<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">X1</font>, <font color="Maroon" title="c2">X2</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">D1</font>, <font color="Olive" title="b2">D2</font> being 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> <br/> for <font color="Olive" title="b3">f1</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">X1</font>,<font color="Olive" title="b1">D1</font><br/> for <font color="Olive" title="b4">f2</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c2">X2</font>,<font color="Olive" title="b2">D2</font> holds  <span class="p1"><a href="funct_3.html#K16" title="FUNCT_3:func.16">[:</a><span class="default"><font color="Olive" title="b3">f1</font>,<font color="Olive" title="b4">f2</font></span><a href="funct_3.html#K16" title="FUNCT_3:func.16">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="funct_3.html#K13" title="FUNCT_3:func.13">&lt;:</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b3">f1</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p3">(<span class="default"><a href="funct_3.html#K9" title="FUNCT_3:func.9">pr1</a> <font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c2">X2</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b4">f2</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p3">(<span class="default"><a href="funct_3.html#K10" title="FUNCT_3:func.10">pr2</a> <font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c2">X2</font></span>)</span></span>)</span></span><a href="funct_3.html#K13" title="FUNCT_3:func.13">:&gt;</a></span></span><br/><b>let </b><font color="Maroon" title="c3">D1</font>, <font color="Maroon" title="c4">D2</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> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c3">D1</font><br/> for <font color="Olive" title="b2">f2</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c2">X2</font>,<font color="Maroon" title="c4">D2</font> holds  <span class="p1"><a href="funct_3.html#K16" title="FUNCT_3:func.16">[:</a><span class="default"><font color="Olive" title="b1">f1</font>,<font color="Olive" title="b2">f2</font></span><a href="funct_3.html#K16" title="FUNCT_3:func.16">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="funct_3.html#K13" title="FUNCT_3:func.13">&lt;:</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">f1</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p3">(<span class="default"><a href="funct_3.html#K9" title="FUNCT_3:func.9">pr1</a> <font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c2">X2</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b2">f2</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p3">(<span class="default"><a href="funct_3.html#K10" title="FUNCT_3:func.10">pr2</a> <font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c2">X2</font></span>)</span></span>)</span></span><a href="funct_3.html#K13" title="FUNCT_3:func.13">:&gt;</a></span></span><br/><b>let </b><font color="Maroon" title="c5">f1</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c3">D1</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">f2</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c2">X2</font>,<font color="Maroon" title="c4">D2</font> holds  <span class="p1"><a href="funct_3.html#K16" title="FUNCT_3:func.16">[:</a><span class="default"><font color="Maroon" title="c5">f1</font>,<font color="Olive" title="b1">f2</font></span><a href="funct_3.html#K16" title="FUNCT_3:func.16">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="funct_3.html#K13" title="FUNCT_3:func.13">&lt;:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">f1</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p3">(<span class="default"><a href="funct_3.html#K9" title="FUNCT_3:func.9">pr1</a> <font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c2">X2</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b1">f2</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p3">(<span class="default"><a href="funct_3.html#K10" title="FUNCT_3:func.10">pr2</a> <font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c2">X2</font></span>)</span></span>)</span></span><a href="funct_3.html#K13" title="FUNCT_3:func.13">:&gt;</a></span></span><br/><b>let </b><font color="Maroon" title="c6">f2</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c2">X2</font>,<font color="Maroon" title="c4">D2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1"><a href="funct_3.html#K16" title="FUNCT_3:func.16">[:</a><span class="default"><font color="Maroon" title="c5">f1</font>,<font color="Maroon" title="c6">f2</font></span><a href="funct_3.html#K16" title="FUNCT_3:func.16">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="funct_3.html#K13" title="FUNCT_3:func.13">&lt;:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">f1</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p3">(<span class="default"><a href="funct_3.html#K9" title="FUNCT_3:func.9">pr1</a> <font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c2">X2</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">f2</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p3">(<span class="default"><a href="funct_3.html#K10" title="FUNCT_3:func.10">pr2</a> <font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c2">X2</font></span>)</span></span>)</span></span><a href="funct_3.html#K13" title="FUNCT_3:func.13">:&gt;</a></span></span><br/>











<a NAME="E1:92"/>
(  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c5">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">X1</font> &amp;  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c6">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">X2</font> )
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<b>hence </b><a NAME="E2:92"/>
<span class="p1"><a href="funct_3.html#K16" title="FUNCT_3:func.16">[:</a><span class="default"><font color="Maroon" title="c5">f1</font>,<font color="Maroon" title="c6">f2</font></span><a href="funct_3.html#K16" title="FUNCT_3:func.16">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="funct_3.html#K13" title="FUNCT_3:func.13">&lt;:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">f1</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p3">(<span class="default"><a href="funct_3.html#K9" title="FUNCT_3:func.9">pr1</a> <font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c2">X2</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">f2</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p3">(<span class="default"><a href="funct_3.html#K10" title="FUNCT_3:func.10">pr2</a> <font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c2">X2</font></span>)</span></span>)</span></span><a href="funct_3.html#K13" title="FUNCT_3:func.13">:&gt;</a></span>
 <b>by </b><i><a class="ref" href="funct_3.html#T87" target="_self" title="FUNCT_3:th.87">Th87</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>
