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<b>let </b><font color="Maroon" title="c1">C</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</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">f1</font>, <font color="Olive" title="b2">f</font>, <font color="Olive" title="b3">g1</font>, <font color="Olive" title="b4">g</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c1">C</font>, <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>  holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">f1</font> <a href="cfunct_1.html#K1" title="CFUNCT_1:func.1">/</a> <font color="Olive" title="b2">f</font></span>)</span> <a href="valued_1.html#K2" title="VALUED_1:func.2">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">g1</font> <a href="cfunct_1.html#K1" title="CFUNCT_1:func.1">/</a> <font color="Olive" title="b4">g</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">f1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Olive" title="b4">g</font></span>)</span> <a href="valued_1.html#K2" title="VALUED_1:func.2">+</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">g1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Olive" title="b2">f</font></span>)</span></span>)</span> <a href="cfunct_1.html#K1" title="CFUNCT_1:func.1">/</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Olive" title="b4">g</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">f1</font>, <font color="Maroon" title="c3">f</font>, <font color="Maroon" title="c4">g1</font>, <font color="Maroon" title="c5">g</font> be   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c1">C</font>, <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> ; <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"><font color="Maroon" title="c2">f1</font> <a href="cfunct_1.html#K1" title="CFUNCT_1:func.1">/</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="valued_1.html#K2" title="VALUED_1:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="cfunct_1.html#K1" title="CFUNCT_1:func.1">/</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="valued_1.html#K2" title="VALUED_1:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c3">f</font></span>)</span></span>)</span> <a href="cfunct_1.html#K1" title="CFUNCT_1:func.1">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span></span><br/>









<i><font color="Green" title="E34">A1</font></i>:  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="cfunct_1.html#K1" title="CFUNCT_1:func.1">/</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="valued_1.html#K2" title="VALUED_1:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="cfunct_1.html#K1" title="CFUNCT_1:func.1">/</a> <font color="Maroon" title="c5">g</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="cfunct_1.html#K1" title="CFUNCT_1:func.1">/</a> <font color="Maroon" title="c3">f</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="cfunct_1.html#K1" title="CFUNCT_1:func.1">/</a> <font color="Maroon" title="c5">g</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="valued_1.html#D1" title="VALUED_1:def.1">VALUED_1:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">f1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p4"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="cfunct_1.html#K1" title="CFUNCT_1:func.1">/</a> <font color="Maroon" title="c5">g</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="cfunct_1.html#D1" target="_self" title="CFUNCT_1:def.1">Def1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">f1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p4"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">g1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p4"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="cfunct_1.html#D1" target="_self" title="CFUNCT_1:def.1">Def1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">f1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p5"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">g1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p4"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="cfunct_1.html#T15" target="_self" title="CFUNCT_1:th.15">Th15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p5"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">f1</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p5"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">g1</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="cfunct_1.html#T15" target="_self" title="CFUNCT_1:th.15">Th15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p4"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">f1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p0"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p3">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">g1</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T16" title="XBOOLE_1:th.16">XBOOLE_1:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p4"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">f1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p0"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">g1</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T16" title="XBOOLE_1:th.16">XBOOLE_1:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p4"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">f1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p4">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c5">g</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p5"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">g1</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T16" title="XBOOLE_1:th.16">XBOOLE_1:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p4"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p5"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">g1</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="cfunct_1.html#T5" target="_self" title="CFUNCT_1:th.5">Th5