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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="Red">::  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> 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/><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="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="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/><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="Red">::  thesis: </font></span></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/><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  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="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/>









<a NAME="E1:35"/><span class="lab"><font color="Green" title="E17">A1</font></span>: 
( <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> )
 
<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="E2:35"/><span class="lab"><font color="Green" title="E18">A2</font></span>: 
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/>

<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> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S</font><span class="kw"> such that </span><br/><a NAME="E4:35"/><span class="lab"><font color="Green" title="E19">A3</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="mcart_1.html#K2" title="MCART_1:func.2">`2</a> 
 <span class="kw">and </span><br/><a NAME="E5:35"/><span class="lab"><font color="Green" title="E20">A4</font></span>: 
<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
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmring1.html#D12" target="_self" title="SCMRING1:def.12">Def12</a></span>;<br/>
<a NAME="E6:35"/>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:35"><span class="lab"><font color="Green" title="E18">A2</font></span></a>, <a class="txt" href="#E4:35"><span class="lab"><font color="Green" title="E19">A3</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="E7:35"/>
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:35"><span class="lab"><font color="Green" title="E20">A4</font></span></a>, <a class="txt" href="#E1:35"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="ref" href="finseq_4.html#T26" title="FINSEQ_4:th.26">FINSEQ_4:26</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="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/>

<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> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S</font><span class="kw"> such that </span><br/><a NAME="E9:35"/><span class="lab"><font color="Green" title="E21">A5</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="mcart_1.html#K2" title="MCART_1:func.2">`2</a> 
 <span class="kw">and </span><br/><a NAME="E10:35"/><span class="lab"><font color="Green" title="E22">A6</font></span>: 
<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
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:35"><span class="lab"><font color="Green" title="E18">A2</font></span></a>, <a class="ref" href="scmring1.html#D13" target="_self" title="SCMRING1:def.13">Def13</a></span>;<br/>
<a NAME="E11:35"/>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:35"><span class="lab"><font color="Green" title="E18">A2</font></span></a>, <a class="txt" href="#E9:35"><span class="lab"><font color="Green" title="E21">A5</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="E12:35"/>
<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 class="kw">by</span> <span class="lab"><a class="txt" href="#E1:35"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="txt" href="#E10:35"><span class="lab"><font color="Green" title="E22">A6</font></span></a>, <a class="ref" href="finseq_4.html#T26" title="FINSEQ_4:th.26">FINSEQ_4:26</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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