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<span class="kw">let </span><font color="Maroon" title="c1">X</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">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">M</font> being   <a href="measure1.html#NM5" title="MEASURE1:NM.5">sigma_Measure</a> of <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b3">F</font> being   <a href="mesfunc2.html#NM1" title="MESFUNC2:NM.1">Finite_Sep_Sequence</a> of <font color="Olive" title="b1">S</font> holds  <font color="Olive" title="b3">F</font> is   <a href="mesfunc2.html#NM1" title="MESFUNC2:NM.1">Finite_Sep_Sequence</a> of  <a href="measure3.html#K2" title="MEASURE3:func.2">COM</a> (<font color="Olive" title="b1">S</font>,<font color="Olive" title="b2">M</font>)</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">M</font> being   <a href="measure1.html#NM5" title="MEASURE1:NM.5">sigma_Measure</a> of <font color="Maroon" title="c2">S</font><br/>  for <font color="Olive" title="b2">F</font> being   <a href="mesfunc2.html#NM1" title="MESFUNC2:NM.1">Finite_Sep_Sequence</a> of <font color="Maroon" title="c2">S</font> holds  <font color="Olive" title="b2">F</font> is   <a href="mesfunc2.html#NM1" title="MESFUNC2:NM.1">Finite_Sep_Sequence</a> of  <a href="measure3.html#K2" title="MEASURE3:func.2">COM</a> (<font color="Maroon" title="c2">S</font>,<font color="Olive" title="b1">M</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c3">M</font> be   <a href="measure1.html#NM5" title="MEASURE1:NM.5">sigma_Measure</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">F</font> being   <a href="mesfunc2.html#NM1" title="MESFUNC2:NM.1">Finite_Sep_Sequence</a> of <font color="Maroon" title="c2">S</font> holds  <font color="Olive" title="b1">F</font> is   <a href="mesfunc2.html#NM1" title="MESFUNC2:NM.1">Finite_Sep_Sequence</a> of  <a href="measure3.html#K2" title="MEASURE3:func.2">COM</a> (<font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">M</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c4">F</font> be   <a href="mesfunc2.html#NM1" title="MESFUNC2:NM.1">Finite_Sep_Sequence</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"> <font color="Maroon" title="c4">F</font> is   <a href="mesfunc2.html#NM1" title="MESFUNC2:NM.1">Finite_Sep_Sequence</a> of  <a href="measure3.html#K2" title="MEASURE3:func.2">COM</a> (<font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">M</font>)</span><br/>







<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="38_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">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c4">F</font> holds <br/><font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="measure3.html#K2" title="MEASURE3:func.2">COM</a> (<font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">M</font>)</span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c5">y</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="c5">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c4">F</font> implies <font color="Maroon" title="c5">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="measure3.html#K2" title="MEASURE3:func.2">COM</a> (<font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">M</font>) )</span><br/><span class="kw">assume </span><a NAME="E1:38_1"/>
<font color="Maroon" title="c5">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c4">F</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="c5">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="measure3.html#K2" title="MEASURE3:func.2">COM</a> (<font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">M</font>)</span><br/><a NAME="E2:38_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">y</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="measure3.html#K2" title="MEASURE3:func.2">COM</a> (<font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">M</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="mesfun14.html#T27" target="_self" onmouseover="rs('mesfun14/T27')" onmouseout="rh()">Th27</a></span>;<br/><span class="kw">hence </span><a NAME="E3:38_1"/>
<font color="Maroon" title="c5">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="measure3.html#K2" title="MEASURE3:func.2">COM</a> (<font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">M</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"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E2:38"/><span class="kw">then </span>
 <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c4">F</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="measure3.html#K2" title="MEASURE3:func.2">COM</a> (<font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">M</font>)
 
;<br/>
<span class="kw">hence </span><a NAME="E3:38"/>
<font color="Maroon" title="c4">F</font> is   <a href="mesfunc2.html#NM1" title="MESFUNC2:NM.1">Finite_Sep_Sequence</a> of  <a href="measure3.html#K2" title="MEASURE3:func.2">COM</a> (<font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">M</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D4" onmouseover="rs('finseq_1/D4')" onmouseout="rh()">FINSEQ_1:def 4</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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