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p4"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">g1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p5"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T16" title="XBOOLE_1:th.16">XBOOLE_1:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p5"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p3">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">g1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p5"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T16" title="XBOOLE_1:th.16">XBOOLE_1:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p4"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">g1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p0"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T16" title="XBOOLE_1:th.16">XBOOLE_1:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p4"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">g1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p4">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p5"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T16" title="XBOOLE_1:th.16">XBOOLE_1:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p4"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c3">f</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p5"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="cfunct_1.html#T5" target="_self" title="CFUNCT_1:th.5">Th5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c3">f</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p5"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p5"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T16" title="XBOOLE_1:th.16">XBOOLE_1:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c3">f</font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p4"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p4"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T16" title="XBOOLE_1:th.16">XBOOLE_1:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="valued_1.html#K2" title="VALUED_1:func.2">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c3">f</font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p4"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p4"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="valued_1.html#D1" title="VALUED_1:def.1">VALUED_1:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="valued_1.html#K2" title="VALUED_1:func.2">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c3">f</font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="cfunct_1.html#T16" target="_self" title="CFUNCT_1:th.16">Th16</a></i>
<br/>.= 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="valued_1.html#K2" title="VALUED_1:func.2">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c3">f</font></span>)</span></span>)</span> <a href="cfunct_1.html#K1" title="CFUNCT_1:func.1">/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="cfunct_1.html#D1" target="_self" title="CFUNCT_1:def.1">Def1</a></i>
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="45_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c6">c</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">C</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c6">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="cfunct_1.html#K1" title="CFUNCT_1:func.1">/</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="valued_1.html#K2" title="VALUED_1:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="cfunct_1.html#K1" title="CFUNCT_1:func.1">/</a> <font color="Maroon" title="c5">g</font></span>)</span></span>)</span> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="cfunct_1.html#K1" title="CFUNCT_1:func.1">/</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="valued_1.html#K2" title="VALUED_1:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="cfunct_1.html#K1" title="CFUNCT_1:func.1">/</a> <font color="Maroon" title="c5">g</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="valued_1.html#K2" title="VALUED_1:func.2">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c3">f</font></span>)</span></span>)</span> <a href="cfunct_1.html#K1" title="CFUNCT_1:func.1">/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font> )</span><br/><b>assume </b><a NAME="E1:45_2"/><i><font color="Green" title="E35">A2</font></i>: 
<font color="Maroon" title="c6">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="cfunct_1.html#K1" title="CFUNCT_1:func.1">/</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="valued_1.html#K2" title="VALUED_1:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="cfunct_1.html#K1" title="CFUNCT_1:func.1">/</a> <font color="Maroon" title="c5">g</font></span>)</span></span>)</span>
 ; <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"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="cfunct_1.html#K1" title="CFUNCT_1:func.1">/</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="valued_1.html#K2" title="VALUED_1:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="cfunct_1.html#K1" title="CFUNCT_1:func.1">/</a> <font color="Maroon" title="c5">g</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="valued_1.html#K2" title="VALUED_1:func.2">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c3">f</font></span>)</span></span>)</span> <a href="cfunct_1.html#K1" title="CFUNCT_1:func.1">/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span><br/><a NAME="E2:45_2"/><b>then </b><i><font color="Green" title="E36">A3</font></i>: 
<font color="Maroon" title="c6">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="cfunct_1.html#K1" title="CFUNCT_1:func.1">/</a> <font color="Maroon" title="c3">f</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="cfunct_1.html#K1" title="CFUNCT_1:func.1">/</a> <font color="Maroon" title="c5">g</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="valued_1.html#D1" title="VALUED_1:def.1">VALUED_1:def 1</a></i>;<br/><a NAME="E3:45_2"/><b>then </b><i><font color="Green" title="E37">A4</font></i>: 
