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<span class="kw">let </span><font color="Maroon" title="c1">X</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">D</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">F</font> being   <a href="seqfunc.html#NM1" title="SEQFUNC:NM.1">Functional_Sequence</a> of <font color="Maroon" title="c1">X</font>,<a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a><br/>  for <font color="Olive" title="b3">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds <br/> ( <span class="p1">(<span class="default"><a href="mesfun7c.html#K11" title="MESFUN7C:func.11">Re</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">F</font> <a href="mesfun9c.html#K1" title="MESFUN9C:func.1">||</a> <font color="Olive" title="b1">D</font></span>)</span></span>)</span> <a href="mesfunc5.html#K4" title="MESFUNC5:func.4">.</a> <font color="Olive" title="b3">n</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mesfun7c.html#K11" title="MESFUN7C:func.11">Re</a> <font color="Olive" title="b2">F</font></span>)</span> <a href="mesfunc5.html#K4" title="MESFUNC5:func.4">.</a> <font color="Olive" title="b3">n</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Olive" title="b1">D</font> &amp; <span class="p1">(<span class="default"><a href="mesfun7c.html#K12" title="MESFUN7C:func.12">Im</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">F</font> <a href="mesfun9c.html#K1" title="MESFUN9C:func.1">||</a> <font color="Olive" title="b1">D</font></span>)</span></span>)</span> <a href="mesfunc5.html#K4" title="MESFUNC5:func.4">.</a> <font color="Olive" title="b3">n</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mesfun7c.html#K12" title="MESFUN7C:func.12">Im</a> <font color="Olive" title="b2">F</font></span>)</span> <a href="mesfunc5.html#K4" title="MESFUNC5:func.4">.</a> <font color="Olive" title="b3">n</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Olive" title="b1">D</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">D</font> be    <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="seqfunc.html#NM1" title="SEQFUNC:NM.1">Functional_Sequence</a> of <font color="Maroon" title="c1">X</font>,<a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a><br/>  for <font color="Olive" title="b2">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds <br/> ( <span class="p1">(<span class="default"><a href="mesfun7c.html#K11" title="MESFUN7C:func.11">Re</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">F</font> <a href="mesfun9c.html#K1" title="MESFUN9C:func.1">||</a> <font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="mesfunc5.html#K4" title="MESFUNC5:func.4">.</a> <font color="Olive" title="b2">n</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mesfun7c.html#K11" title="MESFUN7C:func.11">Re</a> <font color="Olive" title="b1">F</font></span>)</span> <a href="mesfunc5.html#K4" title="MESFUNC5:func.4">.</a> <font color="Olive" title="b2">n</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c2">D</font> &amp; <span class="p1">(<span class="default"><a href="mesfun7c.html#K12" title="MESFUN7C:func.12">Im</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">F</font> <a href="mesfun9c.html#K1" title="MESFUN9C:func.1">||</a> <font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="mesfunc5.html#K4" title="MESFUNC5:func.4">.</a> <font color="Olive" title="b2">n</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mesfun7c.html#K12" title="MESFUN7C:func.12">Im</a> <font color="Olive" title="b1">F</font></span>)</span> <a href="mesfunc5.html#K4" title="MESFUNC5:func.4">.</a> <font color="Olive" title="b2">n</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c2">D</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">F</font> be   <a href="seqfunc.html#NM1" title="SEQFUNC:NM.1">Functional_Sequence</a> of <font color="Maroon" title="c1">X</font>,<a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</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">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds <br/> ( <span class="p1">(<span class="default"><a href="mesfun7c.html#K11" title="MESFUN7C:func.11">Re</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="mesfun9c.html#K1" title="MESFUN9C:func.1">||</a> <font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="mesfunc5.html#K4" title="MESFUNC5:func.4">.</a> <font color="Olive" title="b1">n</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mesfun7c.html#K11" title="MESFUN7C:func.11">Re</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="mesfunc5.html#K4" title="MESFUNC5:func.4">.</a> <font color="Olive" title="b1">n</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c2">D</font> &amp; <span class="p1">(<span class="default"><a href="mesfun7c.html#K12" title="MESFUN7C:func.12">Im</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="mesfun9c.html#K1" title="MESFUN9C:func.1">||</a> <font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="mesfunc5.html#K4" title="MESFUNC5:func.4">.</a> <font color="Olive" title="b1">n</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mesfun7c.html#K12" title="MESFUN7C:func.12">Im</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="mesfunc5.html#K4" title="MESFUNC5:func.4">.</a> <font color="Olive" title="b1">n</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c2">D</font> )</span><br/>





<span class="kw">set </span><font color="Maroon" title="c4">G</font> = <font color="Maroon" title="c3">F</font> <a href="mesfun9c.html#K1" title="MESFUN9C:func.1">||</a> <font color="Maroon" title="c2">D</font>;<br/>
<span class="kw">let </span><font color="Maroon" title="c5">n</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</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"> ( <span class="p1">(<span class="default"><a href="mesfun7c.html#K11" title="MESFUN7C:func.11">Re</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="mesfun9c.html#K1" title="MESFUN9C:func.1">||</a> <font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="mesfunc5.html#K4" title="MESFUNC5:func.4">.</a> <font color="Maroon" title="c5">n</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mesfun7c.html#K11" title="MESFUN7C:func.11">Re</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="mesfunc5.html#K4" title="MESFUNC5:func.4">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c2">D</font> &amp; <span class="p1">(<span class="default"><a href="mesfun7c.html#K12" title="MESFUN7C:func.12">Im</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="mesfun9c.html#K1" title="MESFUN9C:func.1">||</a> <font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="mesfunc5.html#K4" title="MESFUNC5:func.4">.</a> <font color="Maroon" title="c5">n</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mesfun7c.html#K12" title="MESFUN7C:func.12">Im</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="mesfunc5.html#K4" title="MESFUNC5:func.4">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c2">D</font> )</span><br/>

