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<b>let </b><font color="Maroon">c<sub>1</sub></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">c<sub>2</sub></font> be   <a href="prob_1.html#NM3">SigmaField</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="measure1.html#M3">sigma_Measure</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be   <a href="partfun1.html#NM1">PartFunc</a> of <font color="Maroon">c<sub>1</sub></font>, <a href="numbers.html#K6">ExtREAL</a> ;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:67"/><i><font color="Green">E64</font></i>: 
ex <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M2">Element</a> of <font color="Maroon">c<sub>2</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="mesfunc1.html#R2">is_measurable_on</a> <font color="Olive">b<sub>1</sub></font> )
 <b>and </b><br/><a NAME="E2:67"/><i><font color="Green">E65</font></i>: 
ex <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M2">Element</a> of <font color="Maroon">c<sub>2</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="mesfunc1.html#R2">is_measurable_on</a> <font color="Olive">b<sub>1</sub></font> )
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>6</sub></font> being    <a href="subset_1.html#M2">Element</a> of <font color="Maroon">c<sub>2</sub></font><b> such that </b><br/><a NAME="E4:67"/><i><font color="Green">E66</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="mesfunc1.html#R2">is_measurable_on</a> <font color="Maroon">c<sub>6</sub></font> )
 <b>by </b><i><a class="txt" href="mesfunc5.html#E1:67"><i><font color="Green">E64</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>7</sub></font> being    <a href="subset_1.html#M2">Element</a> of <font color="Maroon">c<sub>2</sub></font><b> such that </b><br/><a NAME="E6:67"/><i><font color="Green">E67</font></i>: 
( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="mesfunc1.html#R2">is_measurable_on</a> <font color="Maroon">c<sub>7</sub></font> )
 <b>by </b><i><a class="txt" href="mesfunc5.html#E2:67"><i><font color="Green">E65</font></i></a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>9</sub></font> = <font color="Maroon">c<sub>4</sub></font> <a href="partfun1.html#K2">|</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>10</sub></font> = <font color="Maroon">c<sub>5</sub></font> <a href="partfun1.html#K2">|</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>;<br/>
<a NAME="E7:67"/><i><font color="Green">E68</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>7</sub></font> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/>
<a NAME="E8:67"/><b>then </b>
( <font color="Maroon">c<sub>4</sub></font> <a href="mesfunc1.html#R2">is_measurable_on</a> <font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="mesfunc1.html#R2">is_measurable_on</a> <font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font> )
 
<b>by </b><i><a class="txt" href="mesfunc5.html#E4:67"><i><font color="Green">E66</font></i></a>, <a class="txt" href="mesfunc5.html#E6:67"><i><font color="Green">E67</font></i></a>, <a class="ref" href="mesfunc1.html#T34">MESFUNC1:34</a></i>;<br/>
<a NAME="E9:67"/><b>then </b><i><font color="Green">E69</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="partfun1.html#K2">|</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="mesfunc1.html#R2">is_measurable_on</a> <font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="partfun1.html#K2">|</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="mesfunc1.html#R2">is_measurable_on</a> <font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font> )
 
<b>by </b><i><a class="txt" href="mesfunc5.html#E66"><i><font color="Green">Lemma61</font></i></a></i>;<br/>
<a NAME="E10:67"/>
(  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="partfun1.html#K2">|</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> &amp;  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partfun1.html#K2">|</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="funct_1.html#T68">FUNCT_1:68</a></i>;<br/>
<a NAME="E11:67"/><b>then </b><i><font color="Green">E70</font></i>: 
(  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="partfun1.html#K2">|</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font> &amp;  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partfun1.html#K2">|</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font> )
 
<b>by </b><i><a class="txt" href="mesfunc5.html#E4:67"><i><font color="Green">E66</font></i></a>, <a class="txt" href="mesfunc5.html#E6:67"><i><font color="Green">E67</font></i></a>, <a class="txt" href="mesfunc5.html#E7:67"><i><font color="Green">E68</font></i></a>, <a class="ref" href="xboole_1.html#T28">XBOOLE_1:28</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>11</sub></font> being    <a href="subset_1.html#M2">Element</a> of <font color="Maroon">c<sub>2</sub></font><b> such that </b><br/><a NAME="E13:67"/><i><font color="Green">E71</font></i>: 
( <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="partfun1.html#K2">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="mesfunc1.html#K13">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partfun1.html#K2">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="partfun1.html#K2">|</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="mesfunc1.html#K13">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partfun1.html#K2">|</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="mesfunc1.html#R2">is_measurable_on</a> <font color="Maroon">c<sub>11</sub></font> )
