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<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="10_1"><span class="kw">now </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">  for <font color="Olive" title="b1">p</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_1.html#K9" title="MATRIX_1:func.9">Permutations</a> 2 holds <br/><font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2">(<span class="default"><a href="finseq_2.html#K1" title="FINSEQ_2:func.1">idseq</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_5.html#K3" title="FINSEQ_5:func.3">Rev</a> <span class="p3">(<span class="default"><a href="finseq_2.html#K1" title="FINSEQ_2:func.1">idseq</a> 2</span>)</span></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c1">p</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</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"> ( <font color="Maroon" title="c1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_1.html#K9" title="MATRIX_1:func.9">Permutations</a> 2 implies <font color="Maroon" title="c1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2">(<span class="default"><a href="finseq_2.html#K1" title="FINSEQ_2:func.1">idseq</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_5.html#K3" title="FINSEQ_5:func.3">Rev</a> <span class="p3">(<span class="default"><a href="finseq_2.html#K1" title="FINSEQ_2:func.1">idseq</a> 2</span>)</span></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> )</span><br/><span class="kw">assume </span><a NAME="E1:10_1"/>
<font color="Maroon" title="c1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_1.html#K9" title="MATRIX_1:func.9">Permutations</a> 2
 ; <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"> <font color="Maroon" title="c1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2">(<span class="default"><a href="finseq_2.html#K1" title="FINSEQ_2:func.1">idseq</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_5.html#K3" title="FINSEQ_5:func.3">Rev</a> <span class="p3">(<span class="default"><a href="finseq_2.html#K1" title="FINSEQ_2:func.1">idseq</a> 2</span>)</span></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span></span><br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c2">q</font> = <font color="Maroon" title="c1">p</font> as   <a href="funct_2.html#NM2" title="FUNCT_2:NM.2">Permutation</a> of <span class="p1">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 2</span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#D12" onmouseover="rs('matrix_1/D12')" onmouseout="rh()">MATRIX_1:def 12</a></span>;<br/><a NAME="E3:10_1"/><span class="lab"><font color="Green" title="E9">A1</font></span>: 
 <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c2">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 2
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D3" onmouseover="rs('funct_2/D3')" onmouseout="rh()">FUNCT_2:def 3</a></span>;<br/><a NAME="E4:10_1"/><span class="lab"><font color="Green" title="E10">A2</font></span>: 
 <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c2">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 2
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T52" onmouseover="rs('funct_2/T52')" onmouseout="rh()">FUNCT_2:52</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c3">q</font> = <font color="Maroon" title="c2">q</font> as   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D2" onmouseover="rs('finseq_1/D2')" onmouseout="rh()">FINSEQ_1:def 2</a></span>;<br/><a NAME="E6:10_1"/>
( <font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_2.html#K1" title="FINSEQ_2:func.1">idseq</a> 2 or <font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_5.html#K3" title="FINSEQ_5:func.3">Rev</a> <span class="p1">(<span class="default"><a href="finseq_2.html#K1" title="FINSEQ_2:func.1">idseq</a> 2</span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:10_1"><span class="lab"><font color="Green" title="E9">A1</font></span></a>, <a class="txt" href="#E4:10_1"><span class="lab"><font color="Green" title="E10">A2</font></span></a>, <a class="ref" href="matrix_9.html#T3" target="_self" onmouseover="rs('matrix_9/T3')" onmouseout="rh()">Th3</a></span>;<br/><span class="kw">hence </span><a NAME="E7:10_1"/>
<font color="Maroon" title="c1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2">(<span class="default"><a href="finseq_2.html#K1" title="FINSEQ_2:func.1">idseq</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_5.html#K3" title="FINSEQ_5:func.3">Rev</a> <span class="p3">(<span class="default"><a href="finseq_2.html#K1" title="FINSEQ_2:func.1">idseq</a> 2</span>)</span></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D2" onmouseover="rs('tarski/D2')" onmouseout="rh()">TARSKI:def 2</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>
<a NAME="E2:10"/><span class="kw">then </span><span class="lab"><font color="Green" title="E9">A3</font></span>: 
