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<span class="kw">consider </span><font color="Maroon" title="c1">X</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <span class="kw"> such that </span><br/><a NAME="E2:20_1_1"/><span class="lab"><font color="Green" title="E12">A1</font></span>: 
 <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">proj2</a> <a href="scm_inst.html#K3" title="SCM_INST:func.3">SCM-Instr</a> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">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" onmouseover="rs('finseq_1/T85')" onmouseout="rh()">FINSEQ_1:85</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c1">X</font>
; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="compos_0.html#D1" onmouseover="rs('compos_0/D1')" onmouseout="rh()">COMPOS_0:def 1</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="scm_inst.html#K3" title="SCM_INST:func.3">SCM-Instr</a>  <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#NK1" title="NUMBERS:NK.1">NAT</a>,<span class="p2">(<span class="default"><a href="numbers.html#NK1" title="NUMBERS:NK.1">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="c1">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="E3:20_1_1"/><span class="lab"><font color="Green" title="E13">A2</font></span>: 
 <a href="scm_inst.html#K3" title="SCM_INST:func.3">SCM-Instr</a>  <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#NK1" title="NUMBERS:NK.1">NAT</a>,<span class="p2">(<span class="default"><a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a></span>)</span>,<span class="p2">(<span class="default"><a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">proj2</a> <a href="scm_inst.html#K3" title="SCM_INST:func.3">SCM-Instr</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="scm_inst.html#T8" target="_self" onmouseover="rs('scm_inst/T8')" onmouseout="rh()">Th8</a></span>;<br/>
<a NAME="E4:20_1_1"/>
<span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>,<span class="p2">(<span class="default"><a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a></span>)</span>,<span class="p2">(<span class="default"><a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">proj2</a> <a href="scm_inst.html#K3" title="SCM_INST:func.3">SCM-Instr</a></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#NK1" title="NUMBERS:NK.1">NAT</a>,<span class="p2">(<span class="default"><a href="numbers.html#NK1" title="NUMBERS:NK.1">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="c1">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="#E2:20_1_1"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="ref" href="mcart_1.html#T73" onmouseover="rs('mcart_1/T73')" onmouseout="rh()">MCART_1:73</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:20_1_1"/>
 <a href="scm_inst.html#K3" title="SCM_INST:func.3">SCM-Instr</a>  <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#NK1" title="NUMBERS:NK.1">NAT</a>,<span class="p2">(<span class="default"><a href="numbers.html#NK1" title="NUMBERS:NK.1">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="c1">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="#E3:20_1_1"><span class="lab"><font color="Green" title="E13">A2</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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