( <font color="Maroon" title="c6">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="cfunct_1.html#K1" title="CFUNCT_1:func.1">/</a> <font color="Maroon" title="c3">f</font></span>)</span> &amp; <font color="Maroon" title="c6">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="cfunct_1.html#K1" title="CFUNCT_1:func.1">/</a> <font color="Maroon" title="c5">g</font></span>)</span> )
 <b>by </b><i><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E4:45_2"/>
<font color="Maroon" title="c6">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="cfunct_1.html#K2" title="CFUNCT_1:func.2">^</a> </span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="cfunct_1.html#K1" title="CFUNCT_1:func.1">/</a> <font color="Maroon" title="c5">g</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E2:45_2"><i><font color="Green" title="E36">A3</font></i></a>, <a class="ref" href="cfunct_1.html#T51" target="_self" title="CFUNCT_1:th.51">Th51</a></i>;<br/><a NAME="E5:45_2"/><b>then </b>
<font color="Maroon" title="c6">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="cfunct_1.html#K2" title="CFUNCT_1:func.2">^</a> </span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="cfunct_1.html#K2" title="CFUNCT_1:func.2">^</a> </span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="cfunct_1.html#T51" target="_self" title="CFUNCT_1:th.51">Th51</a></i>;<br/><a NAME="E6:45_2"/><b>then </b>
( <font color="Maroon" title="c6">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="cfunct_1.html#K2" title="CFUNCT_1:func.2">^</a> </span>)</span></span>)</span> &amp; <font color="Maroon" title="c6">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="cfunct_1.html#K2" title="CFUNCT_1:func.2">^</a> </span>)</span></span>)</span> )
 <b>by </b><i><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E7:45_2"/><b>then </b>
( <font color="Maroon" title="c6">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">f1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="cfunct_1.html#K2" title="CFUNCT_1:func.2">^</a> </span>)</span></span>)</span> &amp; <font color="Maroon" title="c6">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">g1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="cfunct_1.html#K2" title="CFUNCT_1:func.2">^</a> </span>)</span></span>)</span> )
 <b>by </b><i><a class="ref" href="cfunct_1.html#T5" target="_self" title="CFUNCT_1:th.5">Th5</a></i>;<br/><a NAME="E8:45_2"/><b>then </b><i><font color="Green" title="E38">A5</font></i>: 
( <font color="Maroon" title="c6">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">f1</font> &amp; <font color="Maroon" title="c6">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="cfunct_1.html#K2" title="CFUNCT_1:func.2">^</a> </span>)</span> &amp; <font color="Maroon" title="c6">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">g1</font> &amp; <font color="Maroon" title="c6">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="cfunct_1.html#K2" title="CFUNCT_1:func.2">^</a> </span>)</span> )
 <b>by </b><i><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E9:45_2"/><b>then </b><i><font color="Green" title="E39">A6</font></i>: 
( <font color="Maroon" title="c3">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a>  &amp; <font color="Maroon" title="c5">g</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a>  )
 <b>by </b><i><a class="ref" href="cfunct_1.html#T17" target="_self" title="CFUNCT_1:th.17">Th17</a></i>;<br/><a NAME="E10:45_2"/>
( <font color="Maroon" title="c6">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">f1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">g1</font></span>)</span> &amp; <font color="Maroon" title="c6">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="cfunct_1.html#K2" title="CFUNCT_1:func.2">^</a> </span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="cfunct_1.html#K2" title="CFUNCT_1:func.2">^</a> </span>)</span></span>)</span> )
 <b>by </b><i><a class="txt" href="#E8:45_2"><i><font color="Green" title="E38">A5</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E11:45_2"/><b>then </b>
( <font color="Maroon" title="c6">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">f1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">g1</font></span>)</span> &amp; <font color="Maroon" title="c6">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="cfunct_1.html#K2" title="CFUNCT_1:func.2">^</a> </span>)</span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="cfunct_1.html#K2" title="CFUNCT_1:func.2">^</a> </span>)</span></span>)</span> )
 <b>by </b><i><a class="ref" href="cfunct_1.html#T5" target="_self" title="CFUNCT_1:th.5">Th5</a></i>;<br/><a NAME="E12:45_2"/><b>then </b><i><font color="Green" title="E40">A7</font></i>: 
( <font color="Maroon" title="c6">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">f1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">g1</font></span>)</span> &amp; <font color="Maroon" title="c6">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="cfunct_1.html#K2" title="CFUNCT_1:func.2">^</a> </span>)</span> )
 <b>by </b><i><a class="ref" href="cfunct_1.html#T45" target="_self" title="CFUNCT_1:th.45">Th45</a></i>;<br/><a NAME="E13:45_2"/><i><font color="Green" title="E41">A8</font></i>: 
(  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="cfunct_1.html#K2" title="CFUNCT_1:func.2">^</a> </span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c5">g</font> &amp;  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="cfunct_1.html#K2" title="CFUNCT_1:func.2">^</a> </span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f</font> )
 <b>by </b><i><a class="ref" href="cfunct_1.html#T15" target="_self" title="CFUNCT_1:th.15">Th15</a></i>;<br/><a NAME="E14:45_2"/><b>then </b>
