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<b>let </b><font color="Maroon">X</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">S</font> be   <a href="prob_1.html#NM3">SigmaField</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">f</font> be   <a href="partfun1.html#NM1">PartFunc</a> of <font color="Maroon">X</font>, <a href="supinf_1.html#K3">REAL</a> ;<br/><b>let </b><font color="Maroon">g</font> be   <a href="partfun1.html#NM1">PartFunc</a> of <font color="Maroon">X</font>, <a href="supinf_1.html#K3">REAL</a> ;<br/><b>let </b><font color="Maroon">A</font> be    <a href="subset_1.html#M2">Element</a> of <font color="Maroon">S</font>;<br/>









<b>assume </b><b>that </b><br/><a NAME="E1:35"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">f</font> <a href="mesfunc6.html#R1" target="_self">is_measurable_on</a> <font color="Maroon">A</font> &amp; <font color="Maroon">g</font> <a href="mesfunc6.html#R1" target="_self">is_measurable_on</a> <font color="Maroon">A</font> )
 <b>and </b><br/><a NAME="E2:35"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">A</font> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">g</font>
 ;<br/>

<a NAME="E3:35"/><i><font color="Green">E43</font></i>: 
(  <a href="mesfunc5.html#K1">R_EAL</a> <font color="Maroon">f</font> <a href="mesfunc2.html#R1">is_finite</a>  &amp;  <a href="mesfunc5.html#K1">R_EAL</a> <span class="p1">(<span class="default"><a href="seq_1.html#K16">-</a> <font color="Maroon">g</font></span>)</span> <a href="mesfunc2.html#R1">is_finite</a>  )
 
<b>by </b><i/>;<br/>
<a NAME="E4:35"/><i><font color="Green">E45</font></i>: 
(  <a href="mesfunc5.html#K1">R_EAL</a> <font color="Maroon">f</font> <a href="mesfunc1.html#R2">is_measurable_on</a> <font color="Maroon">A</font> &amp;  <a href="mesfunc5.html#K1">R_EAL</a> <font color="Maroon">g</font> <a href="mesfunc1.html#R2">is_measurable_on</a> <font color="Maroon">A</font> )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E5:35"/><b>then </b>
<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="mesfunc1.html#K8">(#)</a> <span class="p1">(<span class="default"><a href="mesfunc5.html#K1">R_EAL</a> <font color="Maroon">g</font></span>)</span> <a href="mesfunc1.html#R2">is_measurable_on</a> <font color="Maroon">A</font>
 
<b>by </b><i>, <a class="ref" href="mesfunc1.html#T41">MESFUNC1:41</a></i>;<br/>
<a NAME="E6:35"/><b>then </b>
 <a href="mesfunc1.html#K9">-</a> <span class="p1">(<span class="default"><a href="mesfunc5.html#K1">R_EAL</a> <font color="Maroon">g</font></span>)</span> <a href="mesfunc1.html#R2">is_measurable_on</a> <font color="Maroon">A</font>
 
<b>by </b><i><a class="ref" href="mesfunc2.html#T11">MESFUNC2:11</a></i>;<br/>
<a NAME="E7:35"/><b>then </b>
 <a href="mesfunc5.html#K1">R_EAL</a> <span class="p1">(<span class="default"><a href="seq_1.html#K16">-</a> <font color="Maroon">g</font></span>)</span> <a href="mesfunc1.html#R2">is_measurable_on</a> <font color="Maroon">A</font>
 
<b>by </b><i/>;<br/>
<a NAME="E8:35"/><b>then </b>
<span class="p1">(<span class="default"><a href="mesfunc5.html#K1">R_EAL</a> <font color="Maroon">f</font></span>)</span> <a href="mesfunc1.html#K13">+</a> <span class="p1">(<span class="default"><a href="mesfunc5.html#K1">R_EAL</a> <span class="p2">(<span class="default"><a href="seq_1.html#K16">-</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="mesfunc1.html#R2">is_measurable_on</a> <font color="Maroon">A</font>
 
<b>by </b><i>, , <a class="ref" href="mesfunc2.html#T7">MESFUNC2:7</a></i>;<br/>
<a NAME="E9:35"/><b>then </b>
<span class="p1">(<span class="default"><a href="mesfunc5.html#K1">R_EAL</a> <font color="Maroon">f</font></span>)</span> <a href="mesfunc1.html#K6">-</a> <span class="p1">(<span class="default"><a href="mesfunc5.html#K1">R_EAL</a> <font color="Maroon">g</font></span>)</span> <a href="mesfunc1.html#R2">is_measurable_on</a> <font color="Maroon">A</font>
 
<b>by </b><i/>;<br/>
<a NAME="E10:35"/><b>then </b>
 <a href="mesfunc5.html#K1">R_EAL</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="seq_1.html#K7">-</a> <font color="Maroon">g</font></span>)</span> <a href="mesfunc1.html#R2">is_measurable_on</a> <font color="Maroon">A</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E11:35"/>
<font color="Maroon">f</font> <a href="seq_1.html#K7">-</a> <font color="Maroon">g</font> <a href="mesfunc6.html#R1" target="_self">is_measurable_on</a> <font color="Maroon">A</font>
 <b>by </b><i/>;<br/>


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