 <a href="matrix_1.html#K9" title="MATRIX_1:func.9">Permutations</a> 2 <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2">(<span class="default"><a href="finseq_2.html#K1" title="FINSEQ_2:func.1">idseq</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_5.html#K3" title="FINSEQ_5:func.3">Rev</a> <span class="p3">(<span class="default"><a href="finseq_2.html#K1" title="FINSEQ_2:func.1">idseq</a> 2</span>)</span></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D3" onmouseover="rs('tarski/D3')" onmouseout="rh()">TARSKI:def 3</a></span>;<br/>
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="10_2"><span class="kw">now </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">  for <font color="Olive" title="b1">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2">(<span class="default"><a href="finseq_2.html#K1" title="FINSEQ_2:func.1">idseq</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_5.html#K3" title="FINSEQ_5:func.3">Rev</a> <span class="p3">(<span class="default"><a href="finseq_2.html#K1" title="FINSEQ_2:func.1">idseq</a> 2</span>)</span></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> holds <br/><font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_1.html#K9" title="MATRIX_1:func.9">Permutations</a> 2</span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c1">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</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"> ( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2">(<span class="default"><a href="finseq_2.html#K1" title="FINSEQ_2:func.1">idseq</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_5.html#K3" title="FINSEQ_5:func.3">Rev</a> <span class="p3">(<span class="default"><a href="finseq_2.html#K1" title="FINSEQ_2:func.1">idseq</a> 2</span>)</span></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> implies <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_1.html#K9" title="MATRIX_1:func.9">Permutations</a> 2 )</span><br/><span class="kw">assume </span><a NAME="E1:10_2"/>
<font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2">(<span class="default"><a href="finseq_2.html#K1" title="FINSEQ_2:func.1">idseq</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_5.html#K3" title="FINSEQ_5:func.3">Rev</a> <span class="p3">(<span class="default"><a href="finseq_2.html#K1" title="FINSEQ_2:func.1">idseq</a> 2</span>)</span></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</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"> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_1.html#K9" title="MATRIX_1:func.9">Permutations</a> 2</span><br/><a NAME="E2:10_2"/><span class="kw">then </span>
( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_2.html#K1" title="FINSEQ_2:func.1">idseq</a> 2 or <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_5.html#K3" title="FINSEQ_5:func.3">Rev</a> <span class="p1">(<span class="default"><a href="finseq_2.html#K1" title="FINSEQ_2:func.1">idseq</a> 2</span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D2" onmouseover="rs('tarski/D2')" onmouseout="rh()">TARSKI:def 2</a></span>;<br/><span class="kw">hence </span><a NAME="E3:10_2"/>
<font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_1.html#K9" title="MATRIX_1:func.9">Permutations</a> 2
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_9.html#T4" target="_self" onmouseover="rs('matrix_9/T4')" onmouseout="rh()">Th4</a>, <a class="ref" href="matrix_1.html#D12" onmouseover="rs('matrix_1/D12')" onmouseout="rh()">MATRIX_1:def 12</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>
<a NAME="E4:10"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2">(<span class="default"><a href="finseq_2.html#K1" title="FINSEQ_2:func.1">idseq</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_5.html#K3" title="FINSEQ_5:func.3">Rev</a> <span class="p3">(<span class="default"><a href="finseq_2.html#K1" title="FINSEQ_2:func.1">idseq</a> 2</span>)</span></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="matrix_1.html#K9" title="MATRIX_1:func.9">Permutations</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D3" onmouseover="rs('tarski/D3')" onmouseout="rh()">TARSKI:def 3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:10"/>
 <a href="matrix_1.html#K9" title="MATRIX_1:func.9">Permutations</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2">(<span class="default"><a href="finseq_2.html#K1" title="FINSEQ_2:func.1">idseq</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_5.html#K3" title="FINSEQ_5:func.3">Rev</a> <span class="p3">(<span class="default"><a href="finseq_2.html#K1" title="FINSEQ_2:func.1">idseq</a> 2</span>)</span></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10"><span class="lab"><font color="Green" title="E9">A3</font></span></a>, <a class="ref" href="xboole_0.html#D10" onmouseover="rs('xboole_0/D10')" onmouseout="rh()">XBOOLE_0:def 10</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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