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<span class="kw">thus </span><a NAME="E1:3_1_1"/>
 not  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmring2.html#D1" target="_self" title="SCMRING2:def.1">Def1</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="struct_0.html#D1" title="STRUCT_0:def.1">STRUCT_0:def 1</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font> is  <a href="compos_1.html#V3" title="COMPOS_1:attr.3">standard-ins</a> </span><br/>

<span class="kw">consider </span><font color="Maroon" title="c2">X</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E3:3_1_1"/><span class="lab"><font color="Green" title="E2">A1</font></span>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <span class="p1">(<span class="default"><a href="scmring1.html#K1" title="SCMRING1:func.1">SCM-Instr</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">X</font> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T85" title="FINSEQ_1:th.85">FINSEQ_1:85</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c2">X</font>
; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="compos_1.html#D4" title="COMPOS_1:def.4">COMPOS_1:def 4</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>,<span class="p2">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a></span>)</span></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span></span><br/>

<a NAME="E4:3_1_1"/><span class="lab"><font color="Green" title="E3">A2</font></span>: 
 <a href="scmring1.html#K1" title="SCMRING1:func.1">SCM-Instr</a> <font color="Maroon" title="c1">R</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>,<span class="p2">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a></span>)</span>,<span class="p2">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <span class="p3">(<span class="default"><a href="scmring1.html#K1" title="SCMRING1:func.1">SCM-Instr</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring1.html#T17" title="SCMRING1:th.17">SCMRING1:17</a></span>;<br/>
<a NAME="E5:3_1_1"/>
<span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>,<span class="p2">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a></span>)</span>,<span class="p2">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <span class="p3">(<span class="default"><a href="scmring1.html#K1" title="SCMRING1:func.1">SCM-Instr</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>,<span class="p2">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a></span>)</span></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:3_1_1"><span class="lab"><font color="Green" title="E2">A1</font></span></a>, <a class="ref" href="mcart_1.html#T73" title="MCART_1:th.73">MCART_1:73</a></span>;<br/>
<a NAME="E6:3_1_1"/><span class="kw">then </span>
 <a href="scmring1.html#K1" title="SCMRING1:func.1">SCM-Instr</a> <font color="Maroon" title="c1">R</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>,<span class="p2">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a></span>)</span></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:3_1_1"><span class="lab"><font color="Green" title="E3">A2</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:3_1_1"/>
 the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>,<span class="p2">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a></span>)</span></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmring2.html#D1" target="_self" title="SCMRING2:def.1">Def1</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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