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<span class="kw">let </span><font color="Maroon" title="c1">Y</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">a</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">Y</font>,<a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</a><br/>  for <font color="Olive" title="b2">G</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="bvfunc_2.html#K1" title="BVFUNC_2:func.1">PARTITIONS</a> <font color="Maroon" title="c1">Y</font></span>)</span><br/>  for <font color="Olive" title="b3">PA</font>, <font color="Olive" title="b4">PB</font> being    <a href="eqrel_1.html#M1" title="EQREL_1:mode.1">a_partition</a> of <font color="Maroon" title="c1">Y</font> holds   <a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">PA</font>,<font color="Olive" title="b2">G</font>) <a href="bvfunc_1.html#R1" title="BVFUNC_1:pred.1">'&lt;'</a>  <a href="bvfunc_2.html#K7" title="BVFUNC_2:func.7">Ex</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b4">PB</font>,<font color="Olive" title="b2">G</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">Y</font>,<a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</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">G</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="bvfunc_2.html#K1" title="BVFUNC_2:func.1">PARTITIONS</a> <font color="Maroon" title="c1">Y</font></span>)</span><br/>  for <font color="Olive" title="b2">PA</font>, <font color="Olive" title="b3">PB</font> being    <a href="eqrel_1.html#M1" title="EQREL_1:mode.1">a_partition</a> of <font color="Maroon" title="c1">Y</font> holds   <a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c2">a</font>,<font color="Olive" title="b2">PA</font>,<font color="Olive" title="b1">G</font>) <a href="bvfunc_1.html#R1" title="BVFUNC_1:pred.1">'&lt;'</a>  <a href="bvfunc_2.html#K7" title="BVFUNC_2:func.7">Ex</a> (<font color="Maroon" title="c2">a</font>,<font color="Olive" title="b3">PB</font>,<font color="Olive" title="b1">G</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c3">G</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="bvfunc_2.html#K1" title="BVFUNC_2:func.1">PARTITIONS</a> <font color="Maroon" title="c1">Y</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">  for <font color="Olive" title="b1">PA</font>, <font color="Olive" title="b2">PB</font> being    <a href="eqrel_1.html#M1" title="EQREL_1:mode.1">a_partition</a> of <font color="Maroon" title="c1">Y</font> holds   <a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c2">a</font>,<font color="Olive" title="b1">PA</font>,<font color="Maroon" title="c3">G</font>) <a href="bvfunc_1.html#R1" title="BVFUNC_1:pred.1">'&lt;'</a>  <a href="bvfunc_2.html#K7" title="BVFUNC_2:func.7">Ex</a> (<font color="Maroon" title="c2">a</font>,<font color="Olive" title="b2">PB</font>,<font color="Maroon" title="c3">G</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c4">PA</font>, <font color="Maroon" title="c5">PB</font> be    <a href="eqrel_1.html#M1" title="EQREL_1:mode.1">a_partition</a> of <font color="Maroon" title="c1">Y</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="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">PA</font>,<font color="Maroon" title="c3">G</font>) <a href="bvfunc_1.html#R1" title="BVFUNC_1:pred.1">'&lt;'</a>  <a href="bvfunc_2.html#K7" title="BVFUNC_2:func.7">Ex</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">PB</font>,<font color="Maroon" title="c3">G</font>)</span><br/>







<a NAME="E1:17"/>
(  <a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">PA</font>,<font color="Maroon" title="c3">G</font>) <a href="bvfunc_1.html#R1" title="BVFUNC_1:pred.1">'&lt;'</a> <font color="Maroon" title="c2">a</font> &amp; <font color="Maroon" title="c2">a</font> <a href="bvfunc_1.html#R1" title="BVFUNC_1:pred.1">'&lt;'</a>  <a href="bvfunc_2.html#K7" title="BVFUNC_2:func.7">Ex</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">PB</font>,<font color="Maroon" title="c3">G</font>) )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="bvfunc_2.html#T11" onmouseover="rs('bvfunc_2/T11')" onmouseout="rh()">BVFUNC_2:11</a>, <a class="ref" href="bvfunc_2.html#T12" onmouseover="rs('bvfunc_2/T12')" onmouseout="rh()">BVFUNC_2:12</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:17"/>
 <a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">PA</font>,<font color="Maroon" title="c3">G</font>) <a href="bvfunc_1.html#R1" title="BVFUNC_1:pred.1">'&lt;'</a>  <a href="bvfunc_2.html#K7" title="BVFUNC_2:func.7">Ex</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">PB</font>,<font color="Maroon" title="c3">G</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="bvfunc_1.html#T15" onmouseover="rs('bvfunc_1/T15')" onmouseout="rh()">BVFUNC_1:15</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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