 <b>by </b><i><a class="txt" href="mesfunc5.html#E9:67"><i><font color="Green">E69</font></i></a>, <a class="txt" href="mesfunc5.html#E67"><i><font color="Green">Lemma62</font></i></a></i>;<br/>
<a NAME="E14:67"/><i><font color="Green">E72</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="partfun1.html#K2">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="mesfunc1.html#K13">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partfun1.html#K2">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="partfun1.html#K2">|</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partfun1.html#K2">|</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="partfun1.html#K2">|</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="relset_1.html#K11">"</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><a href="supinf_1.html#K2">-infty</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partfun1.html#K2">|</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="relset_1.html#K11">"</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><a href="supinf_1.html#K1">+infty</a> </span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="partfun1.html#K2">|</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="relset_1.html#K11">"</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><a href="supinf_1.html#K1">+infty</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partfun1.html#K2">|</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="relset_1.html#K11">"</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><a href="supinf_1.html#K2">-infty</a> </span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="mesfunc1.html#D3">MESFUNC1:def 3</a></i>;<br/>
<a NAME="E15:67"/><i><font color="Green">E73</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="partfun1.html#K2">|</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="relset_1.html#K11">"</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="supinf_1.html#K2">-infty</a> </span><a href="tarski.html#K1">}</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><a href="supinf_1.html#K2">-infty</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="partfun1.html#K2">|</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="relset_1.html#K11">"</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="supinf_1.html#K1">+infty</a> </span><a href="tarski.html#K1">}</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><a href="supinf_1.html#K1">+infty</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partfun1.html#K2">|</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="relset_1.html#K11">"</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="supinf_1.html#K2">-infty</a> </span><a href="tarski.html#K1">}</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><a href="supinf_1.html#K2">-infty</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partfun1.html#K2">|</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="relset_1.html#K11">"</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="supinf_1.html#K1">+infty</a> </span><a href="tarski.html#K1">}</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><a href="supinf_1.html#K1">+infty</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> )
 
<b>by </b><i><a class="ref" href="funct_1.html#T139">FUNCT_1:139</a></i>;<br/>
<b>then </b><i><font color="Green">E74</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="partfun1.html#K2">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><a href="supinf_1.html#K2">-infty</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partfun1.html#K2">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><a href="supinf_1.html#K1">+infty</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><a href="supinf_1.html#K2">-infty</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="relset_1.html#K11">"</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><a href="supinf_1.html#K1">+infty</a> </span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T16">XBOOLE_1:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><a href="supinf_1.html#K2">-infty</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="measure1.html#K3">/\</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="relset_1.html#K11">"</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><a href="supinf_1.html#K1">+infty</a> </span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T16">XBOOLE_1:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K11">"</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><a href="supinf_1.html#K2">-infty</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="relset_1.html#K11">"</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><a href="supinf_1.html#K1">+infty</a> </span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T16">XBOOLE_1:16</a></i>
