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<b>let </b><font color="Maroon" title="c1">X</font>, <font color="Maroon" title="c2">Y</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">A</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <br/> for <font color="Olive" title="b2">B</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="finsub_1.html#K5" title="FINSUB_1:func.5">Fin</a> <font color="Maroon" title="c1">X</font><br/> for <font color="Olive" title="b3">f</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font><br/> for <font color="Olive" title="b4">g</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c2">Y</font>, <a href="finsub_1.html#K5" title="FINSUB_1:func.5">Fin</a> <font color="Olive" title="b1">A</font> holds   <a href="setwiseo.html#K10" title="SETWISEO:func.10">FinUnion</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">f</font> <a href="setwiseo.html#K8" title="SETWISEO:func.8">.:</a> <font color="Olive" title="b2">B</font></span>)</span>,<font color="Olive" title="b4">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="setwiseo.html#K10" title="SETWISEO:func.10">FinUnion</a> <font color="Olive" title="b2">B</font>,<span class="p1">(<span class="default"><font color="Olive" title="b4">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b3">f</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c3">A</font> be    <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">B</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="finsub_1.html#K5" title="FINSUB_1:func.5">Fin</a> <font color="Maroon" title="c1">X</font><br/> for <font color="Olive" title="b2">f</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font><br/> for <font color="Olive" title="b3">g</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c2">Y</font>, <a href="finsub_1.html#K5" title="FINSUB_1:func.5">Fin</a> <font color="Maroon" title="c3">A</font> holds   <a href="setwiseo.html#K10" title="SETWISEO:func.10">FinUnion</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">f</font> <a href="setwiseo.html#K8" title="SETWISEO:func.8">.:</a> <font color="Olive" title="b1">B</font></span>)</span>,<font color="Olive" title="b3">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="setwiseo.html#K10" title="SETWISEO:func.10">FinUnion</a> <font color="Olive" title="b1">B</font>,<span class="p1">(<span class="default"><font color="Olive" title="b3">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b2">f</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c4">B</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="finsub_1.html#K5" title="FINSUB_1:func.5">Fin</a> <font color="Maroon" title="c1">X</font>; <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">f</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font><br/> for <font color="Olive" title="b2">g</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c2">Y</font>, <a href="finsub_1.html#K5" title="FINSUB_1:func.5">Fin</a> <font color="Maroon" title="c3">A</font> holds   <a href="setwiseo.html#K10" title="SETWISEO:func.10">FinUnion</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">f</font> <a href="setwiseo.html#K8" title="SETWISEO:func.8">.:</a> <font color="Maroon" title="c4">B</font></span>)</span>,<font color="Olive" title="b2">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="setwiseo.html#K10" title="SETWISEO:func.10">FinUnion</a> <font color="Maroon" title="c4">B</font>,<span class="p1">(<span class="default"><font color="Olive" title="b2">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b1">f</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c5">f</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font>; <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">g</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c2">Y</font>, <a href="finsub_1.html#K5" title="FINSUB_1:func.5">Fin</a> <font color="Maroon" title="c3">A</font> holds   <a href="setwiseo.html#K10" title="SETWISEO:func.10">FinUnion</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="setwiseo.html#K8" title="SETWISEO:func.8">.:</a> <font color="Maroon" title="c4">B</font></span>)</span>,<font color="Olive" title="b1">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="setwiseo.html#K10" title="SETWISEO:func.10">FinUnion</a> <font color="Maroon" title="c4">B</font>,<span class="p1">(<span class="default"><font color="Olive" title="b1">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c6">g</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c2">Y</font>, <a href="finsub_1.html#K5" title="FINSUB_1:func.5">Fin</a> <font color="Maroon" title="c3">A</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="setwiseo.html#K10" title="SETWISEO:func.10">FinUnion</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="setwiseo.html#K8" title="SETWISEO:func.8">.:</a> <font color="Maroon" title="c4">B</font></span>)</span>,<font color="Maroon" title="c6">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="setwiseo.html#K10" title="SETWISEO:func.10">FinUnion</a> <font color="Maroon" title="c4">B</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span></span><br/>











<b>thus </b> <a href="setwiseo.html#K10" title="SETWISEO:func.10">FinUnion</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="setwiseo.html#K8" title="SETWISEO:func.8">.:</a> <font color="Maroon" title="c4">B</font></span>)</span>,<font color="Maroon" title="c6">g</font> = 
 <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="setwiseo.html#K8" title="SETWISEO:func.8">.:</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="setwiseo.html#K8" title="SETWISEO:func.8">.:</a> <font color="Maroon" title="c4">B</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="setwiseo.html#T61" target="_self" title="SETWISEO:th.61">Th61</a></i>
<br/>.= 
 <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span> <a href="setwiseo.html#K8" title="SETWISEO:func.8">.:</a> <font color="Maroon" title="c4">B</font></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T159" title="RELAT_1:th.159">RELAT_1:159</a></i>
<br/>.= 
 <a href="setwiseo.html#K10" title="SETWISEO:func.10">FinUnion</a> <font color="Maroon" title="c4">B</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>
<b>by </b><i><a class="ref" href="setwiseo.html#T61" target="_self" title="SETWISEO:th.61">Th61</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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