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<b>let </b><font color="Maroon" title="c1">E</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">A</font>, <font color="Olive" title="b2">B</font> being  <a href="rpr_1.html#NM2" title="RPR_1:NM.2">Event</a> of <font color="Maroon" title="c1">E</font> holds  <span class="p1">(<span class="default"><a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <font color="Olive" title="b1">A</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <font color="Olive" title="b2">B</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">A</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Olive" title="b2">B</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">A</font>, <font color="Maroon" title="c3">B</font> be   <a href="rpr_1.html#NM2" title="RPR_1:NM.2">Event</a> of <font color="Maroon" title="c1">E</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <font color="Maroon" title="c3">B</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c3">B</font></span>)</span></span><br/>



<a NAME="E1:36"/>
 <a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">B</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <font color="Maroon" title="c3">B</font>
 
<b>by </b><i><a class="ref" href="rpr_1.html#T44" target="_self" title="RPR_1:th.44">Th44</a>, <a class="ref" href="xboole_1.html#T17" title="XBOOLE_1:th.17">XBOOLE_1:17</a></i>;<br/>
<a NAME="E2:36"/><b>then </b>
<span class="p1">(<span class="default"><a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <font color="Maroon" title="c3">B</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">B</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="real_1.html#T92" title="REAL_1:th.92">REAL_1:92</a></i>;<br/>
<b>hence </b><a NAME="E3:36"/>
<span class="p1">(<span class="default"><a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <font color="Maroon" title="c3">B</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c3">B</font></span>)</span>
 <b>by </b><i><a class="ref" href="rpr_1.html#T49" target="_self" title="RPR_1:th.49">Th49</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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