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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">S</font> being   <a href="prob_1.html#NM3" title="PROB_1:NM.3">SigmaField</a> of <font color="Maroon" title="c1">X</font><br/>  for <font color="Olive" title="b2">E</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b3">m</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b4">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>  st (  for <font color="Olive" title="b5">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds  <font color="Olive" title="b4">F</font> <a href="mesfunc5.html#K4" title="MESFUNC5:func.4">.</a> <font color="Olive" title="b5">n</font> is <font color="Olive" title="b2">E</font> <a href="mesfun6c.html#V1" title="MESFUN6C:attr.1">-measurable</a>  ) holds <br/>( <span class="p1">(<span class="default"><a href="mesfun7c.html#K11" title="MESFUN7C:func.11">Re</a> <font color="Olive" title="b4">F</font></span>)</span> <a href="mesfunc5.html#K4" title="MESFUNC5:func.4">.</a> <font color="Olive" title="b3">m</font> is <font color="Olive" title="b2">E</font> <a href="mesfunc6.html#V1" title="MESFUNC6:attr.1">-measurable</a>  &amp; <span class="p1">(<span class="default"><a href="mesfun7c.html#K12" title="MESFUN7C:func.12">Im</a> <font color="Olive" title="b4">F</font></span>)</span> <a href="mesfunc5.html#K4" title="MESFUNC5:func.4">.</a> <font color="Olive" title="b3">m</font> is <font color="Olive" title="b2">E</font> <a href="mesfunc6.html#V1" title="MESFUNC6:attr.1">-measurable</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">S</font> be   <a href="prob_1.html#NM3" title="PROB_1:NM.3">SigmaField</a> of <font color="Maroon" title="c1">X</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">  for <font color="Olive" title="b1">E</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">S</font><br/>  for <font color="Olive" title="b2">m</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b3">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>  st (  for <font color="Olive" title="b4">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds  <font color="Olive" title="b3">F</font> <a href="mesfunc5.html#K4" title="MESFUNC5:func.4">.</a> <font color="Olive" title="b4">n</font> is <font color="Olive" title="b1">E</font> <a href="mesfun6c.html#V1" title="MESFUN6C:attr.1">-measurable</a>  ) holds <br/>( <span class="p1">(<span class="default"><a href="mesfun7c.html#K11" title="MESFUN7C:func.11">Re</a> <font color="Olive" title="b3">F</font></span>)</span> <a href="mesfunc5.html#K4" title="MESFUNC5:func.4">.</a> <font color="Olive" title="b2">m</font> is <font color="Olive" title="b1">E</font> <a href="mesfunc6.html#V1" title="MESFUNC6:attr.1">-measurable</a>  &amp; <span class="p1">(<span class="default"><a href="mesfun7c.html#K12" title="MESFUN7C:func.12">Im</a> <font color="Olive" title="b3">F</font></span>)</span> <a href="mesfunc5.html#K4" title="MESFUNC5:func.4">.</a> <font color="Olive" title="b2">m</font> is <font color="Olive" title="b1">E</font> <a href="mesfunc6.html#V1" title="MESFUNC6:attr.1">-measurable</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">E</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">S</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">  for <font color="Olive" title="b1">m</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</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>  st (  for <font color="Olive" title="b3">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds  <font color="Olive" title="b2">F</font> <a href="mesfunc5.html#K4" title="MESFUNC5:func.4">.</a> <font color="Olive" title="b3">n</font> is <font color="Maroon" title="c3">E</font> <a href="mesfun6c.html#V1" title="MESFUN6C:attr.1">-measurable</a>  ) holds <br/>( <span class="p1">(<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="b1">m</font> is <font color="Maroon" title="c3">E</font> <a href="mesfunc6.html#V1" title="MESFUNC6:attr.1">-measurable</a>  &amp; <span class="p1">(<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="b1">m</font> is <font color="Maroon" title="c3">E</font> <a href="mesfunc6.html#V1" title="MESFUNC6:attr.1">-measurable</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">m</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">  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>  st (  for <font color="Olive" title="b2">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds  <font color="Olive" title="b1">F</font> <a href="mesfunc5.html#K4" title="MESFUNC5:func.4">.</a> <font color="Olive" title="b2">n</font> is <font color="Maroon" title="c3">E</font> <a href="mesfun6c.html#V1" title="MESFUN6C:attr.1">-measurable</a>  ) holds <br/>( <span class="p1">(<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="Maroon" title="c4">m</font> is <font color="Maroon" title="c3">E</font> <a href="mesfunc6.html#V1" title="MESFUNC6:attr.1">-measurable</a>  &amp; <span class="p1">(<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="Maroon" title="c4">m</font> is <font color="Maroon" title="c3">E</font> <a href="mesfunc6.html#V1" title="MESFUNC6:attr.1">-measurable</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c5">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  <font color="Maroon" title="c5">F</font> <a href="mesfunc5.html#K4" title="MESFUNC5:func.4">.</a> <font color="Olive" title="b1">n</font> is <font color="Maroon" title="c3">E</font> <a href="mesfun6c.html#V1" title="MESFUN6C:attr.1">-measurable</a>  ) implies ( <span class="p1">(<span class="default"><a href="mesfun7c.html#K11" title="MESFUN7C:func.11">Re</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="mesfunc5.html#K4" title="MESFUNC5:func.4">.</a> <font color="Maroon" title="c4">m</font> is <font color="Maroon" title="c3">E</font> <a href="mesfunc6.html#V1" title="MESFUNC6:attr.1">-measurable</a>  &amp; <span class="p1">(<span class="default"><a href="mesfun7c.html#K12" title="MESFUN7C:func.12">Im</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="mesfunc5.html#K4" title="MESFUNC5:func.4">.</a> <font color="Maroon" title="c4">m</font> is <font color="Maroon" title="c3">E</font> <a href="mesfunc6.html#V1" title="MESFUNC6:attr.1">-measurable</a>  ) )</span><br/>