;<br/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="partfun1.html#K2">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><a href="supinf_1.html#K1">+infty</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partfun1.html#K2">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><a href="supinf_1.html#K2">-infty</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><a href="supinf_1.html#K1">+infty</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="relset_1.html#K11">"</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><a href="supinf_1.html#K2">-infty</a> </span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="mesfunc5.html#E15:67"><i><font color="Green">E73</font></i></a>, <a class="ref" href="xboole_1.html#T16">XBOOLE_1:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><a href="supinf_1.html#K1">+infty</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="measure1.html#K3">/\</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="relset_1.html#K11">"</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><a href="supinf_1.html#K2">-infty</a> </span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T16">XBOOLE_1:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K11">"</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><a href="supinf_1.html#K1">+infty</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="relset_1.html#K11">"</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><a href="supinf_1.html#K2">-infty</a> </span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T16">XBOOLE_1:16</a></i>
;<br/>
<a NAME="E18:67"/><b>then </b><i><font color="Green">E75</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="partfun1.html#K2">|</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="relset_1.html#K11">"</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><a href="supinf_1.html#K2">-infty</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partfun1.html#K2">|</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="relset_1.html#K11">"</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><a href="supinf_1.html#K1">+infty</a> </span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="partfun1.html#K2">|</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="relset_1.html#K11">"</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><a href="supinf_1.html#K1">+infty</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partfun1.html#K2">|</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="relset_1.html#K11">"</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><a href="supinf_1.html#K2">-infty</a> </span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K11">"</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><a href="supinf_1.html#K2">-infty</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="relset_1.html#K11">"</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><a href="supinf_1.html#K1">+infty</a> </span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K11">"</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><a href="supinf_1.html#K1">+infty</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="relset_1.html#K11">"</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><a href="supinf_1.html#K2">-infty</a> </span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="mesfunc5.html#E16:67"><i><font color="Green">E74</font></i></a>, <a class="ref" href="xboole_1.html#T23">XBOOLE_1:23</a></i>;<br/>
<a NAME="E19:67"/><i><font color="Green">E76</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K11">"</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><a href="supinf_1.html#K2">-infty</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="relset_1.html#K11">"</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><a href="supinf_1.html#K1">+infty</a> </span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K11">"</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><a href="supinf_1.html#K1">+infty</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="relset_1.html#K11">"</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><a href="supinf_1.html#K2">-infty</a> </span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="mesfunc1.html#D3">MESFUNC1:def 3</a></i>;<br/>
<a NAME="E20:67"/><b>then </b><i><font color="Green">E77</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="txt" href="mesfunc5.html#E18:67"><i><font color="Green">E75</font></i></a>, <a class="txt" href="mesfunc5.html#E13:67"><i><font color="Green">E71</font></i></a>, <a class="txt" href="mesfunc5.html#E11:67"><i><font color="Green">E70</font></i></a>, <a class="txt" href="mesfunc5.html#E14:67"><i><font color="Green">E72</font></i></a>, <a class="ref" href="xboole_1.html#T47">XBOOLE_1:47</a>, <a class="txt" href="mesfunc5.html#E4:67"><i><font color="Green">E66</font></i></a>, <a class="txt" href="mesfunc5.html#E6:67"><i><font color="Green">E67</font></i></a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>11</sub></font>
;<br/>

<a NAME="E21:67"/><i><font color="Green">E78</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partfun1.html#K2">|</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="ref" href="funct_1.html#T68">FUNCT_1:68</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>12</sub></font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>assume </b><a NAME="E1:67_3"/><i><font color="Green">E79</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partfun1.html#K2">|</a> <font color="Maroon">c<sub>11</sub></font></span>)</span>
 ;<br/><a NAME="E2:67_3"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>11</sub></font>
 <b>by </b><i><a class="ref" href="funct_1.html#T68">FUNCT_1:68</a></i>;<br/><a NAME="E3:67_3"/><b>then </b><i><font color="Green">E80</font></i>: 
( <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>11</sub></font> )
