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<span class="kw">let </span><font color="Maroon" title="c1">D</font> be   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> ; <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">f</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c1">D</font>  st <font color="Olive" title="b1">f</font> is  <a href="jordan23.html#V3" title="JORDAN23:attr.3">poorly-one-to-one</a>  &amp; <font color="Olive" title="b1">f</font> is  <a href="finseq_6.html#V1" title="FINSEQ_6:attr.1">circular</a>  holds <br/> for <font color="Olive" title="b2">p</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">D</font> holds   <a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> (<font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">p</font>) is  <a href="jordan23.html#V3" title="JORDAN23:attr.3">poorly-one-to-one</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">f</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c1">D</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"> ( <font color="Maroon" title="c2">f</font> is  <a href="jordan23.html#V3" title="JORDAN23:attr.3">poorly-one-to-one</a>  &amp; <font color="Maroon" title="c2">f</font> is  <a href="finseq_6.html#V1" title="FINSEQ_6:attr.1">circular</a>  implies  for <font color="Olive" title="b1">p</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">D</font> holds   <a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> (<font color="Maroon" title="c2">f</font>,<font color="Olive" title="b1">p</font>) is  <a href="jordan23.html#V3" title="JORDAN23:attr.3">poorly-one-to-one</a>  )</span><br/>



<span class="kw">assume </span><a NAME="E1:27"/><span class="lab"><font color="Green" title="E12">A1</font></span>: 
( <font color="Maroon" title="c2">f</font> is  <a href="jordan23.html#V3" title="JORDAN23:attr.3">poorly-one-to-one</a>  &amp; <font color="Maroon" title="c2">f</font> is  <a href="finseq_6.html#V1" title="FINSEQ_6:attr.1">circular</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">  for <font color="Olive" title="b1">p</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">D</font> holds   <a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> (<font color="Maroon" title="c2">f</font>,<font color="Olive" title="b1">p</font>) is  <a href="jordan23.html#V3" title="JORDAN23:attr.3">poorly-one-to-one</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c3">p</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">D</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_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> (<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font>) is  <a href="jordan23.html#V3" title="JORDAN23:attr.3">poorly-one-to-one</a> </span><br/>

<a NAME="E2:27"/><span class="lab"><font color="Green" title="E13">A2</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> (<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">f</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_6.html#T179" onmouseover="rs('finseq_6/T179')" onmouseout="rh()">FINSEQ_6:179</a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="27_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="E1:27_1"/>
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">f</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 2 or  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="27_1_1"><span class="kw">suppose </span></a><a NAME="E1:27_1_1"/><span class="lab"><font color="Green" title="E14">A3</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">f</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</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">  <a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> (<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font>) is  <a href="jordan23.html#V3" title="JORDAN23:attr.3">poorly-one-to-one</a> </span><br/><div class="add"><a NAME="E2:27_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">f</font> is  <a href="jordan23.html#V2" title="JORDAN23:attr.2">weakly-one-to-one</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:27"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="ref" href="jordan23.html#T7" target="_self" onmouseover="rs('jordan23/T7')" onmouseout="rh()">Th7</a></span>;<br/><a NAME="E3:27_1_1"/><span class="kw">then </span>
 <a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> (<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font>) is  <a href="jordan23.html#V2" title="JORDAN23:attr.2">weakly-one-to-one</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:27"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="ref" href="jordan23.html#T12" target="_self" onmouseover="rs('jordan23/T12')" onmouseout="rh()">Th12</a></span>;<br/><span class="kw">hence </span><a NAME="E4:27_1_1"/>
 <a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> (<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font>) is  <a href="jordan23.html#V3" title="JORDAN23:attr.3">poorly-one-to-one</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:27"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="txt" href="#E1:27_1_1"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="ref" href="jordan23.html#T7" target="_self" onmouseover="rs('jordan23/T7')" onmouseout="rh()">Th7</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="27_1_2"><span class="kw">suppose </span></a><a NAME="E1:27_1_2"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">  <a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> (<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font>) is  <a href="jordan23.html#V3" title="JORDAN23:attr.3">poorly-one-to-one</a> </span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:27_1_2"/>
 <a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> (<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">p</font>) is  <a href="jordan23.html#V3" title="JORDAN23:attr.3">poorly-one-to-one</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:27"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="ref" href="jordan23.html#D3" target="_self" onmouseover="rs('jordan23/D3')" onmouseout="rh()">Def3</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><span class="kw">end;</span></div>

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