<font color="Maroon" title="c6">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c5">g</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E8:45_2"><i><font color="Green" title="E38">A5</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E15:45_2"/><b>then </b><i><font color="Green" title="E42">A9</font></i>: 
<font color="Maroon" title="c6">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span>
 <b>by </b><i><a class="ref" href="cfunct_1.html#T5" target="_self" title="CFUNCT_1:th.5">Th5</a></i>;<br/><a NAME="E16:45_2"/>
( <font color="Maroon" title="c6">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">f1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c5">g</font></span>)</span> &amp; <font color="Maroon" title="c6">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">g1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f</font></span>)</span> )
 <b>by </b><i><a class="txt" href="#E8:45_2"><i><font color="Green" title="E38">A5</font></i></a>, <a class="txt" href="#E13:45_2"><i><font color="Green" title="E41">A8</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E17:45_2"/><b>then </b><i><font color="Green" title="E43">A10</font></i>: 
( <font color="Maroon" title="c6">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span> &amp; <font color="Maroon" title="c6">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c3">f</font></span>)</span> )
 <b>by </b><i><a class="ref" href="cfunct_1.html#T5" target="_self" title="CFUNCT_1:th.5">Th5</a></i>;<br/><a NAME="E18:45_2"/><b>then </b>
<font color="Maroon" title="c6">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c3">f</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E19:45_2"/><b>then </b><i><font color="Green" title="E44">A11</font></i>: 
<font color="Maroon" title="c6">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="valued_1.html#K2" title="VALUED_1:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c3">f</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="valued_1.html#D1" title="VALUED_1:def.1">VALUED_1:def 1</a></i>;<br/><a NAME="E20:45_2"/><b>then </b>
<font color="Maroon" title="c6">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="valued_1.html#K2" title="VALUED_1:func.2">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c3">f</font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="cfunct_1.html#K2" title="CFUNCT_1:func.2">^</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E12:45_2"><i><font color="Green" title="E40">A7</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E21:45_2"/><b>then </b>
<font color="Maroon" title="c6">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="valued_1.html#K2" title="VALUED_1:func.2">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c3">f</font></span>)</span></span>)</span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="cfunct_1.html#K2" title="CFUNCT_1:func.2">^</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="cfunct_1.html#T5" target="_self" title="CFUNCT_1:th.5">Th5</a></i>;<br/><a NAME="E22:45_2"/><b>then </b><i><font color="Green" title="E45">A12</font></i>: 
<font color="Maroon" title="c6">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="valued_1.html#K2" title="VALUED_1:func.2">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c3">f</font></span>)</span></span>)</span> <a href="cfunct_1.html#K1" title="CFUNCT_1:func.1">/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="cfunct_1.html#T51" target="_self" title="CFUNCT_1:th.51">Th51</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="cfunct_1.html#K1" title="CFUNCT_1:func.1">/</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="valued_1.html#K2" title="VALUED_1:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="cfunct_1.html#K1" title="CFUNCT_1:func.1">/</a> <font color="Maroon" title="c5">g</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="cfunct_1.html#K1" title="CFUNCT_1:func.1">/</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K8" title="COMPLEX1:func.8">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="cfunct_1.html#K1" title="CFUNCT_1:func.1">/</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span>
<b>by </b><i><a class="txt" href="#E1:45_2"><i><font color="Green" title="E35">A2</font></i></a>, <a class="ref" href="cfunct_1.html#T3" target="_self" title="CFUNCT_1:th.3">Th3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K12" title="COMPLEX1:func.12">"</a> </span>)</span></span>)</span> <a href="complex1.html#K8" title="COMPLEX1:func.8">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="cfunct_1.html#K1" title="CFUNCT_1:func.1">/</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span>
<b>by </b><i><a class="txt" href="#E3:45_2"><i><font color="Green" title="E37">A4</font></i></a>, <a class="ref" href="cfunct_1.html#D1" target="_self" title="CFUNCT_1:def.1">Def1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p2">(<span class="default"><a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a>  <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K12" title="COMPLEX1:func.12">"</a> </span>)</span></span>)</span></span>)</span> <a href="complex1.html#K8" title="COMPLEX1:func.8">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> </span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K12" title="COMPLEX1:func.12">"</a> </span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E3:45_2"><i><font color="Green" title="E37">A4</font></i></a>, <a class="ref" href="cfunct_1.html#D1" target="_self" title="CFUNCT_1:def.1">Def1</a>, <a class="ref" href="complex1.html#D7" title="COMPLEX1:def.7">COMPLEX1:def 7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K12" title="COMPLEX1:func.12">"</a> </span>)</span></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K12" title="COMPLEX1:func.12">"</a> </span>)</span></span>)</span></span>)</span> <a href="complex1.html#K8" title="COMPLEX1:func.8">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p2">(<span class="default"><a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a>  <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K12" title="COMPLEX1:func.12">"</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E9:45_2"><i><font color="Green" title="E39">A6</font></i></a>, <a class="ref" href="complex1.html#D7" title="COMPLEX1:def.7">COMPLEX1:def 7</a>, <a class="ref" href="xcmplx_0.html#D7" title="XCMPLX_0:def.7">XCMPLX_0:def 7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K12" title="COMPLEX1:func.12">"</a> </span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K12" title="COMPLEX1:func.12">"</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K8" title="COMPLEX1:func.8">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K12" title="COMPLEX1:func.12">"</a> </span>)</span></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K12" title="COMPLEX1:func.12">"</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E9:45_2"><i><font color="Green" title="E39">A6</font></i></a>, <a class="ref" href="complex1.html#D7" title="COMPLEX1:def.7">COMPLEX1:def 7</a>, <a class="ref" href="xcmplx_0.html#D7" title="XCMPLX_0:def.7">XCMPLX_0:def 7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span></span>)</span> <a href="complex1.html#K12" title="COMPLEX1:func.12">"</a> </span>)</span></span>)</span></span>)</span> <a href="complex1.html#K8" title="COMPLEX1:func.8">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K12" title="COMPLEX1:func.12">"</a> </span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K12" title="COMPLEX1:func.12">"</a> </span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T205" title="XCMPLX_1:th.205">XCMPLX_1:205</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span></span>)</span> <a href="complex1.html#K12" title="COMPLEX1:func.12">"</a> </span>)</span></span>)</span></span>)</span> <a href="complex1.html#K8" title="COMPLEX1:func.8">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span></span>)</span> <a href="complex1.html#K12" title="COMPLEX1:func.12">"</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T205" title="XCMPLX_1:th.205">XCMPLX_1:205</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K12" title="COMPLEX1:func.12">"</a> </span>)</span></span>)</span></span>)</span> <a href="complex1.html#K8" title="COMPLEX1:func.8">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span></span>)</span> <a href="complex1.html#K12" title="COMPLEX1:func.12">"</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E15:45_2"><i><font color="Green" title="E42">A9</font></i></a>, <a class="ref" href="cfunct_1.html#T5" target="_self" title="CFUNCT_1:th.5">Th5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K12" title="COMPLEX1:func.12">"</a> </span>)</span></span>)</span> <a href="complex1.html#K8" title="COMPLEX1:func.8">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K12" title="COMPLEX1:func.12">"</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E15:45_2"><i><font color="Green" title="E42">A9</font></i></a>, <a class="ref" href="cfunct_1.html#T5" target="_self" title="CFUNCT_1:th.5">Th5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K12" title="COMPLEX1:func.12">"</a> </span>)</span></span>)</span> <a href="complex1.html#K8" title="COMPLEX1:func.8">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K12" title="COMPLEX1:func.12">"</a> </span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E17:45_2"><i><font color="Green" title="E43">A10</font></i></a>, <a class="ref" href="cfunct_1.html#T5" target="_self" title="CFUNCT_1:th.5">Th5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K12" title="COMPLEX1:func.12">"</a> </span>)</span></span>)</span> <a href="complex1.html#K8" title="COMPLEX1:func.8">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K12" title="COMPLEX1:func.12">"</a> </span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E17:45_2"><i><font color="Green" title="E43">A10</font></i></a>, <a class="ref" href="cfunct_1.html#T5" target="_self" title="CFUNCT_1:th.5">Th5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K8" title="COMPLEX1:func.8">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K12" title="COMPLEX1:func.12">"</a> </span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="valued_1.html#K2" title="VALUED_1:func.2">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c3">f</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="complex1.html#K12" title="COMPLEX1:func.12">"</a> </span>)</span>
<b>by </b><i><a class="txt" href="#E19:45_2"><i><font color="Green" title="E44">A11</font></i></a>, <a class="ref" href="cfunct_1.html#T3" target="_self" title="CFUNCT_1:th.3">Th3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="valued_1.html#K2" title="VALUED_1:func.2">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c3">f</font></span>)</span></span>)</span> <a href="cfunct_1.html#K1" title="CFUNCT_1:func.1">/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">c</font>
<b>by </b><i><a class="txt" href="#E22:45_2"><i><font color="Green" title="E45">A12</font></i></a>, <a class="ref" href="cfunct_1.html#D1" target="_self" title="CFUNCT_1:def.1">Def1</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:45"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="cfunct_1.html#K1" title="CFUNCT_1:func.1">/</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="valued_1.html#K2" title="VALUED_1:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="cfunct_1.html#K1" title="CFUNCT_1:func.1">/</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="valued_1.html#K2" title="VALUED_1:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c3">f</font></span>)</span></span>)</span> <a href="cfunct_1.html#K1" title="CFUNCT_1:func.1">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E1:45"><i><font color="Green" title="E34">A1</font></i></a>, <a class="ref" href="partfun2.html#T3" title="PARTFUN2:th.3">PARTFUN2:3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
