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<span class="kw">let </span><font color="Maroon" title="c1">i</font>, <font color="Maroon" title="c2">j</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="scmfsa_i.html#K2" title="SCMFSA_I:func.2">SCM+FSA-Instr</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="compos_0.html#D5" onmouseover="rs('compos_0/D5')" onmouseout="rh()">COMPOS_0:def 5</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"> (  not  <a href="compos_0.html#K5" title="COMPOS_0:func.5">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_0.html#K5" title="COMPOS_0:func.5">InsCode</a> <font color="Maroon" title="c2">j</font> or  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c1">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c2">j</font></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E1:18_1_1"/><span class="lab"><font color="Green" title="E11">A1</font></span>: 
 <a href="compos_0.html#K5" title="COMPOS_0:func.5">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_0.html#K5" title="COMPOS_0:func.5">InsCode</a> <font color="Maroon" title="c2">j</font>
 ; <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="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c1">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c2">j</font></span>)</span></span><br/>

<a NAME="E2:18_1_1"/>
 <a href="compos_0.html#K5" title="COMPOS_0:func.5">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 12
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="scmfsa_i.html#E17"><span class="lab"><font color="Green" title="E8">Lm2</font></span></a></span>;<br/>
<a NAME="E3:18_1_1"/><span class="kw">then </span>
 not  not  <a href="compos_0.html#K5" title="COMPOS_0:func.5">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp;  ...  &amp;  not  <a href="compos_0.html#K5" title="COMPOS_0:func.5">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 12
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T60" onmouseover="rs('nat_1/T60')" onmouseout="rh()">NAT_1:60</a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="18_1_1_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:18_1_1_1"/><span class="kw">then </span>
(  <a href="compos_0.html#K5" title="COMPOS_0:func.5">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  or  <a href="compos_0.html#K5" title="COMPOS_0:func.5">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or  <a href="compos_0.html#K5" title="COMPOS_0:func.5">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 or  <a href="compos_0.html#K5" title="COMPOS_0:func.5">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 or  <a href="compos_0.html#K5" title="COMPOS_0:func.5">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 or  <a href="compos_0.html#K5" title="COMPOS_0:func.5">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5 or  <a href="compos_0.html#K5" title="COMPOS_0:func.5">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6 or  <a href="compos_0.html#K5" title="COMPOS_0:func.5">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7 or  <a href="compos_0.html#K5" title="COMPOS_0:func.5">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8 or  <a href="compos_0.html#K5" title="COMPOS_0:func.5">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 9 or  <a href="compos_0.html#K5" title="COMPOS_0:func.5">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 10 or  <a href="compos_0.html#K5" title="COMPOS_0:func.5">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 11 or  <a href="compos_0.html#K5" title="COMPOS_0:func.5">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 12 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="18_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:18_1_1_1_1"/>
(  <a href="compos_0.html#K5" title="COMPOS_0:func.5">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  or  <a href="compos_0.html#K5" title="COMPOS_0:func.5">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or  <a href="compos_0.html#K5" title="COMPOS_0:func.5">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 or  <a href="compos_0.html#K5" title="COMPOS_0:func.5">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 or  <a href="compos_0.html#K5" title="COMPOS_0:func.5">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 or  <a href="compos_0.html#K5" title="COMPOS_0:func.5">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5 or  <a href="compos_0.html#K5" title="COMPOS_0:func.5">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6 or  <a href="compos_0.html#K5" title="COMPOS_0:func.5">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7 or  <a href="compos_0.html#K5" title="COMPOS_0:func.5">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8 )
 ; <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="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c1">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c2">j</font></span>)</span></span><br/><div class="add"><a NAME="E2:18_1_1_1_1"/><span class="kw">then </span>
( <font color="Maroon" title="c1">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="scm_inst.html#K3" title="SCM_INST:func.3">SCM-Instr</a>  &amp; <font color="Maroon" title="c2">j</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="scm_inst.html#K3" title="SCM_INST:func.3">SCM-Instr</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:18_1_1"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="ref" href="scmfsa_i.html#T7" target="_self" onmouseover="rs('scmfsa_i/T7')" onmouseout="rh()">Th7</a></span>;<br/><span class="kw">hence </span><a NAME="E3:18_1_1_1_1"/>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c1">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c2">j</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:18_1_1"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="ref" href="compos_0.html#D5" onmouseover="rs('compos_0/D5')" onmouseout="rh()">COMPOS_0:def 5</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="18_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:18_1_1_1_2"/>
(  <a href="compos_0.html#K5" title="COMPOS_0:func.5">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 9 or  <a href="compos_0.html#K5" title="COMPOS_0:func.5">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 10 )
 ; <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="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c1">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c2">j</font></span>)</span></span><br/><div class="add"><a NAME="E2:18_1_1_1_2"/><span class="kw">then </span>
(  <a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c2">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:18_1_1"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="txt" href="scmfsa_i.html#E18"><span class="lab"><font color="Green" title="E9">Lm3</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E3:18_1_1_1_2"/>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c1">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c2">j</font></span>)</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="18_1_1_1_3"><span class="kw">suppose </span></a><a NAME="E1:18_1_1_1_3"/>
(  <a href="compos_0.html#K5" title="COMPOS_0:func.5">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 11 or  <a href="compos_0.html#K5" title="COMPOS_0:func.5">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 12 )
 ; <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="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c1">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c2">j</font></span>)</span></span><br/><div class="add"><a NAME="E2:18_1_1_1_3"/><span class="kw">then </span>
(  <a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c2">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:18_1_1"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="txt" href="scmfsa_i.html#E19"><span class="lab"><font color="Green" title="E10">Lm4</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E3:18_1_1_1_3"/>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c1">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c2">j</font></span>)</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/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

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