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<span class="kw">let </span><font color="Maroon" title="c1">I</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="card_1.html#K7" title="CARD_1:func.7">Segm</a> 8; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">S</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="struct_0.html#L1" title="STRUCT_0:struct.1">1-sorted</a> <br/>  for <font color="Olive" title="b2">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="scmring1.html#K1" title="SCMRING1:func.1">SCM-Instr</a> <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b3">mk</font>, <font color="Olive" title="b4">ml</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>   st <font color="Olive" title="b2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c1">I</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<span class="p2"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Olive" title="b3">mk</font>,<font color="Olive" title="b4">ml</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> holds <br/>( <font color="Olive" title="b2">x</font> <a href="scmring1.html#K7" title="SCMRING1:func.7">address_1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">mk</font> &amp; <font color="Olive" title="b2">x</font> <a href="scmring1.html#K8" title="SCMRING1:func.8">address_2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">ml</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">S</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="struct_0.html#L1" title="STRUCT_0:struct.1">1-sorted</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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="scmring1.html#K1" title="SCMRING1:func.1">SCM-Instr</a> <font color="Maroon" title="c2">S</font><br/>  for <font color="Olive" title="b2">mk</font>, <font color="Olive" title="b3">ml</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>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c1">I</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<span class="p2"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Olive" title="b2">mk</font>,<font color="Olive" title="b3">ml</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> holds <br/>( <font color="Olive" title="b1">x</font> <a href="scmring1.html#K7" title="SCMRING1:func.7">address_1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">mk</font> &amp; <font color="Olive" title="b1">x</font> <a href="scmring1.html#K8" title="SCMRING1:func.8">address_2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">ml</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">x</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="scmring1.html#K1" title="SCMRING1:func.1">SCM-Instr</a> <font color="Maroon" title="c2">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">mk</font>, <font color="Olive" title="b2">ml</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>   st <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c1">I</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<span class="p2"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Olive" title="b1">mk</font>,<font color="Olive" title="b2">ml</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> holds <br/>( <font color="Maroon" title="c3">x</font> <a href="scmring1.html#K7" title="SCMRING1:func.7">address_1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">mk</font> &amp; <font color="Maroon" title="c3">x</font> <a href="scmring1.html#K8" title="SCMRING1:func.8">address_2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">ml</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">mk</font>, <font color="Maroon" title="c5">ml</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="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c1">I</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<span class="p2"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c4">mk</font>,<font color="Maroon" title="c5">ml</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> implies ( <font color="Maroon" title="c3">x</font> <a href="scmring1.html#K7" title="SCMRING1:func.7">address_1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">mk</font> &amp; <font color="Maroon" title="c3">x</font> <a href="scmring1.html#K8" title="SCMRING1:func.8">address_2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">ml</font> ) )</span><br/>







<span class="kw">assume </span><a NAME="E1:25"/><span class="lab"><font color="Green" title="E11">A1</font></span>: 
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c1">I</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<span class="p2"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c4">mk</font>,<font color="Maroon" title="c5">ml</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">x</font> <a href="scmring1.html#K7" title="SCMRING1:func.7">address_1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">mk</font> &amp; <font color="Maroon" title="c3">x</font> <a href="scmring1.html#K8" title="SCMRING1:func.8">address_2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">ml</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> <span class="kw"> such that </span><br/><a NAME="E3:25"/><span class="lab"><font color="Green" title="E12">A2</font></span>: 
<font color="Maroon" title="c6">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x</font> <a href="recdef_2.html#K3" title="RECDEF_2:func.3">`3_3</a> 
 <span class="kw">and </span><br/><a NAME="E4:25"/><span class="lab"><font color="Green" title="E13">A3</font></span>: 
<font color="Maroon" title="c3">x</font> <a href="scmring1.html#K7" title="SCMRING1:func.7">address_1</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="scmring1.html#D7" target="_self" title="SCMRING1:def.7">Def7</a></span>;<br/>
<a NAME="E5:25"/>
<font color="Maroon" title="c6">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c4">mk</font>,<font color="Maroon" title="c5">ml</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:25"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="txt" href="#E3:25"><span class="lab"><font color="Green" title="E12">A2</font></span></a>, <a class="ref" href="recdef_2.html#D3" title="RECDEF_2:def.3">RECDEF_2:def 3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:25"/>
<font color="Maroon" title="c3">x</font> <a href="scmring1.html#K7" title="SCMRING1:func.7">address_1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">mk</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:25"><span class="lab"><font color="Green" title="E13">A3</font></span></a>, <a class="ref" href="finseq_4.html#T17" title="FINSEQ_4:th.17">FINSEQ_4:17</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">x</font> <a href="scmring1.html#K8" title="SCMRING1:func.8">address_2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">ml</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> <span class="kw"> such that </span><br/><a NAME="E8:25"/><span class="lab"><font color="Green" title="E14">A4</font></span>: 
<font color="Maroon" title="c7">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x</font> <a href="recdef_2.html#K3" title="RECDEF_2:func.3">`3_3</a> 
 <span class="kw">and </span><br/><a NAME="E9:25"/><span class="lab"><font color="Green" title="E15">A5</font></span>: 
<font color="Maroon" title="c3">x</font> <a href="scmring1.html#K8" title="SCMRING1:func.8">address_2</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="#E1:25"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="ref" href="scmring1.html#D8" target="_self" title="SCMRING1:def.8">Def8</a></span>;<br/>
<a NAME="E10:25"/>
<font color="Maroon" title="c7">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c4">mk</font>,<font color="Maroon" title="c5">ml</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:25"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="txt" href="#E8:25"><span class="lab"><font color="Green" title="E14">A4</font></span></a>, <a class="ref" href="recdef_2.html#D3" title="RECDEF_2:def.3">RECDEF_2:def 3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E11:25"/>
<font color="Maroon" title="c3">x</font> <a href="scmring1.html#K8" title="SCMRING1:func.8">address_2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">ml</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:25"><span class="lab"><font color="Green" title="E15">A5</font></span></a>, <a class="ref" href="finseq_4.html#T17" title="FINSEQ_4:th.17">FINSEQ_4:17</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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