<span class="kw">assume </span><a NAME="E1:42"/>
 for <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds  <font color="Maroon" title="c5">F</font> <a href="mesfunc5.html#K4" title="MESFUNC5:func.4">.</a> <font color="Olive" title="b1">n</font> is <font color="Maroon" title="c3">E</font> <a href="mesfun6c.html#V1" title="MESFUN6C:attr.1">-measurable</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> <font color="Maroon" title="c5">F</font></span>)</span> <a href="mesfunc5.html#K4" title="MESFUNC5:func.4">.</a> <font color="Maroon" title="c4">m</font> is <font color="Maroon" title="c3">E</font> <a href="mesfunc6.html#V1" title="MESFUNC6:attr.1">-measurable</a>  &amp; <span class="p1">(<span class="default"><a href="mesfun7c.html#K12" title="MESFUN7C:func.12">Im</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="mesfunc5.html#K4" title="MESFUNC5:func.4">.</a> <font color="Maroon" title="c4">m</font> is <font color="Maroon" title="c3">E</font> <a href="mesfunc6.html#V1" title="MESFUNC6:attr.1">-measurable</a>  )</span><br/>

<a NAME="E2:42"/><span class="kw">then </span>
<font color="Maroon" title="c5">F</font> <a href="mesfunc5.html#K4" title="MESFUNC5:func.4">.</a> <font color="Maroon" title="c4">m</font> is <font color="Maroon" title="c3">E</font> <a href="mesfun6c.html#V1" title="MESFUN6C:attr.1">-measurable</a> 
 
;<br/>
<a NAME="E3:42"/><span class="kw">then </span>
(  <a href="comseq_3.html#K5" title="COMSEQ_3:func.5">Re</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="mesfunc5.html#K4" title="MESFUNC5:func.4">.</a> <font color="Maroon" title="c4">m</font></span>)</span> is <font color="Maroon" title="c3">E</font> <a href="mesfunc6.html#V1" title="MESFUNC6:attr.1">-measurable</a>  &amp;  <a href="comseq_3.html#K6" title="COMSEQ_3:func.6">Im</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="mesfunc5.html#K4" title="MESFUNC5:func.4">.</a> <font color="Maroon" title="c4">m</font></span>)</span> is <font color="Maroon" title="c3">E</font> <a href="mesfunc6.html#V1" title="MESFUNC6:attr.1">-measurable</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mesfun6c.html#D1" onmouseover="rs('mesfun6c/D1')" onmouseout="rh()">MESFUN6C:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:42"/>
( <span class="p1">(<span class="default"><a href="mesfun7c.html#K11" title="MESFUN7C:func.11">Re</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="mesfunc5.html#K4" title="MESFUNC5:func.4">.</a> <font color="Maroon" title="c4">m</font> is <font color="Maroon" title="c3">E</font> <a href="mesfunc6.html#V1" title="MESFUNC6:attr.1">-measurable</a>  &amp; <span class="p1">(<span class="default"><a href="mesfun7c.html#K12" title="MESFUN7C:func.12">Im</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="mesfunc5.html#K4" title="MESFUNC5:func.4">.</a> <font color="Maroon" title="c4">m</font> is <font color="Maroon" title="c3">E</font> <a href="mesfunc6.html#V1" title="MESFUNC6:attr.1">-measurable</a>  )
 <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>; <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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