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<div class="add">

<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#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">F</font> being  <a href="prob_1.html#NM1" title="PROB_1:NM.1">Field_Subset</a> of <font color="Maroon" title="c1">X</font><br/> for <font color="Olive" title="b2">m</font> being  <a href="measure1.html#NM1" title="MEASURE1:NM.1">Measure</a> of <font color="Olive" title="b1">F</font>  st <font color="Olive" title="b2">m</font> is  <a href="measure8.html#V1" title="MEASURE8:attr.1">completely-additive</a>  holds <br/> ex <font color="Olive" title="b3">M</font> being  <a href="measure1.html#NM5" title="MEASURE1:NM.5">sigma_Measure</a> of <span class="p1">(<span class="default"><a href="prob_1.html#K10" title="PROB_1:func.10">sigma</a> <font color="Olive" title="b1">F</font></span>)</span> st <br/>( <font color="Olive" title="b3">M</font> <a href="measure8.html#R1" title="MEASURE8:pred.1">is_extension_of</a> <font color="Olive" title="b2">m</font> &amp; <font color="Olive" title="b3">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="measure4.html#K4" title="MEASURE4:func.4">sigma_Meas</a> <span class="p2">(<span class="default"><a href="measure8.html#K9" title="MEASURE8:func.9">C_Meas</a> <font color="Olive" title="b2">m</font></span>)</span></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="prob_1.html#K10" title="PROB_1:func.10">sigma</a> <font color="Olive" title="b1">F</font></span>)</span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">F</font> be   <a href="prob_1.html#NM1" title="PROB_1:NM.1">Field_Subset</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">m</font> being  <a href="measure1.html#NM1" title="MEASURE1:NM.1">Measure</a> of <font color="Maroon" title="c2">F</font>  st <font color="Olive" title="b1">m</font> is  <a href="measure8.html#V1" title="MEASURE8:attr.1">completely-additive</a>  holds <br/> ex <font color="Olive" title="b2">M</font> being  <a href="measure1.html#NM5" title="MEASURE1:NM.5">sigma_Measure</a> of <span class="p1">(<span class="default"><a href="prob_1.html#K10" title="PROB_1:func.10">sigma</a> <font color="Maroon" title="c2">F</font></span>)</span> st <br/>( <font color="Olive" title="b2">M</font> <a href="measure8.html#R1" title="MEASURE8:pred.1">is_extension_of</a> <font color="Olive" title="b1">m</font> &amp; <font color="Olive" title="b2">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="measure4.html#K4" title="MEASURE4:func.4">sigma_Meas</a> <span class="p2">(<span class="default"><a href="measure8.html#K9" title="MEASURE8:func.9">C_Meas</a> <font color="Olive" title="b1">m</font></span>)</span></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="prob_1.html#K10" title="PROB_1:func.10">sigma</a> <font color="Maroon" title="c2">F</font></span>)</span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">m</font> be   <a href="measure1.html#NM1" title="MEASURE1:NM.1">Measure</a> of <font color="Maroon" title="c2">F</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">m</font> is  <a href="measure8.html#V1" title="MEASURE8:attr.1">completely-additive</a>  implies  ex <font color="Olive" title="b1">M</font> being  <a href="measure1.html#NM5" title="MEASURE1:NM.5">sigma_Measure</a> of <span class="p1">(<span class="default"><a href="prob_1.html#K10" title="PROB_1:func.10">sigma</a> <font color="Maroon" title="c2">F</font></span>)</span> st <br/>( <font color="Olive" title="b1">M</font> <a href="measure8.html#R1" title="MEASURE8:pred.1">is_extension_of</a> <font color="Maroon" title="c3">m</font> &amp; <font color="Olive" title="b1">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="measure4.html#K4" title="MEASURE4:func.4">sigma_Meas</a> <span class="p2">(<span class="default"><a href="measure8.html#K9" title="MEASURE8:func.9">C_Meas</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="prob_1.html#K10" title="PROB_1:func.10">sigma</a> <font color="Maroon" title="c2">F</font></span>)</span> ) )</span><br/>





<span class="kw">assume </span><a NAME="E1:57"/><span class="lab"><font color="Green" title="E42">A1</font></span>: 
<font color="Maroon" title="c3">m</font> is  <a href="measure8.html#V1" title="MEASURE8:attr.1">completely-additive</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">M</font> being  <a href="measure1.html#NM5" title="MEASURE1:NM.5">sigma_Measure</a> of <span class="p1">(<span class="default"><a href="prob_1.html#K10" title="PROB_1:func.10">sigma</a> <font color="Maroon" title="c2">F</font></span>)</span> st <br/>( <font color="Olive" title="b1">M</font> <a href="measure8.html#R1" title="MEASURE8:pred.1">is_extension_of</a> <font color="Maroon" title="c3">m</font> &amp; <font color="Olive" title="b1">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="measure4.html#K4" title="MEASURE4:func.4">sigma_Meas</a> <span class="p2">(<span class="default"><a href="measure8.html#K9" title="MEASURE8:func.9">C_Meas</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="prob_1.html#K10" title="PROB_1:func.10">sigma</a> <font color="Maroon" title="c2">F</font></span>)</span> )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c4">M</font> = <span class="p1">(<span class="default"><a href="measure4.html#K4" title="MEASURE4:func.4">sigma_Meas</a> <span class="p2">(<span class="default"><a href="measure8.html#K9" title="MEASURE8:func.9">C_Meas</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="prob_1.html#K10" title="PROB_1:func.10">sigma</a> <font color="Maroon" title="c2">F</font></span>)</span>;<br/>