 <b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E4:67_3"/><i><font color="Green">E81</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="mesfunc5.html#E13:67"><i><font color="Green">E71</font></i></a>, <a class="txt" href="mesfunc5.html#E11:67"><i><font color="Green">E70</font></i></a>, <a class="txt" href="mesfunc5.html#E14:67"><i><font color="Green">E72</font></i></a>, <a class="ref" href="xboole_1.html#T36">XBOOLE_1:36</a></i>;<br/><i><font color="Green">E82</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partfun1.html#K2">|</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="mesfunc1.html#K4">.</a> <font color="Maroon">c<sub>12</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="mesfunc1.html#K4">.</a> <font color="Maroon">c<sub>12</sub></font>
<b>by </b><i><a class="txt" href="mesfunc5.html#E1:67_3"><i><font color="Green">E79</font></i></a>, <a class="ref" href="funct_1.html#T70">FUNCT_1:70</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="mesfunc1.html#K4">.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="supinf_2.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="mesfunc1.html#K4">.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="mesfunc5.html#E3:67_3"><i><font color="Green">E80</font></i></a>, <a class="ref" href="mesfunc1.html#D3">MESFUNC1:def 3</a></i>
;<br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="partfun1.html#K2">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="mesfunc1.html#K13">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partfun1.html#K2">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span> <a href="mesfunc1.html#K4">.</a> <font color="Maroon">c<sub>12</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="partfun1.html#K2">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="mesfunc1.html#K4">.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="supinf_2.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partfun1.html#K2">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="mesfunc1.html#K4">.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="mesfunc5.html#E20:67"><i><font color="Green">E77</font></i></a>, <a class="txt" href="mesfunc5.html#E21:67"><i><font color="Green">E78</font></i></a>, <a class="txt" href="mesfunc5.html#E13:67"><i><font color="Green">E71</font></i></a>, <a class="txt" href="mesfunc5.html#E1:67_3"><i><font color="Green">E79</font></i></a>, <a class="ref" href="mesfunc1.html#D3">MESFUNC1:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="mesfunc1.html#K4">.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="supinf_2.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partfun1.html#K2">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="mesfunc1.html#K4">.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="mesfunc5.html#E4:67_3"><i><font color="Green">E81</font></i></a>, <a class="txt" href="mesfunc5.html#E11:67"><i><font color="Green">E70</font></i></a>, <a class="txt" href="mesfunc5.html#E3:67_3"><i><font color="Green">E80</font></i></a>, <a class="ref" href="funct_1.html#T70">FUNCT_1:70</a></i>
;<br/><b>hence </b><a NAME="E7:67_3"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partfun1.html#K2">|</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="mesfunc1.html#K4">.</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="partfun1.html#K2">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="mesfunc1.html#K13">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partfun1.html#K2">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span> <a href="mesfunc1.html#K4">.</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="txt" href="mesfunc5.html#E5:67_3"><i><font color="Green">E82</font></i></a>, <a class="txt" href="mesfunc5.html#E4:67_3"><i><font color="Green">E81</font></i></a>, <a class="txt" href="mesfunc5.html#E11:67"><i><font color="Green">E70</font></i></a>, <a class="txt" href="mesfunc5.html#E3:67_3"><i><font color="Green">E80</font></i></a>, <a class="ref" href="funct_1.html#T70">FUNCT_1:70</a></i>;<br/></div><b>end;</b></div>
<a NAME="E23:67"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partfun1.html#K2">|</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="partfun1.html#K2">|</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="mesfunc1.html#K13">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partfun1.html#K2">|</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="measure1.html#K3">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="mesfunc5.html#E20:67"><i><font color="Green">E77</font></i></a>, <a class="txt" href="mesfunc5.html#E21:67"><i><font color="Green">E78</font></i></a>, <a class="txt" href="mesfunc5.html#E13:67"><i><font color="Green">E71</font></i></a>, <a class="ref" href="partfun1.html#T34">PARTFUN1:34</a></i>;<br/>
<b>hence </b><a NAME="E24:67"/>
( <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">c<sub>5</sub></font> <a href="mesfunc1.html#R2">is_measurable_on</a> <font color="Maroon">c<sub>11</sub></font> )
 <b>by </b><i><a class="txt" href="mesfunc5.html#E19:67"><i><font color="Green">E76</font></i></a>, <a class="txt" href="mesfunc5.html#E18:67"><i><font color="Green">E75</font></i></a>, <a class="txt" href="mesfunc5.html#E13:67"><i><font color="Green">E71</font></i></a>, <a class="txt" href="mesfunc5.html#E11:67"><i><font color="Green">E70</font></i></a>, <a class="txt" href="mesfunc5.html#E14:67"><i><font color="Green">E72</font></i></a>, <a class="ref" href="xboole_1.html#T47">XBOOLE_1:47</a>, <a class="txt" href="mesfunc5.html#E4:67"><i><font color="Green">E66</font></i></a>, <a class="txt" href="mesfunc5.html#E6:67"><i><font color="Green">E67</font></i></a>, <a class="txt" href="mesfunc5.html#E66"><i><font color="Green">Lemma61</font></i></a></i>;<br/>


</div>
