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<span class="kw">let </span><font color="Maroon" title="c1">Omega</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">Sigma</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">ASeq</font> being   <a href="prob_1.html#NM4" title="PROB_1:NM.4">SetSequence</a> of <font color="Olive" title="b1">Sigma</font><br/>  for <font color="Olive" title="b3">P</font> being    <a href="prob_1.html#M2" title="PROB_1:mode.2">Probability</a> of <font color="Olive" title="b1">Sigma</font> holds  <font color="Olive" title="b3">P</font> <a href="prob_1.html#K8" title="PROB_1:func.8">*</a> <span class="p1">(<span class="default"><a href="prob_3.html#K2" title="PROB_3:func.2">Partial_Union</a> <font color="Olive" title="b2">ASeq</font></span>)</span> is  <a href="valued_0.html#V7" title="VALUED_0:attr.7">non-decreasing</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">Sigma</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">ASeq</font> being   <a href="prob_1.html#NM4" title="PROB_1:NM.4">SetSequence</a> of <font color="Maroon" title="c2">Sigma</font><br/>  for <font color="Olive" title="b2">P</font> being    <a href="prob_1.html#M2" title="PROB_1:mode.2">Probability</a> of <font color="Maroon" title="c2">Sigma</font> holds  <font color="Olive" title="b2">P</font> <a href="prob_1.html#K8" title="PROB_1:func.8">*</a> <span class="p1">(<span class="default"><a href="prob_3.html#K2" title="PROB_3:func.2">Partial_Union</a> <font color="Olive" title="b1">ASeq</font></span>)</span> is  <a href="valued_0.html#V7" title="VALUED_0:attr.7">non-decreasing</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">ASeq</font> be   <a href="prob_1.html#NM4" title="PROB_1:NM.4">SetSequence</a> of <font color="Maroon" title="c2">Sigma</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">P</font> being    <a href="prob_1.html#M2" title="PROB_1:mode.2">Probability</a> of <font color="Maroon" title="c2">Sigma</font> holds  <font color="Olive" title="b1">P</font> <a href="prob_1.html#K8" title="PROB_1:func.8">*</a> <span class="p1">(<span class="default"><a href="prob_3.html#K2" title="PROB_3:func.2">Partial_Union</a> <font color="Maroon" title="c3">ASeq</font></span>)</span> is  <a href="valued_0.html#V7" title="VALUED_0:attr.7">non-decreasing</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c4">P</font> be    <a href="prob_1.html#M2" title="PROB_1:mode.2">Probability</a> of <font color="Maroon" title="c2">Sigma</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"> <font color="Maroon" title="c4">P</font> <a href="prob_1.html#K8" title="PROB_1:func.8">*</a> <span class="p1">(<span class="default"><a href="prob_3.html#K2" title="PROB_3:func.2">Partial_Union</a> <font color="Maroon" title="c3">ASeq</font></span>)</span> is  <a href="valued_0.html#V7" title="VALUED_0:attr.7">non-decreasing</a> </span><br/>







<a NAME="E1:32"/>
 <a href="prob_3.html#K2" title="PROB_3:func.2">Partial_Union</a> <font color="Maroon" title="c3">ASeq</font> is <a href="prob_1.html#V3" title="PROB_1:attr.3">V75</a>()
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="prob_3.html#T11" target="_self" onmouseover="rs('prob_3/T11')" onmouseout="rh()">Th11</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:32"/>
<font color="Maroon" title="c4">P</font> <a href="prob_1.html#K8" title="PROB_1:func.8">*</a> <span class="p1">(<span class="default"><a href="prob_3.html#K2" title="PROB_3:func.2">Partial_Union</a> <font color="Maroon" title="c3">ASeq</font></span>)</span> is  <a href="valued_0.html#V7" title="VALUED_0:attr.7">non-decreasing</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="prob_3.html#T6" target="_self" onmouseover="rs('prob_3/T6')" onmouseout="rh()">Th6</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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