<a NAME="E2:57"/><span class="lab"><font color="Green" title="E43">A2</font></span>: 
<font color="Maroon" title="c2">F</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="measure4.html#K1" title="MEASURE4:func.1">sigma_Field</a> <span class="p1">(<span class="default"><a href="measure8.html#K9" title="MEASURE8:func.9">C_Meas</a> <font color="Maroon" title="c3">m</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="measure8.html#T20" target="_self" title="MEASURE8:th.20">Th20</a></span>;<br/>
<a NAME="E3:57"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A3</font></span>: 
 <a href="prob_1.html#K10" title="PROB_1:func.10">sigma</a> <font color="Maroon" title="c2">F</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="measure4.html#K1" title="MEASURE4:func.1">sigma_Field</a> <span class="p1">(<span class="default"><a href="measure8.html#K9" title="MEASURE8:func.9">C_Meas</a> <font color="Maroon" title="c3">m</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="prob_1.html#D14" title="PROB_1:def.14">PROB_1:def 14</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c5">M</font> = <span class="p1">(<span class="default"><a href="measure4.html#K4" title="MEASURE4:func.4">sigma_Meas</a> <span class="p2">(<span class="default"><a href="measure8.html#K9" title="MEASURE8:func.9">C_Meas</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="prob_1.html#K10" title="PROB_1:func.10">sigma</a> <font color="Maroon" title="c2">F</font></span>)</span> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><a href="prob_1.html#K10" title="PROB_1:func.10">sigma</a> <font color="Maroon" title="c2">F</font></span>)</span>,<a href="numbers.html#K7" title="NUMBERS:func.7">ExtREAL</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T38" title="FUNCT_2:th.38">FUNCT_2:38</a></span>;<br/>
<a NAME="E5:57"/><span class="lab"><font color="Green" title="E45">A4</font></span>: 
for <font color="Olive" title="b1">SS</font> being  <a href="measure8.html#NM3" title="MEASURE8:NM.3">Sep_Sequence</a> of <span class="p1">(<span class="default"><a href="prob_1.html#K10" title="PROB_1:func.10">sigma</a> <font color="Maroon" title="c2">F</font></span>)</span> holds   <a href="supinf_2.html#K20" title="SUPINF_2:func.20">SUM</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">M</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b1">SS</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">M</font> <a href="mesfunc9.html#K1" title="MESFUNC9:func.1">.</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <span class="p2">(<span class="default"><a href="measure1.html#K4" title="MEASURE1:func.4">rng</a> <font color="Olive" title="b1">SS</font></span>)</span></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c6">SS</font> be   <a href="measure8.html#NM3" title="MEASURE8:NM.3">Sep_Sequence</a> of <span class="p1">(<span class="default"><a href="prob_1.html#K10" title="PROB_1:func.10">sigma</a> <font color="Maroon" title="c2">F</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="supinf_2.html#K20" title="SUPINF_2:func.20">SUM</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">M</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c6">SS</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">M</font> <a href="mesfunc9.html#K1" title="MESFUNC9:func.1">.</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <span class="p2">(<span class="default"><a href="measure1.html#K4" title="MEASURE1:func.4">rng</a> <font color="Maroon" title="c6">SS</font></span>)</span></span>)</span></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c7">SS9</font> = <font color="Maroon" title="c6">SS</font> as   <a href="measure8.html#NM3" title="MEASURE8:NM.3">Sep_Sequence</a> of <span class="p1">(<span class="default"><a href="measure4.html#K1" title="MEASURE4:func.1">sigma_Field</a> <span class="p2">(<span class="default"><a href="measure8.html#K9" title="MEASURE8:func.9">C_Meas</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:57"><span class="lab"><font color="Green" title="E44">A3</font></span></a>, <a class="ref" href="funct_2.html#T9" title="FUNCT_2:th.9">FUNCT_2:9</a></span>;<br/>
<a NAME="E2:57_1"/><span class="lab"><font color="Green" title="E46">A5</font></span>: 
 <a href="measure1.html#K4" title="MEASURE1:func.4">rng</a> <font color="Maroon" title="c6">SS</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="prob_1.html#K10" title="PROB_1:func.10">sigma</a> <font color="Maroon" title="c2">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D19" title="RELAT_1:def.19">RELAT_1:def 19</a></span>;<br/>
