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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="srings_3.html#M2" title="SRINGS_3:mode.2">semialgebra_of_sets</a> of <font color="Maroon" title="c1">X</font><br/>  for <font color="Olive" title="b2">P</font> being    <a href="measure9.html#M1" title="MEASURE9:mode.1">pre-Measure</a> of <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b3">M</font> being    <a href="measure9.html#M2" title="MEASURE9:mode.2">induced_Measure</a> of <font color="Olive" title="b1">S</font>,<font color="Olive" title="b2">P</font> holds  <font color="Olive" title="b3">M</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><a href="measure8.html#K9" title="MEASURE8:func.9">C_Meas</a> <font color="Olive" title="b3">M</font></span>)</span> <a href="funct_3.html#K17" title="FUNCT_3:func.17">|</a> <span class="p1">(<span class="default"><a href="srings_3.html#K4" title="SRINGS_3:func.4">Field_generated_by</a> <font color="Olive" title="b1">S</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">S</font> be    <a href="srings_3.html#M2" title="SRINGS_3:mode.2">semialgebra_of_sets</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">P</font> being    <a href="measure9.html#M1" title="MEASURE9:mode.1">pre-Measure</a> of <font color="Maroon" title="c2">S</font><br/>  for <font color="Olive" title="b2">M</font> being    <a href="measure9.html#M2" title="MEASURE9:mode.2">induced_Measure</a> of <font color="Maroon" title="c2">S</font>,<font color="Olive" title="b1">P</font> holds  <font color="Olive" title="b2">M</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><a href="measure8.html#K9" title="MEASURE8:func.9">C_Meas</a> <font color="Olive" title="b2">M</font></span>)</span> <a href="funct_3.html#K17" title="FUNCT_3:func.17">|</a> <span class="p1">(<span class="default"><a href="srings_3.html#K4" title="SRINGS_3:func.4">Field_generated_by</a> <font color="Maroon" title="c2">S</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">P</font> be    <a href="measure9.html#M1" title="MEASURE9:mode.1">pre-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">M</font> being    <a href="measure9.html#M2" title="MEASURE9:mode.2">induced_Measure</a> of <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">P</font> holds  <font color="Olive" title="b1">M</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><a href="measure8.html#K9" title="MEASURE8:func.9">C_Meas</a> <font color="Olive" title="b1">M</font></span>)</span> <a href="funct_3.html#K17" title="FUNCT_3:func.17">|</a> <span class="p1">(<span class="default"><a href="srings_3.html#K4" title="SRINGS_3:func.4">Field_generated_by</a> <font color="Maroon" title="c2">S</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">M</font> be    <a href="measure9.html#M2" title="MEASURE9:mode.2">induced_Measure</a> of <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">P</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">M</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><a href="measure8.html#K9" title="MEASURE8:func.9">C_Meas</a> <font color="Maroon" title="c4">M</font></span>)</span> <a href="funct_3.html#K17" title="FUNCT_3:func.17">|</a> <span class="p1">(<span class="default"><a href="srings_3.html#K4" title="SRINGS_3:func.4">Field_generated_by</a> <font color="Maroon" title="c2">S</font></span>)</span></span><br/>







<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="111_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">A</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="srings_3.html#K4" title="SRINGS_3:func.4">Field_generated_by</a> <font color="Maroon" title="c2">S</font> holds  <font color="Maroon" title="c4">M</font> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measure8.html#K9" title="MEASURE8:func.9">C_Meas</a> <font color="Maroon" title="c4">M</font></span>)</span> <a href="funct_3.html#K17" title="FUNCT_3:func.17">|</a> <span class="p2">(<span class="default"><a href="srings_3.html#K4" title="SRINGS_3:func.4">Field_generated_by</a> <font color="Maroon" title="c2">S</font></span>)</span></span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Olive" title="b1">A</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c5">A</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="srings_3.html#K4" title="SRINGS_3:func.4">Field_generated_by</a> <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">M</font> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c5">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measure8.html#K9" title="MEASURE8:func.9">C_Meas</a> <font color="Maroon" title="c4">M</font></span>)</span> <a href="funct_3.html#K17" title="FUNCT_3:func.17">|</a> <span class="p2">(<span class="default"><a href="srings_3.html#K4" title="SRINGS_3:func.4">Field_generated_by</a> <font color="Maroon" title="c2">S</font></span>)</span></span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c5">A</font></span><br/><a NAME="E1:111_1"/>
<font color="Maroon" title="c4">M</font> is  <a href="measure8.html#V1" title="MEASURE8:attr.1">completely-additive</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="measure9.html#T60" onmouseover="rs('measure9/T60')" onmouseout="rh()">MEASURE9:60</a></span>;<br/><a NAME="E2:111_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">M</font> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c5">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="measure8.html#K9" title="MEASURE8:func.9">C_Meas</a> <font color="Maroon" title="c4">M</font></span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c5">A</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="measure8.html#T18" onmouseover="rs('measure8/T18')" onmouseout="rh()">MEASURE8:18</a></span>;<br/><span class="kw">hence </span><a NAME="E3:111_1"/>
<font color="Maroon" title="c4">M</font> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c5">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measure8.html#K9" title="MEASURE8:func.9">C_Meas</a> <font color="Maroon" title="c4">M</font></span>)</span> <a href="funct_3.html#K17" title="FUNCT_3:func.17">|</a> <span class="p2">(<span class="default"><a href="srings_3.html#K4" title="SRINGS_3:func.4">Field_generated_by</a> <font color="Maroon" title="c2">S</font></span>)</span></span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c5">A</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T49" onmouseover="rs('funct_1/T49')" onmouseout="rh()">FUNCT_1:49</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>
<span class="kw">hence </span><a NAME="E2:111"/>
<font color="Maroon" title="c4">M</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><a href="measure8.html#K9" title="MEASURE8:func.9">C_Meas</a> <font color="Maroon" title="c4">M</font></span>)</span> <a href="funct_3.html#K17" title="FUNCT_3:func.17">|</a> <span class="p1">(<span class="default"><a href="srings_3.html#K4" title="SRINGS_3:func.4">Field_generated_by</a> <font color="Maroon" title="c2">S</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D8" onmouseover="rs('funct_2/D8')" onmouseout="rh()">FUNCT_2:def 8</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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