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<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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#M2" title="SUBSET_1:mode.2">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> 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="b4">r</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">S</font>  st <font color="Olive" title="b2">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="scmring1.html#K12" title="SCMRING1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b3">mk</font>,<font color="Olive" title="b4">r</font></span><a href="scmring1.html#K12" title="SCMRING1:func.12">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> holds <br/>( <font color="Olive" title="b2">x</font> <a href="scmring1.html#K13" title="SCMRING1:func.13">const_address</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#K14" title="SCMRING1:func.14">const_value</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">r</font> )</span><br/><b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">x</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">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> 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">r</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">S</font>  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="scmring1.html#K12" title="SCMRING1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b2">mk</font>,<font color="Olive" title="b3">r</font></span><a href="scmring1.html#K12" title="SCMRING1:func.12">*&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="scmring1.html#K13" title="SCMRING1:func.13">const_address</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#K14" title="SCMRING1:func.14">const_value</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">r</font> )</span><br/><b>let </b><font color="Maroon" title="c3">x</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">mk</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">r</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">S</font>  st <font color="Maroon" title="c3">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="scmring1.html#K12" title="SCMRING1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">mk</font>,<font color="Olive" title="b2">r</font></span><a href="scmring1.html#K12" title="SCMRING1:func.12">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> holds <br/>( <font color="Maroon" title="c3">x</font> <a href="scmring1.html#K13" title="SCMRING1:func.13">const_address</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#K14" title="SCMRING1:func.14">const_value</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">r</font> )</span><br/><b>let </b><font color="Maroon" title="c4">mk</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">r</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">S</font>  st <font color="Maroon" title="c3">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="scmring1.html#K12" title="SCMRING1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c4">mk</font>,<font color="Olive" title="b1">r</font></span><a href="scmring1.html#K12" title="SCMRING1:func.12">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> holds <br/>( <font color="Maroon" title="c3">x</font> <a href="scmring1.html#K13" title="SCMRING1:func.13">const_address</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#K14" title="SCMRING1:func.14">const_value</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">r</font> )</span><br/><b>let </b><font color="Maroon" title="c5">r</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c1">I</font>,<span class="p2"><a href="scmring1.html#K12" title="SCMRING1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c4">mk</font>,<font color="Maroon" title="c5">r</font></span><a href="scmring1.html#K12" title="SCMRING1:func.12">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> implies ( <font color="Maroon" title="c3">x</font> <a href="scmring1.html#K13" title="SCMRING1:func.13">const_address</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#K14" title="SCMRING1:func.14">const_value</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">r</font> ) )</span><br/>









<b>assume </b><a NAME="E1:39"/><i><font color="Green" title="E17">A1</font></i>: 
<font color="Maroon" title="c3">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="scmring1.html#K12" title="SCMRING1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c4">mk</font>,<font color="Maroon" title="c5">r</font></span><a href="scmring1.html#K12" title="SCMRING1:func.12">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">x</font> <a href="scmring1.html#K13" title="SCMRING1:func.13">const_address</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#K14" title="SCMRING1:func.14">const_value</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">r</font> )</span><br/>

<b>then consider </b><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> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S</font><b> such that </b><br/><a NAME="E3:39"/><i><font color="Green" title="E18">A2</font></i>: 
( <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="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  &amp; <font color="Maroon" title="c3">x</font> <a href="scmring1.html#K13" title="SCMRING1:func.13">const_address</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 )
 <b>by </b><i><a class="ref" href="scmring1.html#D12" target="_self" title="SCMRING1:def.12">Def12</a></i>;<br/>
<a NAME="E4:39"/><i><font color="Green" title="E19">A3</font></i>: 
<font color="Maroon" title="c6">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="scmring1.html#K12" title="SCMRING1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c4">mk</font>,<font color="Maroon" title="c5">r</font></span><a href="scmring1.html#K12" title="SCMRING1:func.12">*&gt;</a></span>
 
<b>by </b><i><a class="txt" href="scmring1.html#E1:39"><i><font color="Green" title="E17">A1</font></i></a>, <a class="txt" href="scmring1.html#E3:39"><i><font color="Green" title="E18">A2</font></i></a>, <a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>;<br/>
<a NAME="E5:39"/><i><font color="Green" title="E20">A4</font></i>: 
( <font color="Maroon" title="c4">mk</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> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S</font> &amp; <font color="Maroon" title="c5">r</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> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S</font> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<b>hence </b><a NAME="E6:39"/>
<font color="Maroon" title="c3">x</font> <a href="scmring1.html#K13" title="SCMRING1:func.13">const_address</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">mk</font>
 <b>by </b><i><a class="txt" href="scmring1.html#E3:39"><i><font color="Green" title="E18">A2</font></i></a>, <a class="txt" href="scmring1.html#E4:39"><i><font color="Green" title="E19">A3</font></i></a>, <a class="ref" href="finseq_4.html#T26" title="FINSEQ_4:th.26">FINSEQ_4:26</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">x</font> <a href="scmring1.html#K14" title="SCMRING1:func.14">const_value</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">r</font></span><br/>

<b>consider </b><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> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S</font><b> such that </b><br/><a NAME="E8:39"/><i><font color="Green" title="E21">A5</font></i>: 
( <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="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  &amp; <font color="Maroon" title="c3">x</font> <a href="scmring1.html#K14" title="SCMRING1:func.14">const_value</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 )
 <b>by </b><i><a class="txt" href="scmring1.html#E1:39"><i><font color="Green" title="E17">A1</font></i></a>, <a class="ref" href="scmring1.html#D13" target="_self" title="SCMRING1:def.13">Def13</a></i>;<br/>
<a NAME="E9:39"/>
<font color="Maroon" title="c7">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="scmring1.html#K12" title="SCMRING1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c4">mk</font>,<font color="Maroon" title="c5">r</font></span><a href="scmring1.html#K12" title="SCMRING1:func.12">*&gt;</a></span>
 
<b>by </b><i><a class="txt" href="scmring1.html#E1:39"><i><font color="Green" title="E17">A1</font></i></a>, <a class="txt" href="scmring1.html#E8:39"><i><font color="Green" title="E21">A5</font></i></a>, <a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>;<br/>
<b>hence </b><a NAME="E10:39"/>
<font color="Maroon" title="c3">x</font> <a href="scmring1.html#K14" title="SCMRING1:func.14">const_value</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">r</font>
 <b>by </b><i><a class="txt" href="scmring1.html#E5:39"><i><font color="Green" title="E20">A4</font></i></a>, <a class="txt" href="scmring1.html#E8:39"><i><font color="Green" title="E21">A5</font></i></a>, <a class="ref" href="finseq_4.html#T26" title="FINSEQ_4:th.26">FINSEQ_4:26</a></i>; <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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