<font color="Maroon" title="c5">M</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c6">SS</font> = 
<span class="p1">(<span class="default"><a href="measure4.html#K4" title="MEASURE4:func.4">sigma_Meas</a> <span class="p2">(<span class="default"><a href="measure8.html#K9" title="MEASURE8:func.9">C_Meas</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="prob_1.html#K10" title="PROB_1:func.10">sigma</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="relset_1.html#K6" title="RELSET_1:func.6">|</a> <font color="Maroon" title="c6">SS</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="monoid_1.html#T2" title="MONOID_1:th.2">MONOID_1:2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="measure4.html#K4" title="MEASURE4:func.4">sigma_Meas</a> <span class="p2">(<span class="default"><a href="measure8.html#K9" title="MEASURE8:func.9">C_Meas</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c7">SS9</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:57_1"><span class="lab"><font color="Green" title="E46">A5</font></span></a>, <a class="ref" href="relat_1.html#T125" title="RELAT_1:th.125">RELAT_1:125</a></span>
;<br/>
<a NAME="E4:57_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E47">A6</font></span>: 
 <a href="supinf_2.html#K20" title="SUPINF_2:func.20">SUM</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">M</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c6">SS</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="measure4.html#K4" title="MEASURE4:func.4">sigma_Meas</a> <span class="p2">(<span class="default"><a href="measure8.html#K9" title="MEASURE8:func.9">C_Meas</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="mesfunc9.html#K1" title="MESFUNC9:func.1">.</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <span class="p2">(<span class="default"><a href="measure1.html#K4" title="MEASURE1:func.4">rng</a> <font color="Maroon" title="c7">SS9</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="measure1.html#D11" title="MEASURE1:def.11">MEASURE1:def 11</a></span>;<br/>
<a NAME="E5:57_1"/>
 <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <span class="p1">(<span class="default"><a href="measure1.html#K4" title="MEASURE1:func.4">rng</a> <font color="Maroon" title="c6">SS</font></span>)</span> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="prob_1.html#K10" title="PROB_1:func.10">sigma</a> <font color="Maroon" title="c2">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="measure1.html#T53" title="MEASURE1:th.53">MEASURE1:53</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:57_1"/>
 <a href="supinf_2.html#K20" title="SUPINF_2:func.20">SUM</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">M</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c6">SS</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">M</font> <a href="mesfunc9.html#K1" title="MESFUNC9:func.1">.</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <span class="p2">(<span class="default"><a href="measure1.html#K4" title="MEASURE1:func.4">rng</a> <font color="Maroon" title="c6">SS</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:57_1"><span class="lab"><font color="Green" title="E47">A6</font></span></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<font color="Maroon" title="c5">M</font> <a href="mesfunc9.html#K1" title="MESFUNC9:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  = 
<span class="p1">(<span class="default"><a href="measure4.html#K4" title="MEASURE4:func.4">sigma_Meas</a> <span class="p2">(<span class="default"><a href="measure8.html#K9" title="MEASURE8:func.9">C_Meas</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="mesfunc9.html#K1" title="MESFUNC9:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a>, <a class="ref" href="prob_1.html#T10" title="PROB_1:th.10">PROB_1:10</a></span>
<br/>.= 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="valued_0.html#D19" title="VALUED_0:def.19">VALUED_0:def 19</a></span>
;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c6">M</font> = <font color="Maroon" title="c5">M</font> as   <a href="measure1.html#NM5" title="MEASURE1:NM.5">sigma_Measure</a> of <span class="p1">(<span class="default"><a href="prob_1.html#K10" title="PROB_1:func.10">sigma</a> <font color="Maroon" title="c2">F</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:57"><span class="lab"><font color="Green" title="E45">A4</font></span></a>, <a class="ref" href="measure1.html#D11" title="MEASURE1:def.11">MEASURE1:def 11</a>, <a class="ref" href="mesfunc5.html#T21" title="MESFUNC5:th.21">MESFUNC5:21</a>, <a class="ref" href="valued_0.html#D19" title="VALUED_0:def.19">VALUED_0:def 19</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c6">M</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c6">M</font> <a href="measure8.html#R1" title="MEASURE8:pred.1">is_extension_of</a> <font color="Maroon" title="c3">m</font> &amp; <font color="Maroon" title="c6">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="measure4.html#K4" title="MEASURE4:func.4">sigma_Meas</a> <span class="p2">(<span class="default"><a href="measure8.html#K9" title="MEASURE8:func.9">C_Meas</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="prob_1.html#K10" title="PROB_1:func.10">sigma</a> <font color="Maroon" title="c2">F</font></span>)</span> )</span><br/>

