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<span class="kw">let </span><font color="Maroon" title="c1">p</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</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">Omega</font>, <font color="Olive" title="b2">Omega2</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b3">F</font> being   <a href="prob_1.html#NM3" title="PROB_1:NM.3">SigmaField</a> of <font color="Olive" title="b1">Omega</font><br/>  for <font color="Olive" title="b4">F2</font> being   <a href="prob_1.html#NM3" title="PROB_1:NM.3">SigmaField</a> of <font color="Olive" title="b2">Omega2</font><br/>  for <font color="Olive" title="b5">G</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">sequence</a> of <span class="p1">(<span class="default"><a href="finance1.html#K6" title="FINANCE1:func.6">set_of_random_variables_on</a> (<font color="Olive" title="b3">F</font>,<font color="Olive" title="b4">F2</font>)</span>)</span> holds   <a href="finance1.html#K9" title="FINANCE1:func.9">Element_Of</a> (<font color="Olive" title="b3">F</font>,<font color="Olive" title="b4">F2</font>,<font color="Olive" title="b5">G</font>,<font color="Maroon" title="c1">p</font>) is   <a href="random_3.html#NM1" title="RANDOM_3:NM.1">random_variable</a> of <font color="Olive" title="b3">F</font>,<font color="Olive" title="b4">F2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">Omega</font>, <font color="Maroon" title="c3">Omega2</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <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">F</font> being   <a href="prob_1.html#NM3" title="PROB_1:NM.3">SigmaField</a> of <font color="Maroon" title="c2">Omega</font><br/>  for <font color="Olive" title="b2">F2</font> being   <a href="prob_1.html#NM3" title="PROB_1:NM.3">SigmaField</a> of <font color="Maroon" title="c3">Omega2</font><br/>  for <font color="Olive" title="b3">G</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">sequence</a> of <span class="p1">(<span class="default"><a href="finance1.html#K6" title="FINANCE1:func.6">set_of_random_variables_on</a> (<font color="Olive" title="b1">F</font>,<font color="Olive" title="b2">F2</font>)</span>)</span> holds   <a href="finance1.html#K9" title="FINANCE1:func.9">Element_Of</a> (<font color="Olive" title="b1">F</font>,<font color="Olive" title="b2">F2</font>,<font color="Olive" title="b3">G</font>,<font color="Maroon" title="c1">p</font>) is   <a href="random_3.html#NM1" title="RANDOM_3:NM.1">random_variable</a> of <font color="Olive" title="b1">F</font>,<font color="Olive" title="b2">F2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">F</font> be   <a href="prob_1.html#NM3" title="PROB_1:NM.3">SigmaField</a> of <font color="Maroon" title="c2">Omega</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">F2</font> being   <a href="prob_1.html#NM3" title="PROB_1:NM.3">SigmaField</a> of <font color="Maroon" title="c3">Omega2</font><br/>  for <font color="Olive" title="b2">G</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">sequence</a> of <span class="p1">(<span class="default"><a href="finance1.html#K6" title="FINANCE1:func.6">set_of_random_variables_on</a> (<font color="Maroon" title="c4">F</font>,<font color="Olive" title="b1">F2</font>)</span>)</span> holds   <a href="finance1.html#K9" title="FINANCE1:func.9">Element_Of</a> (<font color="Maroon" title="c4">F</font>,<font color="Olive" title="b1">F2</font>,<font color="Olive" title="b2">G</font>,<font color="Maroon" title="c1">p</font>) is   <a href="random_3.html#NM1" title="RANDOM_3:NM.1">random_variable</a> of <font color="Maroon" title="c4">F</font>,<font color="Olive" title="b1">F2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">F2</font> be   <a href="prob_1.html#NM3" title="PROB_1:NM.3">SigmaField</a> of <font color="Maroon" title="c3">Omega2</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">G</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">sequence</a> of <span class="p1">(<span class="default"><a href="finance1.html#K6" title="FINANCE1:func.6">set_of_random_variables_on</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> holds   <a href="finance1.html#K9" title="FINANCE1:func.9">Element_Of</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">F2</font>,<font color="Olive" title="b1">G</font>,<font color="Maroon" title="c1">p</font>) is   <a href="random_3.html#NM1" title="RANDOM_3:NM.1">random_variable</a> of <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">F2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c6">G</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">sequence</a> of <span class="p1">(<span class="default"><a href="finance1.html#K6" title="FINANCE1:func.6">set_of_random_variables_on</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">F2</font>)</span>)</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">  <a href="finance1.html#K9" title="FINANCE1:func.9">Element_Of</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">F2</font>,<font color="Maroon" title="c6">G</font>,<font color="Maroon" title="c1">p</font>) is   <a href="random_3.html#NM1" title="RANDOM_3:NM.1">random_variable</a> of <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">F2</font></span><br/>









<a NAME="E1:44"/>
<font color="Maroon" title="c6">G</font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c1">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finance1.html#K6" title="FINANCE1:func.6">set_of_random_variables_on</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">F2</font>)
 
;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">Y</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c2">Omega</font>,<font color="Maroon" title="c3">Omega2</font><span class="kw"> such that </span><br/><a NAME="E3:44"/><span class="lab"><font color="Green" title="E20">A2</font></span>: 
( <font color="Maroon" title="c6">G</font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">Y</font> &amp; <font color="Maroon" title="c7">Y</font> is <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">F2</font> <a href="finance1.html#V1" title="FINANCE1:attr.1">-random_variable-like</a>  )
 ;<br/>
<a NAME="E4:44"/>
 <a href="finance1.html#K9" title="FINANCE1:func.9">Element_Of</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">F2</font>,<font color="Maroon" title="c6">G</font>,<font color="Maroon" title="c1">p</font>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c7">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finance1.html#D9" onmouseover="rs('finance1/D9')" onmouseout="rh()">FINANCE1:def 9</a>, <a class="txt" href="#E3:44"><span class="lab"><font color="Green" title="E20">A2</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:44"/>
 <a href="finance1.html#K9" title="FINANCE1:func.9">Element_Of</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">F2</font>,<font color="Maroon" title="c6">G</font>,<font color="Maroon" title="c1">p</font>) is   <a href="random_3.html#NM1" title="RANDOM_3:NM.1">random_variable</a> of <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">F2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:44"><span class="lab"><font color="Green" title="E20">A2</font></span></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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