">f</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> <span class="kw"> such that </span><br/><a NAME="E17:51"/><span class="lab"><font color="Green" title="E26">A8</font></span>: 
<font color="Maroon" title="c8">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> 
 <span class="kw">and </span><br/><a NAME="E18:51"/><span class="lab"><font color="Green" title="E27">A9</font></span>: 
<font color="Maroon" title="c2">x</font> <a href="scmpds_1.html#K16" title="SCMPDS_1:func.16">P33const</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 3
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:51"><span class="lab"><font color="Green" title="E21">A3</font></span></a>, <a class="ref" href="scmpds_1.html#D16" target="_self" title="SCMPDS_1:def.16">Def16</a></span>;<br/>
<a NAME="E19:51"/>
<font color="Maroon" title="c8">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Maroon" title="c3">d1</font>,<font color="Maroon" title="c4">k1</font>,<font color="Maroon" title="c5">k2</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:51"><span class="lab"><font color="Green" title="E21">A3</font></span></a>, <a class="txt" href="#E17:51"><span class="lab"><font color="Green" title="E26">A8</font></span></a>, <a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></span>;<br/>
<span class="kw">hence </span><a NAME="E20:51"/>
<font color="Maroon" title="c2">x</font> <a href="scmpds_1.html#K16" title="SCMPDS_1:func.16">P33const</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">k2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:51"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="txt" href="#E4:51"><span class="lab"><font color="Green" title="E20">A2</font></span></a>, <a class="txt" href="#E18:51"><span class="lab"><font color="Green" title="E27">A9</font></span></a>, <a class="ref" href="finseq_4.html#T27" title="FINSEQ_4:th.27">FINSEQ_4:27</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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