<a NAME="E8:57"/><span class="lab"><font color="Green" title="E46">A7</font></span>: 
<font color="Maroon" title="c2">F</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="prob_1.html#K10" title="PROB_1:func.10">sigma</a> <font color="Maroon" title="c2">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="prob_1.html#D14" title="PROB_1:def.14">PROB_1:def 14</a></span>;<br/>
<a NAME="E9:57"/>
for <font color="Olive" title="b1">A</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">F</font> holds <br/><font color="Maroon" title="c6">M</font> <a href="mesfunc9.html#K1" title="MESFUNC9:func.1">.</a> <font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">m</font> <a href="mesfunc9.html#K1" title="MESFUNC9:func.1">.</a> <font color="Olive" title="b1">A</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_3"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c7">A</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c7">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">F</font> implies <font color="Maroon" title="c6">M</font> <a href="mesfunc9.html#K1" title="MESFUNC9:func.1">.</a> <font color="Maroon" title="c7">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">m</font> <a href="mesfunc9.html#K1" title="MESFUNC9:func.1">.</a> <font color="Maroon" title="c7">A</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:57_3"/><span class="lab"><font color="Green" title="E47">A8</font></span>: 
<font color="Maroon" title="c7">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">F</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c6">M</font> <a href="mesfunc9.html#K1" title="MESFUNC9:func.1">.</a> <font color="Maroon" title="c7">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">m</font> <a href="mesfunc9.html#K1" title="MESFUNC9:func.1">.</a> <font color="Maroon" title="c7">A</font></span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c8">A9</font> = <font color="Maroon" title="c7">A</font> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> ;<br/>
<font color="Maroon" title="c6">M</font> <a href="mesfunc9.html#K1" title="MESFUNC9:func.1">.</a> <font color="Maroon" title="c7">A</font> = 
<span class="p1">(<span class="default"><a href="measure4.html#K4" title="MEASURE4:func.4">sigma_Meas</a> <span class="p2">(<span class="default"><a href="measure8.html#K9" title="MEASURE8:func.9">C_Meas</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="mesfunc9.html#K1" title="MESFUNC9:func.1">.</a> <font color="Maroon" title="c7">A</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:57"><span class="lab"><font color="Green" title="E46">A7</font></span></a>, <a class="txt" href="#E1:57_3"><span class="lab"><font color="Green" title="E47">A8</font></span></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="measure8.html#K9" title="MEASURE8:func.9">C_Meas</a> <font color="Maroon" title="c3">m</font></span>)</span> <a href="mesfunc9.html#K1" title="MESFUNC9:func.1">.</a> <font color="Maroon" title="c8">A9</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:57"><span class="lab"><font color="Green" title="E43">A2</font></span></a>, <a class="txt" href="#E1:57_3"><span class="lab"><font color="Green" title="E47">A8</font></span></a>, <a class="ref" href="measure4.html#D4" title="MEASURE4:def.4">MEASURE4:def 4</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E4:57_3"/>
<font color="Maroon" title="c6">M</font> <a href="mesfunc9.html#K1" title="MESFUNC9:func.1">.</a> <font color="Maroon" title="c7">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">m</font> <a href="mesfunc9.html#K1" title="MESFUNC9:func.1">.</a> <font color="Maroon" title="c7">A</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:57"><span class="lab"><font color="Green" title="E42">A1</font></span></a>, <a class="txt" href="#E1:57_3"><span class="lab"><font color="Green" title="E47">A8</font></span></a>, <a class="ref" href="measure8.html#T18" target="_self" title="MEASURE8:th.18">Th18</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E10:57"/>
( <font color="Maroon" title="c6">M</font> <a href="measure8.html#R1" title="MEASURE8:pred.1">is_extension_of</a> <font color="Maroon" title="c3">m</font> &amp; <font color="Maroon" title="c6">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="measure4.html#K4" title="MEASURE4:func.4">sigma_Meas</a> <span class="p2">(<span class="default"><a href="measure8.html#K9" title="MEASURE8:func.9">C_Meas</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="prob_1.html#K10" title="PROB_1:func.10">sigma</a> <font color="Maroon" title="c2">F</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="measure8.html#D12" target="_self" title="MEASURE8:def.12">Def12</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
