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<span class="kw">let </span><font color="Maroon" title="c1">Omega</font>, <font color="Maroon" title="c2">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="c1">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="c2">Omega2</font><br/>  for <font color="Olive" title="b3">k</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <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>) holds   <a href="finance1.html#K7" title="FINANCE1:func.7">Change_Element_to_Func</a> (<font color="Olive" title="b1">F</font>,<font color="Olive" title="b2">F2</font>,<font color="Olive" title="b3">k</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="c3">F</font> be   <a href="prob_1.html#NM3" title="PROB_1:NM.3">SigmaField</a> of <font color="Maroon" title="c1">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="c2">Omega2</font><br/>  for <font color="Olive" title="b2">k</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="finance1.html#K6" title="FINANCE1:func.6">set_of_random_variables_on</a> (<font color="Maroon" title="c3">F</font>,<font color="Olive" title="b1">F2</font>) holds   <a href="finance1.html#K7" title="FINANCE1:func.7">Change_Element_to_Func</a> (<font color="Maroon" title="c3">F</font>,<font color="Olive" title="b1">F2</font>,<font color="Olive" title="b2">k</font>) is   <a href="random_3.html#NM1" title="RANDOM_3:NM.1">random_variable</a> of <font color="Maroon" title="c3">F</font>,<font color="Olive" title="b1">F2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">F2</font> be   <a href="prob_1.html#NM3" title="PROB_1:NM.3">SigmaField</a> of <font color="Maroon" title="c2">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">k</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="finance1.html#K6" title="FINANCE1:func.6">set_of_random_variables_on</a> (<font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">F2</font>) holds   <a href="finance1.html#K7" title="FINANCE1:func.7">Change_Element_to_Func</a> (<font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">F2</font>,<font color="Olive" title="b1">k</font>) is   <a href="random_3.html#NM1" title="RANDOM_3:NM.1">random_variable</a> of <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">F2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">k</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="finance1.html#K6" title="FINANCE1:func.6">set_of_random_variables_on</a> (<font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">F2</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">  <a href="finance1.html#K7" title="FINANCE1:func.7">Change_Element_to_Func</a> (<font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">F2</font>,<font color="Maroon" title="c5">k</font>) is   <a href="random_3.html#NM1" title="RANDOM_3:NM.1">random_variable</a> of <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">F2</font></span><br/>







<a NAME="E1:42"/>
 <a href="finance1.html#K7" title="FINANCE1:func.7">Change_Element_to_Func</a> (<font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">F2</font>,<font color="Maroon" title="c5">k</font>) is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"> { <span class="default"> <font color="Olive" title="b1">f</font> where <font color="Olive" title="b1">f</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">Omega</font>,<font color="Maroon" title="c2">Omega2</font> : <font color="Olive" title="b1">f</font> is <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">F2</font> <a href="finance1.html#V1" title="FINANCE1:attr.1">-random_variable-like</a>  </span> } </span> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finance1.html#D7" onmouseover="rs('finance1/D7')" onmouseout="rh()">FINANCE1:def 7</a></span>;<br/>
<a NAME="E2:42"/><span class="kw">then </span>
 <a href="finance1.html#K7" title="FINANCE1:func.7">Change_Element_to_Func</a> (<font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">F2</font>,<font color="Maroon" title="c5">k</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">f</font> where <font color="Olive" title="b1">f</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">Omega</font>,<font color="Maroon" title="c2">Omega2</font> : <font color="Olive" title="b1">f</font> is <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">F2</font> <a href="finance1.html#V1" title="FINANCE1:attr.1">-random_variable-like</a>  </span> } </span> 
 
;<br/>
<a NAME="E3:42"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">Y</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">Omega</font>,<font color="Maroon" title="c2">Omega2</font> st <br/>(  <a href="finance1.html#K7" title="FINANCE1:func.7">Change_Element_to_Func</a> (<font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">F2</font>,<font color="Maroon" title="c5">k</font>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b1">Y</font> &amp; <font color="Olive" title="b1">Y</font> is <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">F2</font> <a href="finance1.html#V1" title="FINANCE1:attr.1">-random_variable-like</a>  )
 
;<br/>
<span class="kw">hence </span><a NAME="E4:42"/>
 <a href="finance1.html#K7" title="FINANCE1:func.7">Change_Element_to_Func</a> (<font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">F2</font>,<font color="Maroon" title="c5">k</font>) is   <a href="random_3.html#NM1" title="RANDOM_3:NM.1">random_variable</a> of <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">F2</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"> verum</span><br/>


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