<a NAME="E1:23"/>
 <a href="comseq_3.html#K5" title="COMSEQ_3:func.5">Re</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="mesfunc5.html#K4" title="MESFUNC5:func.4">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c2">D</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><a href="comseq_3.html#K5" title="COMSEQ_3:func.5">Re</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="mesfunc5.html#K4" title="MESFUNC5:func.4">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c2">D</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mesfun9c.html#T20" target="_self" onmouseover="rs('mesfun9c/T20')" onmouseout="rh()">Th20</a></span>;<br/>
<a NAME="E2:23"/><span class="kw">then </span><span class="lab"><font color="Green" title="E24">A1</font></span>: 
 <a href="comseq_3.html#K5" title="COMSEQ_3:func.5">Re</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="mesfunc5.html#K4" title="MESFUNC5:func.4">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c2">D</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mesfun7c.html#K11" title="MESFUN7C:func.11">Re</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="mesfunc5.html#K4" title="MESFUNC5:func.4">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c2">D</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mesfun7c.html#T24" onmouseover="rs('mesfun7c/T24')" onmouseout="rh()">MESFUN7C:24</a></span>;<br/>
<a NAME="E3:23"/>
 <a href="comseq_3.html#K6" title="COMSEQ_3:func.6">Im</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="mesfunc5.html#K4" title="MESFUNC5:func.4">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c2">D</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><a href="comseq_3.html#K6" title="COMSEQ_3:func.6">Im</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="mesfunc5.html#K4" title="MESFUNC5:func.4">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c2">D</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mesfun9c.html#T20" target="_self" onmouseover="rs('mesfun9c/T20')" onmouseout="rh()">Th20</a></span>;<br/>
<a NAME="E4:23"/><span class="kw">then </span><span class="lab"><font color="Green" title="E25">A2</font></span>: 
 <a href="comseq_3.html#K6" title="COMSEQ_3:func.6">Im</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="mesfunc5.html#K4" title="MESFUNC5:func.4">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c2">D</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mesfun7c.html#K12" title="MESFUN7C:func.12">Im</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="mesfunc5.html#K4" title="MESFUNC5:func.4">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c2">D</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mesfun7c.html#T24" onmouseover="rs('mesfun7c/T24')" onmouseout="rh()">MESFUN7C:24</a></span>;<br/>
<a NAME="E5:23"/>
(  <a href="comseq_3.html#K5" title="COMSEQ_3:func.5">Re</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="mesfun9c.html#K1" title="MESFUN9C:func.1">||</a> <font color="Maroon" title="c2">D</font></span>)</span> <a href="mesfunc5.html#K4" title="MESFUNC5:func.4">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><a href="mesfun7c.html#K11" title="MESFUN7C:func.11">Re</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="mesfun9c.html#K1" title="MESFUN9C:func.1">||</a> <font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="mesfunc5.html#K4" title="MESFUNC5:func.4">.</a> <font color="Maroon" title="c5">n</font> &amp;  <a href="comseq_3.html#K6" title="COMSEQ_3:func.6">Im</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="mesfun9c.html#K1" title="MESFUN9C:func.1">||</a> <font color="Maroon" title="c2">D</font></span>)</span> <a href="mesfunc5.html#K4" title="MESFUNC5:func.4">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><a href="mesfun7c.html#K12" title="MESFUN7C:func.12">Im</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="mesfun9c.html#K1" title="MESFUN9C:func.1">||</a> <font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="mesfunc5.html#K4" title="MESFUNC5:func.4">.</a> <font color="Maroon" title="c5">n</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mesfun7c.html#T24" onmouseover="rs('mesfun7c/T24')" onmouseout="rh()">MESFUN7C:24</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:23"/>
( <span class="p1">(<span class="default"><a href="mesfun7c.html#K11" title="MESFUN7C:func.11">Re</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="mesfun9c.html#K1" title="MESFUN9C:func.1">||</a> <font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="mesfunc5.html#K4" title="MESFUNC5:func.4">.</a> <font color="Maroon" title="c5">n</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mesfun7c.html#K11" title="MESFUN7C:func.11">Re</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="mesfunc5.html#K4" title="MESFUNC5:func.4">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c2">D</font> &amp; <span class="p1">(<span class="default"><a href="mesfun7c.html#K12" title="MESFUN7C:func.12">Im</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="mesfun9c.html#K1" title="MESFUN9C:func.1">||</a> <font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="mesfunc5.html#K4" title="MESFUNC5:func.4">.</a> <font color="Maroon" title="c5">n</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mesfun7c.html#K12" title="MESFUN7C:func.12">Im</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="mesfunc5.html#K4" title="MESFUNC5:func.4">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c2">D</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:23"><span class="lab"><font color="Green" title="E24">A1</font></span></a>, <a class="txt" href="#E4:23"><span class="lab"><font color="Green" title="E25">A2</font></span></a>, <a class="ref" href="mesfun9c.html#D1" target="_self" onmouseover="rs('mesfun9c/D1')" onmouseout="rh()">Def1</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>
